ALBERT

Beschreibung: We propose a diagnostic technique to detect instability waves in a subsonic round jet using a phased microphone array. The detection algorithm is analogous to the beam-forming technique, which is typically used with a far-field microphone array to localize noise sources. By replacing the reference solutions used in the conventional beam-forming with eigenfunctions from linear stability analysis, the amplitudes of instability waves in the axisymmetric and first two azimuthal modes are inferred. Experimental measurements with particle image velocimetry and a database from direct numerical simulation are incorporated to design a conical array that is placed just outside the mixing layer near the nozzle exit. The proposed diagnostic technique is tested in experiments by checking for consistency of the radial decay, streamwise evolution and phase correlation of hydrodynamic pressure. The results demonstrate that in a statistical sense, the pressure field is consistent with instability waves evolving in the turbulent mean flow from the nozzle exit to the end of the potential core, particularly near the most amplified frequency of each azimuthal mode. We apply this technique to study the effects of jet Mach number and temperature ratio on the azimuthal mode balance and evolution of instability waves. We also compare the results from the beam-forming algorithm with the proper orthogonal decomposition and discuss some implications for jet noise. © 2006 Cambridge University Press.

Beschreibung: In this paper we present ray-tracing results on the interaction of inertia-gravity waves with the velocity field of a vortex in a rotating stratified fluid. We consider rays that interact with a Rankine-type vortex with a Gaussian vertical distribution of vertical vorticity. The rays are traced, solving the WKB equations in cylindrical coordinates for vortices with different aspect ratios. The interactions are governed by the value of FrR/λ where Fr is the vortex Froude number, R its radius, and λ the incident wavelength. The Froude number is defined as Fr = Umax/(N R) with Umax the maximum azimuthal velocity and N the buoyancy frequency. When FrR/λ 〉 1, part of the incident wave field strongly decreases in wavelength while its energy is trapped. The vortex aspect ratio, H/R, determines which part of this incident wave field is trapped, and where its energy accumulates in the vortex. Increasing values of FrR/λ are shown to be associated with a narrowing of the trapping region and an increase of the energy amplification of trapped rays. In the inviscid approximation, the infinite energy amplification predicted for unidirectional flows is retrieved in the limit FrR/ λ→∞. When viscous damping is taken into account, the maximal amplification of the wave energy becomes a function of FrR/ λ and a Reynolds number, Rewave = √UL 2+UH2/vk2 with UL and UH typical values of the shear in, respectively, the radial and vertical directions; the kinematic viscosity is v, and the wavenumber k, for the incident waves. In a sequel paper, we compare WKB simulations with experimental results. © 2006 Cambridge University Press.

Beschreibung: The linear stability of a rotating flow in an elliptically deformed cylindrical shell with an imposed radial temperature contrast is studied using local and global approaches. We demonstrate that (i) a stabilizing temperature profile can either increase or decrease the growth rate of the elliptical instability depending on the selected mode and on the strength of the radial buoyancy force; (ii) when the temperature profile is destabilizing, the elliptical instability coexists with two-dimensional convective instabilities at relatively small values of the Rayleigh number, the fastest growing mode depending on the relative values of the Rayleigh number and of the eccentricity; (iii) the elliptical instability totally disappears for larger values of the Rayleigh number. We argue that thermal effects have to be taken into account when looking for the occurrence and influence of inertial instabilities in geophysical and astrophysical systems, especially in planetary cores. © 2006 Cambridge University Press.

Beschreibung: The behaviour of a dispersion of infinitely polarizable slender rods in an electric field is described using theory and numerical simulations. The polarization of the rods results in the formation of dipolar charge clouds around the particle surfaces, which in turn drive nonlinear electrophoretic flows under the action of the applied field. This induced-charge electrophoresis causes no net migration for uncharged particles with fore-aft symmetry, but can lead to rotations and to relative motions as a result of hydrodynamic interactions. A slender-body formulation is derived that accounts for induced-charge electrophoresis based on a thin double layer approximation, and shows that the effects of the electric field on a single rod can be modelled by a linear slip velocity along the rod axis, which causes particle alignment and drives a stresslet flow in the surrounding fluid. Based on this slender-body model, the hydrodynamic interactions between a pair of aligned rods are studied, and we identify domains of attraction and repulsion, which suggest that particle pairing may occur. An efficient method is implemented for the simulation of dispersions of many Brownian rods undergoing induced-charge electrophoresis, that accounts for far-field hydrodynamic interactions up to the stresslet term, as well as near-field lubrication and contact forces. Simulations with negligible Brownian motion show that particle pairing indeed occurs in the suspension, as demonstrated by sharp peaks in the pair distribution function. The superposition of all the electrophoretic flows driven on the rod surfaces is observed to result in a diffusive motion at long times, and hydrodynamic dispersion coefficients are calculated. Results are also presented for colloidal suspensions, in which Brownian fluctuations are found to hinder particle pairing and alignment. Orientation distributions are obtained for various electric field strengths, and are compared to an analytical solution of the Fokker-Planck equation for the orientation probabilities in the limit of infinite dilution. © 2006 Cambridge University Press.

Beschreibung: A straight front separating two semi-infinite regions of uniform potential vorticity (PV) in a rotating shallow-water fluid gives rise to a localized fluid jet and a geostrophically balanced shelf in the free surface. The linear stability of this configuration, consisting of the simplest non-trivial PV distribution, has been studied previously, with ambiguous results. We revisit the problem and show that the flow is weakly unstable when the maximum Rossby number R 〉1. The instability is surprisingly weak, indeed exponentially so, scaling like exp[-4.3/(R - 1)] as R → 1. Even when R = √2 (when the maximum Froude number F=1), the maximum growth rate is only 7.76 × 10-6 times the Coriolis frequency. Its existence nonetheless sheds light on the concept of 'balance' in geophysical flows, i.e. the degree to which the PV controls the dynamical evolution of these flows. © 2006 Cambridge University Press.

Beschreibung: The three-dimensional incompressible flow past a rectangular two-dimensional shallow cavity in a channel is investigated using large-eddy simulation (LES). The aspect ratio (length/depth) of the cavity is L/D=2 and the Reynolds number defined with the cavity depth and the mean velocity in the upstream channel is 3360. The sensitivity of the flow around the cavity to the characteristics of the upstream flow is studied by considering two extreme cases: a developing laminar boundary layer upstream of the cavity and when the upstream flow is fully turbulent. The two simulations are compared in terms of the mean statistics and temporal physics of the flow, including the dynamics of the coherent structures in the region surrounding the cavity. For the laminar inflow case it is found that the flow becomes unstable but remains laminar as it is convected over the cavity. Due to the three-dimensional flow instabilities and the interaction of the jet-like flow inside the recirculation region with the separated shear layer, the spanwise vortices that are shed regularly from the leading cavity edge are disturbed in the spanwise direction and, as they approach the trailing-edge corner, break into an array of hairpin-like vortices that is convected downstream the cavity close to the channel bottom. In the fully turbulent inflow case in which the momentum thickness of the incoming boundary layer is much larger compared to the laminar inflow case, the jittering of the shear layer on top of the cavity by the incoming near-wall coherent structures strongly influences the formation and convection of the eddies inside the separated shear layer. The mass exchange between the cavity and the main channel is investigated by considering the ejection of a passive scalar that is introduced instantaneously inside the cavity. As expected, it is found that the ejection is faster when the incoming flow is turbulent due to the interaction between the turbulent eddies convected from upstream of the cavity with the separated shear layer and also to the increased diffusion induced by the broader range of scales that populate the cavity. In the turbulent case it is shown that the eddies convected from upstream of the cavity can play an important role in accelerating the extraction of high-concentration fluid from inside the cavity. For both laminar and turbulent inflow cases it is shown that the scalar ejection can be described using simple dead-zone theory models in which a single-valued global mass exchange coefficient can be used to describe the scalar mass decay inside cavity over the whole ejection process. © 2006 Cambridge University Press.

Beschreibung: We consider in detail the Taylor-Couette problem for a Bingham fluid, presenting a range of analytical and computational results. First, for co-rotating cylinders it is known that the critical inner cylinder Reynolds number Re1,c, does not increase monotonically with the Bingham number B, over a range of small to moderate B. It is the only situation that we know of where a yield stress fluid flow is less stable that the corresponding Newtonian fluid flow. This effect was discovered independently by Landry (2003, MSc thesis) and Peng & Zhu (J. Fluid Mech. vol. 512, 2004, p. 21), but the mechanism has not been explained. Here we show that the decrease in critical Reynolds number is due to an increase (at small B) in the rate of strain of the basic flow, which amplifies the transfer of energy from the basic flow to the perturbation, via the inertial terms in the energy equation. At larger B, the yielded region contracts and the inertial energy transfer is bounded by the yield stress dissipation. We next consider the effects of large B. For fixed radius and Reynolds number ratios, we show that for sufficiently large B all basic flows have an unyielded fluid layer attached to the outer wall. For these flows we show that there is a similarity mapping that maps both the basic solution and the linear stability problem onto the stability problem for an outer cylinder of radius equal to the yield surface radius. The Reynolds and Bingham numbers of the transformed problems are smaller than that of the original problem, as is the wavenumber k. As B → ∞, the yield surface approaches the inner cylinder, defining a narrow gap limiting problem that differs from the classical narrow gap limit. Via the transformed problem we derive an energy estimate for stability: Re1,ckc ∼ B1.5 as B → ∞, which compares well with our computed results for a stationary outer cylinder: Re1,c ∼ B1.25 and kc ∼ B0.375. We also show how Re1,c ∼ B1.25 can be deduced from a simple order of magnitude analysis, for a stationary outer cylinder. Finally, we consider the second (classical) narrow gap limit in which the radius ratio η, approaches unity, for fixed B and Reynolds number ratio. We show that Re1,c ≳ (k2[1 + O(B)] + π2)/(1 - η)1/2 in this limit. © 2006 Cambridge University Press.

Beschreibung: A weakly nonlinear analysis of one-dimensional viscous Faraday waves in two-dimensional large-aspect-ratio containers is presented. The surface wave is coupled to a viscous long-wave mean flow that is slaved to the free-surface deformation. The relevant Ginzburg-Landau-like amplitude equations are derived from first principles, and can be of three different types, depending on the ratio between wavelength, depth and the viscous length. These three equations are new in the context of Faraday waves. The coefficients of these equations are calculated for arbitrary viscosity and compared with their counterparts in the literature for small viscosity; a discrepancy in the cubic coefficient is due to a dramatic sensitivity of this coefficient on a small wavenumber shift due to interplay between viscous effects and parametric forcing. © 2006 Cambridge University Press.

Beschreibung: Stereoscopic particle image velocimetry (PIV) measurements were taken simultaneously in streamwise-spanwise and streamwise-wall-normal planes in a zero-pressure-gradient turbulent boundary layer over a flat plate. Polarization techniques were employed to allow PIV to be taken in both planes simultaneously. Image preprocessing techniques were used to improve the quality of data near the line of intersection of the planes. Linear stochastic estimation was performed on these data, revealing the streamwise, spanwise, and wall-normal extent of swirl events primarily near the top of the log region of the boundary layer. Swirl events with rotation consistent with the mean vorticity are found to have a large footprint in the lower limit of the log region whereas swirls with opposite-signed vorticity are found to have little influence lower in the boundary layer. These long-time-averaged statistics contain features that are consistent with the hairpin packet model (or its kinematic equivalent). This model also seems to provide a reasonable description of many instantaneous events involving large-scale coherence, where long regions of streamwise momentum deficit are surrounded by vortex cores. © 2006 Cambridge University Press.

Beschreibung: A fundamental characteristic of granular flows is that they are typically restricted to thin layers of rapid surface flow. Thus, a complete understanding of surface flows is key for an accurate representation of the dynamics of the entire flow. Experiments were conducted in three-dimensional tumblers: cylindrical tumblers of various diameters, a double-cone tumbler, and a spherical tumbler, the Froude number for the last two being a function of the local geometry and ranging from 2.6 × 10-5 to 7.5 × 10-4. Surface velocity measurements for 1 mm and 2 mm glass particles were obtained using particle tracking velocimetry. Results indicate that the streamwise surface velocity at the midpoint of the flowing layer is a linear function of local flowing layer length, regardless of tumbler shape, particle size, rotation rate, and fill fraction. In addition, the axial velocity of particles at the free surface is negligible. These results are key for the development of three-dimensional models of granular flows. © 2006 Cambridge University Press.

Beschreibung: An insoluble particle, a solid sphere or a spherical bubble, submerged in a liquid and approached by an advancing solidification front, may be captured by the front or rejected. The particle behaviour is determined by an interplay among van der Waals interactions, thermal conductivity differences between the particle and the melt, solid-liquid interfacial energy, the density change caused by the liquid-solid phase transition, and in the case of a bubble, the Marangoni effect at the liquid-gas interface. We calculate the particle velocity and the deformation of the front when the particle is close to the front, using the lubrication approximation, and investigate how the particle speed, relative to the front, depends on the parameters that characterize the described effects. © 2006 Cambridge University Press.

Beschreibung: In this paper, we investigate the effect of basic-flow modification on the absolute instability in a two-dimensional wake at low Reynolds number with the parallel-flow approximation. Using the method of calculus of variation, we investigate how to modify the basic flow to suppress or enhance the absolute instability and suggest an optimal modification of the basic flow for stabilizing a bluff-body wake. In order to validate the present approach, we also measure the sensitivity of all the eigenvalues including the absolute-instability frequency, using the ε-pseudo-spectrum, showing that small modifications in the basic flow do not destabilize other eigenvalues by more than the original absolute-instability frequency, at least for the Reynolds number considered here. For a two-dimensional parallel model wake and a circular-cylinder wake, the present approach shows that the positive and negative velocity perturbations to the basic flows, respectively, at the wake centreline and separating shear layer suppress the absolute instability. © 2006 Cambridge University Press.

Beschreibung: A perturbation expansion of the Boltzmann equation is used to derive constitutive relations for the granular flow of rough spheres in the limit where the energy dissipation in a collision is small compared to the energy of a particle. In the collision model, the post-collisional relative normal velocity at the point of contact is -en times the pre-collisional normal velocity, and the post-collisional relative tangential velocity at the point of contact is -et times the pre-collisional relative tangential velocity. A perturbation expansion is employed in the limit (1 - en) = ε2 ≪ 1, and (1 - et 2) ∝ ε2 ≪ 1, so that et is close to ±1. In the 'rough' particle model, the normal coefficient of restitution en is close to 1, and the tangential coefficient of restitution et is close to 1. In the 'partially rough' particle model, the normal coefficient of restitution en is close to 1; and the tangential coefficient of restitution et is close to -1 if the angle between the relative velocity vector and the line joining the centres of the particles is greater than the 'roughness angle' (chosen to be (π/4) in the present calculation), and is close to 1 if the angle between the relative velocity vector and the line joining the centres is less than the roughness angle. The conserved variables in this case are mass and momentum; energy is not a conserved variable in the 'adiabatic limit' considered here, when the length scale is large compared to the 'conduction length'. The results for the constitutive relations show that in the Navier-Stokes approximation, the form of the constitutive relation is identical to that for smooth particles, but the coefficient of shear viscosity for rough particles is 10%-50% higher than that for smooth particles. The coefficient of bulk viscosity, which is zero in the dilute limit for smooth particles, is found to be non-zero for rough and partially rough particles, owing to the transport of energy between the translational and rotational modes. In the Burnett approximation, there is an antisymmetric component in the stress tensor for rough and partially rough particles, which is not present for smooth particles. The constitutive relations are used to analyse the 'core region' of a steady granular flow down an inclined plane, where there is a local balance between the production of energy due to the mean shear and the dissipation due to inelastic collisions. It is found that realistic results, such as the decrease in density upon increase in the angle of inclination near close packing, are obtained for the rough and partially rough particle models when the Burnett coefficients are included in the stress tensor, but realistic results are not obtained using the constitutive relations for smooth particles. This shows that the flow dynamics is sensitive to the numerical values of the viscometric coefficients, and provides an indication of the minimal model required to capture the flow dynamics. © 2006 Cambridge University Press.

Beschreibung: Self-similar analytical nonlinear solutions to the hydrostatic Boussinesq equations are derived which describe unbalanced inertial pulsations of anticyclonic lens-like circular vortices in stably stratified rotating fluid. Any steady axisymmetric solution for a finite-volume anticyclonic vortex in the reduced-gravity approximation is shown to correspond to a set of time-periodic solutions with the amplitude of pulsations being within a range limited by the intensity of the stationary vortex. These solutions represent an extension of previous reduced-gravity analytical pulson solutions of particular forms with spatially uniform divergence of horizontal velocity oscillating in time within the vortex volume. In the self-similar form the pulson solution describes the expansion and contraction of a vortex which maintains the same spatial structure in the Lagrangian coordinates. © 2006 Cambridge University Press.

Beschreibung: Multiple states of spatially localized steady convection are found in numerical simulations of water-ethanol mixtures in two dimensions. Realistic boundary conditions at the top and bottom are used, with periodic boundary conditions in the horizontal. The states form by a mechanism similar to the pinning region around a Maxwell point in variational systems, but are located in a parameter regime in which the conduction state is overstable. Despite this the localized states can be stable. The properties of the localized states are described in detail, and the mechanism of their destruction with increasing or decreasing Rayleigh number is elucidated. When the Rayleigh number becomes too large the fronts bounding the state at either end unpin and move apart, allowing steady convection to invade the domain. In contrast, when the Rayleigh number is too small the fronts move inwards, and eliminate the localized state which decays into dispersive chaos. Out of this state spatially localized states re-emerge at irregular times before decaying again. Thus an interval of Rayleigh numbers exists that is characterized by relaxation oscillations between localized convection and dispersive chaos. © 2006 Cambridge University Press.

Beschreibung: A small air bubble (radius a) is injected in water (kinematic viscosity ν) in the vicinity (distance r0) of a propeller (radius rp, angular frequency ω). We study experimentally and theoretically the conditions under which the bubble can be 'captured', i.e. deviated from its vertical trajectory (imposed by gravity g) and moved toward the centre of the propeller (r = 0). We show that the capture frequency ωcapt follows the relationship ωcapt = (2ga2/9βνrp f(Reb)) (r0/rp)2) (1 + cos φ0), where β is a dimensionless parameter characterizing the propeller, f(Reb) is an empirical correction to Stokes' drag law which accounts for finite-Reynolds-number effects and π/2-φ0 is the angle between the axis of the propeller and the line between the centre of the propeller and the point where the bubble is injected. This law is found to be valid as long as the distance d between the propeller and the water surface is larger than 3r0. For smaller distances, the capture frequency increases; using an image technique, we show how the above expression is modified by the presence of the surface. © 2006 Cambridge University Press.

Beschreibung: A linear stability analysis of the Rayleigh-Taylor problem for an incompressible fluid undergoing a liquid-liquid phase transformation is presented. Both inviscid and linearly viscous fluids are considered and interfacial tension is taken into account. Instability is possible only when the phase with the higher density is above that with the lower density. Study of the inviscid case shows that the exchange of mass between the phases decreases significantly both the range of unstable wavenumbers and the maximum growth rate for unstable perturbations as compared to those arising classically. For a linearly viscous fluid, the shear and dilational viscosities of the interface are taken into account as are the migrational viscosities associated with the motion of the interface relative to the underlying fluid. When no mass exchange occurs between the phases in the base state and the interfacial viscosities are neglected, the growth rates exceed by at least an order of magnitude those for the classical Rayleigh-Taylor problem. The various interfacial viscosities slow the growth rates of disturbances, but do not influence the range of unstable wavenumbers. For both the inviscid and viscous cases, interfacial tension plays the same stabilizing role as it does classically. © 2006 Cambridge University Press.

Beschreibung: The problem of a cylindrically or spherically imploding and reflecting shock wave in a flow initially at rest is studied without the use of the strong-shock approximation. Dimensional arguments are first used to show that this flow admits a general solution where an infinitesimally weak shock from infinity strengthens as it converges towards the origin. For a perfect-gas equation of state, this solution depends only on the dimensionality of the flow and on the ratio of specific heats. The Guderley power-law result can then be interpreted as the leading-order, strong-shock approximation, valid near the origin at the implosion centre. We improve the Guderley solution by adding two further terms in the series expansion solution for both the incoming and the reflected shock waves. A series expansion, valid where the shock is still weak and very far from the origin, is also constructed. With an appropriate change of variables and using the exact shock-jump conditions, a numerical, characteristics-based solution is obtained describing the general shock motion from almost infinity to very close to the reflection point. Comparisons are made between the series expansions, the characteristics solution, and the results obtained using an Euler solver. These show that the addition of two terms to the Guderley solution significantly extends the range of validity of the strong-shock series expansion. © 2006 Cambridge University Press.

Beschreibung: Steady-state distributions of water potential and salt concentration in coastal aquifers are typically modelled by the Henry problem, which consists of a fully coupled system of flow and transport equations. Coupling arises from the dependence of water density on salt concentration. The physical behaviour of the system is fully described by two dimensionless groups: (i) the coupling parameter α which encapsulates the relative importance of buoyancy and viscous forces, and (ii) the Péclet number Pe, which quantifies the relative importance of purely convective and dispersive transport mechanisms. We provide a systematic analytical analysis of the Henry problem for a full range of the Péclet number. For moderate Pe, analytical solutions are obtained through perturbation expansions in α. This allows us to elucidate the onset of density-driven vertical flux components and the dependence of the local hydraulic head gradients on the coupling parameter. The perturbation solution identifies the regions where salt concentration is most pronounced and relates their spatial extent to the development of a convection cell. Next, we compare our solution to a solution of the pseudo-coupled model, wherein flow and transport are coupled only via the boundary conditions. This enables us to isolate the effects caused by density-dependent processes from those induced by external forcings (boundary conditions). For small Pe, we develop a perturbation expansion around the exact solution corresponding to Pe = 0, which sheds new light on the interpretation of processes observed in diffusion experiments with variable-density flows in porous media. The limiting case of infinite Péclet numbers is solved exactly for the pseudo-coupled model and compared to numerical simulations of the fully coupled problem for large Pe. The proposed perturbation approach is applicable to a wide range of variable-density flows in porous media, including seawater intrusion into coastal aquifers and temperature or pressure-driven density flows in deep aquifers. © 2006 Cambridge University Press.

Beschreibung: We present the results of direct numerical simulations (DNS) of the evolution of nonlinear random water wave fields. The aim of the work is to validate the hypotheses underlying the statistical theory of nonlinear dispersive waves and to clarify the role of exactly resonant, nearly resonant and non-resonant wave interactions. These basic questions are addressed by examining relatively simple wave systems consisting of a finite number of wave packets localized in Fourier space. For simulation of the long-term evolution of random water wave fields we employ an efficient DNS approach based on the integrodifferential Zakharov equation. The non-resonant cubic terms in the Hamiltonian are excluded by the canonical transformation. The proposed approach does not use a regular grid of harmonics in Fourier space. Instead, wave packets are represented by clusters of discrete Fourier harmonics. The simulations demonstrate the key importance of near-resonant interactions for the nonlinear evolution of statistical characteristics of wave fields, and show that simulations taking account of only exactly resonant interactions lead to physically meaningless results. Moreover, exact resonances can be excluded without a noticeable effect on the field evolution, provided that near-resonant interactions are retained. The field evolution is shown to be robust with respect to the details of the account taken of near-resonant interactions. For a wave system initially far from equilibrium, or driven out of equilibrium by an abrupt change of external forcing, the evolution occurs on the 'dynamical' time scale, that is with quadratic dependence on nonlinearity ε, not on the O(ε-4) time scale predicted by the standard statistical theory. However, if a wave system is initially close to equilibrium and evolves slowly in the presence of an appropriate forcing, this evolution is in quantitative accordance with the predictions of the kinetic equation. We suggest a modified version of the kinetic equation able to describe all stages of evolution. Although the dynamic time scale of quintet interactions ε-3 is smaller than the kinetic time scale ε-4, they are not included in the existing statistical theory, and their effect on the evolution of wave spectra is unknown. We show that these interactions can significantly affect the spectrum evolution, although on a time scale much larger than O(ε-4). However, for waves of high but still realistic steepness ε ∼ 0.25, the scales of evolution are no longer separated. By tracing the evolution of high statistical moments of the wave field, we directly verify one of the main assumptions used in the derivation of the kinetic equation: the quasi-Gaussianity of the wave holds throughout the evolution, both with and without accounting for quintet interactions. The conclusions are not confined to water waves and are applicable to a generic weakly nonlinear dispersive wave field with prohibited triad interactions. © 2006 Cambridge University Press.

Beschreibung: We consider the motion of a single quasi-geostrophic ellipsoid of uniform potential vorticity in equilibrium with a linear background shear flow. This motion depends on four parameters: The height-to-width aspect ratio of the vortex, h/r, and three parameters characterizing the background shear flow, namely the strain rate, γ, the ratio of the background rotation rate to the strain, β, and the angle from which the shear is applied, θ. We generate the equilibria over a large range of these parameters and analyse their linear stability. For the second-order (m = 2) modes which preserve the ellipsoidal form, we are able to derive equations for the eigenmodes and growth rates. For the higher-order modes we use a numerical method to determine the full linear stability to general disturbances (m 〉 2). Overall we find th at the equilibria are stable over most of the parameter space considered, and where instability does occur the marginal instability is usually ellipsoidal. From these results, we determine the parameter values for which the vortex is most stable, and conjecture that these are the vortex characteristics which would be the most commonly observed in turbulent flows. © 2006 Cambridge University Press.

Beschreibung: This paper presents the results of investigations into particular features of laminar-to-turbulent transition of pipe flows. The first part considers transitional flows that occur 'naturally', i.e. without any forcing, when a critical Reynolds number is reached. Measurements are reported that were carried out to study the intermittent nature of pipe flows before they become fully turbulent. The second part of the paper concentrates on forced laminar-to-turbulent transition where the forcing was achieved by ring-type obstacles introduced into the flow close to the pipe inlet. The influence of the ring height was investigated and the results showed a dependence of the critical Reynolds number on the normalized height of the disturbances. The laminar-to-turbulent transition was also investigated when caused by partially closing an iris diaphragm that permitted the flow to be forced to turbulence over short time intervals. Investigations of controlled intermittency became possible in this way and corresponding results are presented. © 2006 Cambridge University Press.

Beschreibung: A body of salt-stratified fluid in a vertical slot can undergo double-diffusive instabilities when laterally heated. A previous study has indicated the possibility that vibrations could induce instabilities in the cases of a strong salinity gradient in regimes that are not only linearly stable, but also nonlinearly stable. We investigate this limit using the method of averaging and confirm that any level of high-frequency vibrations will lead to a reduction in the heating required for instability for a sufficiently strong salinity gradient, but that this is probably not of great importance to terrestrial experimenters. © 2006 Cambridge University Press.

Beschreibung: The connections between the random elements of a discrete random flow field and the uncertainty in the hierarchical set of its spatio-temporal scales, obtained by the symmetric version of the proper orthogonal decomposition (POD) method, are investigated. It is shown that the relevant statistics for the energy levels, the temporal modes and the spatial modes can be expressed in an explicit form as power series of the flow field standard deviation. Such expansions characterize accurately interesting phenomena of mixing between different flow scales. The basis of the present work is the assumption that the randomness is characterized by a Gaussian uncorrelated random field. Two applications of the theory developed are proposed: to the incompressible flow past a cylinder at Reynolds number Re = 100 and to the natural convective flow over an isothermal horizontal plate at Rayleigh number Ra = 4.75 × 106. The theoretical predictions are confirmed well by Monte Carlo simulations and interesting relations between the random flows and the relevant statistics of their POD spatio-temporal scales are determined and discussed. © 2006 Cambridge University Press.

Beschreibung: A computational study is reported of the instability and growth of fingers for liquid films driven over heterogeneous surfaces. Computations are performed using a variation of the precursor-film model, in which a disjoining pressure term is used to introduce variation in the static contact angle, which in turn models surface heterogeneity. The formulation is shown to yield results consistent with the Tanner-Hoffman-Voinov dynamic contact angle formula for sufficiently small values of the precursor film thickness. A modification of the disjoining pressure coefficient is introduced which yields correct variation of dynamic contact angle for finite values of the precursor film thickness. The fingering instability is examined both for cases with ordered strips of different static contact angle and for cases with random variation in static contact angle. Surface heterogeneity is characterized by strip width and amplitude of static contact angle variation for the case with streamwise strips and by correlation length and variance of the static contact angle variation from its mean value for the random distribution case. © 2006 Cambridge University Press.

Beschreibung: Trapped modes in the linearized water-wave problem are free oscillations of an unbounded fluid with a free surface that have finite energy; it has been known for some time that such modes are supported by certain structures when held fixed. This paper investigates the problem of a freely floating structure that is able to move in response to the hydrodynamic forces acting upon it and it is shown that trapped modes also exist in this problem. For a freely floating structure, a trapped mode is a coupled oscillation of the fluid and the structure. © 2006 Cambridge University Press.

Beschreibung: The Boussinesq equations for Rayleigh-Bénard convection are simulated for a cylindrical container with an aspect ratio near 1.5. The transition from an axisymmetric stationary flow to time-dependent flows is studied using nonlinear simulations, linear stability analysis and bifurcation theory. At a Rayleigh number near 25 000, the axisymmetric flow becomes unstable to standing or travelling azimuthal waves. The standing waves are slightly unstable to travelling waves. This scenario is identified as a Hopf bifurcation in a system with O(2) symmetry. © 2006 Cambridge University Press.

Beschreibung: An experimental study is presented on contact angle dynamics during spreading/recoiling of mm-sized water droplets impacting orthogonally on various surfaces with We = O(0.1) - O(10), Ca = O(0.001) - O(0.01), Re = O(100) - O(1000), Oh = O(0.001) and Bo = O (0.1). In this impact regime, inertial, viscous and capillary phenomena act in unison to influence contact angle dynamics. The wetting properties of the target surfaces range from wettable to non-wettable. The experiments feature accelerating and decelerating wetting lines, capillary surface waves in the early impact stages, contact angle hysteresis, and droplet rebound under non-wetting conditions. The objective of the work is to provide insight into the dynamic behaviour of the apparent (macroscopic) contact angle θ and its dependence on contact line velocity VCL at various degrees of surface wetting. By correlating the temporal behaviours of θ and VCL, the angle vs. speed relationship is established for each case examined. The results reveal that surface wettability has a critical influence on dynamic contact angle behaviour. The hydrodynamic wetting theory of Cox (J. Fluid Mech. vol. 357, 1998, p. 249) and the molecular-kinetic theory of wetting by Blake & Haynes (J. Colloid Interface Sci.) vol. 30, 1969, p. 421) are implemented to extract values of the corresponding microscopic wetting parameters required to match the experimentally observed θ data. Application of hydrodynamic theory indicates that in the slow stage of forced spreading the slip length and the microscopic contact angle should be contact line velocity dependent. The hydrodynamic theory performs well during kinematic (fast) spreading, in which solid/liquid interactions are weak. Application of the molecular kinetic theory yields physically reasonable molecular wetting parameters, which, however, vary with impact conditions. The results indicate that even for a single liquid there is no universal expression to relate contact angle with contact line speed. Finally, analysis of the spreading dynamics on the non-wettable surfaces shows that it conforms to the Cassie-Baxter regime (only partial liquid/solid contact is maintained). The present results offer guidance for numerical or analytical studies, which require careful attention to the implementation of boundary conditions at the moving contact line, including the need to specify the dependence of contact angle on contact line speed. © 2006 Cambridge University Press.

Beschreibung: Using experimental transverse velocity data for very high-Reynolds-number turbulence, we suggest a model describing both the formation of intermittency and asymmetry of turbulence. The model, called the 'bump model' is a modification of the ramp model suggested previously. The connection between asymmetry and intermittency makes it possible to study the latter with relatively low moments. © 2006 Cambridge University Press.

Beschreibung: Quantitative planar visualization of molecular mixing dynamics in large- and intermediate-scale coherent structures is reported for the first time in the developing and far-field regions of gaseous planar shear layers. A dual-tracer (nitric oxide and acetone) planar laser-induced fluorescence (PLIF) technique is implemented as the gaseous analogue to acid/base chemical reactions that have previously been used to study molecular mixing in liquid shear layers. Data on low-speed, high-speed, and total molecularly mixed fluid fractions are collected for low- to high-speed velocity ratios from 0.25 to 0.44 and Reynolds numbers, Reδ from 18 600 to 103 000. Within this range of conditions, mixed-fluid probability density functions and ensemble-averaged statistics are highly influenced by the homogenizing effect of large-scale Kelvin-Helmholtz rollers and the competing action of intermediate-scale secondary instabilities. Small-scale turbulence leads to near-unity mixing efficiencies and mixed-fluid probabilities within the shear layer, with subresolution stirring being detected primarily along the interface with free-stream fluid. Current molecular-mixing data compare favourably with previous time-averaged probe-based measurements while providing new insight on the effects of coherent structures, velocity ratio, downstream distance, and differences between low- and high-speed fluid entrainment. © 2006 Cambridge University Press.

Beschreibung: A family of 10 silicone oils with electrical conductivity ∼ 10-13S m-1 (a regime hitherto systematically unexplored) and viscosities ranging from 1 to 2000 m Pa s have been subjected to an electrical field of up to 1.5 kV mm-1 during flow from a needle. The flow behaviour of these liquids is investigated experimentally in the flow rate regime 10-8-10-12 m-3s-1 and we analyse the results using the Ohnesorge number. Due to the low electrical conductivity and high electrical relaxation time of the silicone oils, only unsteady transient jets were found. The onset of this type of jetting has been defined using current measurements and, in contrast to conducting liquids, the non-dimensional jet diameter increases with increase in Ohnesorge number. The time elapsed between the start and finish of jetting increases with increasing Ohnesorge number. © 2006 Cambridge University Press.

Beschreibung: It is shown, by direct numerical simulations, that the skin-friction drag in a fully developed channel can be sustained below that corresponding to the laminar profile when the flow is subjected to surface blowing and suction in the form of an upstream travelling wave. A key mechanism that induces the sub-laminar drag is the creation of positive (negative) Reynolds shear stress in the wall region, where normally negative (positive) Reynolds shear stress is expected given the mean shear. This mechanism is contained in the linearized Navier-Stokes equations, thus allowing linear analysis of the observed phenomena. When applied to a fully developed turbulent channel flow, skin-friction drag is also significantly reduced by an upstream travelling wave, demonstrating that the surface blowing and suction in the form of such a wave is also effective in fully developed turbulent flows. Consideration of the energy budget shows a possibility of net drag reduction in turbulent channel flows with the present open-loop control. © 2006 Cambridge University Press.

Beschreibung: Stress wave emission and cavitation bubble dynamics after optical breakdown in water and a tissue phantom with Nd: YAG laser pulses of 6 ns duration were investigated both experimentally and numerically to obtain a better understanding of the physical mechanisms involved in plasma-mediated laser surgery. Experimental tools were high-speed photography with 50 000 frames s-1, and acoustic measurements. The tissue phantom consisted of a transparent polyacrylamide (PAA) gel, the elastic properties of which can be controlled by modifying the water content. Breakdown in water produced a purely compressive stress wave. By contrast, in stiff PAA samples and for sufficiently large pulse energies, the compression wave was followed by an intense tensile wave, similar to the behaviour previously observed in cornea. The elastic/plastic response of the medium led to a significant decrease of the maximum size of the cavitation bubble and to a shortening of its oscillation period which was found to be related to the generation of the tensile stress wave upon breakdown. For increasing elastic modulus of the PAA, both the amplitudes of the bubble oscillation and of the stress wave emitted during bubble collapse decreased until the bubble oscillation was so strongly damped that no collapse stress wave was emitted. Numerical simulations were performed using a spherical model of bubble dynamics which includes the compressibility and elastic/plastic behaviour of the medium, viscosity, density and surface tension. The calculations revealed that consideration of the elastic/plastic behaviour of the medium surrounding the bubble is essential to describe the experimentally observed bipolar shape of the stress wave emitted upon optical breakdown. Water is a poor tissue model because the shape of the emitted stress waves and the bubble dynamics differ strongly for both materials. The mechanical properties of PAA were also found to be quite different from those of tissues. Experimental and numerical results provided evidence that the dynamic mechanical properties relevant for optical breakdown in PAA and tissue differ by as much as two orders of magnitude from the static values. The discovery of a tensile stress wave after optical breakdown in tissue-like media is of great importance for the assessment of collateral damage in laser surgery because biological tissues are much more susceptible to tensile stress than to compressive stress. © 2006 Cambridge University Press.

Beschreibung: The magnetohydrodynamic evolution of axisymmetric magnetic eddies within which the magnetic field is purely toroidal with Bθ/r piecewise-constant, and the velocity field is poloidal, is studied both analytically and numerically. A family of exact solutions, generalizing Hill's spherical vortex to the case of non-zero magnetic field, is found. These exact solutions are (like Hill's vortex) unstable, so that, under weak disturbance, a narrow spike of vorticity is shed from the neighbourhood of the rear stagnation point. Numerical simulation using a contour-dynamics formulation shows that, for general initial contour shape, a contour singularity appears at a finite time t* like that which appears on a disturbed vortex sheet. Techniques of regularization and sample-point redistribution are used so that the eddy contours can be tracked well beyond t*. When the fluid is initially at rest, the magnetic eddy first contracts towards the axis of symmetry under the action of its Lorentz force distribution; then two spherical fronts form, which propagate in the two opposite directions along the axis of symmetry, in a manner captured well by the exact solution. The magnetic energy remains bounded away from zero despite the fact that there is no topological barrier to its further decrease. Magnetic eddy evolution and the possible existence of steady states under a uniform compressive strain field is also numerically investigated. © 2006 Cambridge University Press.

Beschreibung: The Lagrangian evolution of two-point velocity and scalar increments in turbulence is considered, based on the 'advected delta-vee system' (Li & Meneveau 2005). This system has already been used to show that ubiquitous trends of three-dimensional turbulence such as exponential or stretched exponential tails in the probability density functions of transverse velocity increments, as well as negatively skewed longitudinal velocity increments, emerge quite rapidly and naturally from initially Gaussian ensembles. In this paper, the approach is extended to provide simple explanations for other known intermittency trends in turbulence: (i) that transverse velocity increments tend to be more intermittent than longitudinal ones, (ii) that in two dimensions, vorticity increments are intermittent while velocity increments are not, (iii) that scalar increments typically become more intermittent than velocity increments and, finally, (iv) that velocity increments in four-dimensional turbulence are more intermittent than in three dimensions. While the origin of these important trends can thus be elucidated qualitatively, predicting quantitatively the statistically steady-state levels and dependence on scale remains an open problem that would require including the neglected effects of pressure, inter-scale interactions and viscosity. © 2006 Cambridge University Press.

Beschreibung: Numerical computations and order-of-magnitude estimates are used to describe the stationary creeping flow of a jet of a Newtonian liquid with finite electrical conductivity that is injected into a dielectric medium subject to a uniform electric field. The electric current carried by the jet is computed as a function of the parameters of the problem, showing that it increases with the conductivity and flow rate of the liquid and with the intensity of the electric field. The current also depends on the wetting conditions of the liquid at the injection orifice. Analysis of the transfer of current to the surface of the liquid and of the evolution of the jet under the electric stresses that act at its surface leads to scaling laws for the electric current and other properties of the solution. These laws fit the numerical results and are in qualitative agreement with experimental data. © 2006 Cambridge University Press.

Beschreibung: Observations from a lander fixed to the seafloor over the continental shelf in 124 m of water provide highly resolved velocity measurements through nonlinear internal waves of elevation. From these measurements we determine, for the first time, the non-hydrostatic pressure disturbance (pnh) in nonlinear internal waves. For near-bottom waves of elevation ranging in amplitude, a, from 12 to 33 m, the value of pnh evaluated at the seafloor changes sign from 〉 0 to 〈 ge and back in accordance with weakly nonlinear theory; peak values of range from 25 to 90 N m-2 The external hydrostatic pressure disturbance due to the surface displacement (ηH) is inferred from horizontal accelerations. For elevation waves, ηH 〈 peak values range from 0.1 to 9 mm (1 to 90 Nm-2. The internal hydrostatic pressure perturbation (pWh) caused by isopycnal displacement, is inferred from measured streamlines and an ambient density profile. Its value at the seafloor is 〈 0 for elevation waves; peak values range from 100 to 300 N m-2 ηH and seafloor values of pnh , pWh increase at roughly the same rate with a, no clear trend arises in the degree to which waves become more or less non-hydrotatic as a changes. A distinct bottom pressure signature is determined for bottom-trapped nonlinear waves of elevation, a wave train consisting of a sequence of positive pressure perturbations (dominated by (pWh). By inference, a train of surface-trapped nonlinear internal waves of depression will consist of a sequence of negative pressure perturbations. A result of this analysis is that significant properties of the waves can be discerned from a simple adequately resolved bottom pressure measurement. © 2006 Cambridge University Press.

Beschreibung: We numerically calculate the drag on a sphere or a filament immersed in an incompressible viscous monolayer or membrane on one, or between two, viscous infinitely deep bulk phases. We show that contributions due to the Marangoni effect of the monolayer or membrane account for a significant part of the total drag. Effects of protrusion of objects into the three-dimensional fluids adjacent to the monolayer and membrane are investigated. Known analytical expressions in the limit of a very viscous membrane or monolayer are recovered by our numerics. A sphere in a membrane exhibits maximal drag when symmetrically immersed with the equator coinciding with the membrane plane. No discontinuity of the drag arises when the sphere is totally immersed into the subphase and detaches from the monolayer. Effects of protrusion are more important for objects moving in a membrane or monolayer of low surface viscosity. At large surface shear viscosity protrusions must be larger than the length defined by the ratio of surface to bulk viscosities to alter the drag on the object. Our calculations may be useful for the measurement of hydrodynamic radii of lipid rafts in membranes and for electrocapillary effects of spheres immersed in a surface. © 2006 Cambridge University Press.

Beschreibung: An analysis is presented of the lateral solidification of a semi-infinite mushy region influenced by vertical, buoyancy-driven convection of the residual, interstitial melt. We consider a parameter regime in which the flow is steady on the time scale of the transient evolution of the mushy region. Our idealized model predicts patterns of macrosegregation consistent with earlier experimental studies and sheds light on the mechanisms involved. © 2006 Cambridge University Press.

Beschreibung: The interaction of an oblique shock wave impinging on a turbulent boundary layer at Mach number 2.3 is experimentally investigated for a wide range of shock intensities. Characteristic time and length scales of the unsteady reflected shock and inside the downstream interaction region are obtained and compared with already existing results obtained in compression ramp experiments as well as in subsonic detached flows. Dimensionless characteristic frequencies are highlighted to characterize low-frequency shock unsteadiness as well as the different large scales which develop inside the initial part of the interaction. The possibility of describing the spatial development of the large scales inside the interaction zone using a mixing-layer scheme including compressibility effects is tested for a wide range of Mach numbers, shock intensities and geometrical configurations. Moreover, strong evidence of a statistical link between low-frequency shock movements and the downstream interaction is given. Finally, the downstream evolution of the structures shed into the boundary layer is characterized and shows features specific of our configuration. © 2006 Cambridge University Press.

Beschreibung: The instability behaviour of non-Newtonian liquid jets moving in an inviscid gaseous environment is investigated theoretically for three-dimensional disturbances. The corresponding dispersion relation between the wave growth rate and the wavenumber is derived. Results for axisymmetrical non-Newtonian jets, the Newtonian jets, and the inviscid jets are recovered, and it is shown that two-dimensional disturbances are the most dangerous for the considered set of parameters. © 2006 Cambridge University Press.

Beschreibung: The flow around two stationary cylinders in tandem arrangement at the laminar and early turbulent regime, (RE = 102-103), is studied using two- and three-dimensional direct numerical simulations. A range of spacings between the cylinders from 1.1 to 5.0 diameters is considered with emphasis on identifying the effects of three-dimensionality and cylinder spacing as well as their coupling. To achieve this, we compare the two-dimensional with corresponding three-dimensional results as well as the tandem cylinder system results with those of a single cylinder. The critical spacing for vortex formation and shedding in the gap region depends on the Reynolds number. This dependence is associated with the formation length and base pressure suction variations of a single cylinder with Reynolds number. This association is useful in explaining some of the discrepancies between the two-dimensional and three-dimensional results. A major effect of three-dimensionality is in the exact value of the critical spacing, resulting in deviations from the two-dimensional predictions for the vorticity fields, the forces on the downstream cylinder, and the shedding frequency of the tandem system. Two-dimensional simulations under-predict the critical spacing, leading to erroneous results for the forces and shedding frequencies over a range of spacings where the flow is qualitatively different. To quantify the three-dimensional effects we first employ enstrophy, decomposed into a primary and a secondary component. The primary component involves the vorticity parallel to the cylinder axis, while the secondary component incorporates the streamwise and transverse components of the vorticity vector. Comparison with the single cylinder case reveals that the presence of the downstream cylinder at spacings lower than the critical value has a stabilizing effect on both the primary and secondary enstrophy. Systematic quantification of three-dimensionalities involves finding measures for the intensity of the spanwise fluctuations of the forces. This also verifies the stabilization scenario, suggesting that when the second cylinder is placed at a distance smaller than the critical one, three-dimensional effects are suppressed compared to the single-cylinder case. However, when the spacing exceeds the critical value, the upstream cylinder tends to behave like a single cylinder, but three-dimensionality in the flow generally increases. © 2006 Cambridge University Press.

Beschreibung: The dynamics of gases in permeable media is approached both experimentally and by numerical simulations. The experiments were performed in matrices made of packed beds of spheres in rarefied conditions and a model for the direct simulation of the molecular kinetics is proposed. Comparisons between experimental data and numerical results show the influence of the main parameters of the gas-solid interaction and the range of validity of the model. Moreover it is shown that there is a flow condition for the minimum permeability of the medium to the gas flow. Such a minimum depends upon the Knudsen number, and can be explained by the molecular dynamics as in the well-known Knudsen's experiment on capillaries. © 2006 Cambridge University Press.

Beschreibung: Large-eddy simulations of the Richtmyer-Meshkov instability with reshock are presented and the results are compared with experiments. Several configurations of shocks initially travelling from light (air) to heavy (sulfur hexafluoride, SF6) have been simulated to match previous experiments and good agreement is found in the growth rates of the turbulent mixing zone (TMZ). The stretched-vortex subgrid model used in this study allows for subgrid continuation modelling, where statistics of the unresolved scales of the flow are estimated. In particular, this multiscale modelling allows the anisotropy of the flow to be extended to the dissipation scale, η, and estimates to be formed for the subgrid probability density function of the mixture fraction of air/SF6 based on the subgrid variance, including the effect of Schmidt number. © 2006 Cambridge University Press.

Beschreibung: The buoyant motion of a bubble rising through a continuous liquid phase can be retarded by the adsorption onto the bubble surface of surfactant dissolved in the liquid phase. The reason for this retardation is that adsorbed surfactant is swept to the trailing pole of the bubble where it accumulates and lowers the surface tension relative to the front end. The difference in tension creates a Marangoni force which opposes the surface flow, rigidifies the interface and increases the drag coefficient. Surfactant molecules adsorb onto the bubble surface by diffusing from the bulk to the sublayer of liquid adjoining the surface, and kinetically adsorbing from the sublayer onto the surface. The surface surfactant distribution which defines the Marangoni force is determined by the rate of kinetic adsorption and bulk diffusion relative to the rate of surface convection. In the limit in which the rate of either kinetic or diffusive transport of surfactant to the bubble surface is slow relative to surface convection and surface diffusion is also slow, surfactant collects in a stagnant cap at the back end of the bubble while the front end is stress free and mobile. The size of the cap and correspondingly the drag coefficient increases with the bulk concentration of surfactant until the cap covers the entire surface and the drag coefficient is that of a bubble with a completely tangentially immobile surface. Previous theoretical research on the stagnant cap regime has not studied in detail the competing roles of bulk diffusion and kinetic adsorption in determining the size of the stagnant cap angle, and there have been only a few studies which have attempted to quantitatively correlate simulations with measurements. This paper provides a more complete theoretical study of and a validating set of experiments on the stagnant cap regime. We solve numerically for the cap angle and drag coefficient as a function of the bulk concentration of surfactant for a spherical bubble rising steadily with inertia in a Newtonian fluid, including both bulk diffusion and kinetic adsorption. For the case of diffusion-limited transport (infinite adsorption kinetics), we show clearly that very small bulk concentrations can immobilize the entire surface, and we calculate the critical concentrations which immobilize the surface as a function of the surfactant parameters. We demonstrate that the effect of kinetics is to reduce the cap angle (hence reduce the drag coefficient) for a given bulk concentration of surfactant. We also present experimental results on the drag of a bubble rising in a glycerol-water mixture, as a function of the dissolved concentration of a polyethoxylated non-ionic surfactant whose bulk diffusion coefficient and a lower bound on the kinetic rate constants have been obtained separately by measuring the reduction in dynamic tension as surfactant adsorbs onto a clean interface. For low concentrations of surfactant, the experiments measure drag coefficients which are intermediate between the drag coefficient of a bubble whose surface is tangentially mobile and one whose surface is completely immobilized. Using the separately obtained value for the diffusion coefficient of the polyethoxylate, we undertake simulations which provide, upon comparison with the measured drag coefficients, a tighter bound on the kinetic rate constants than were otherwise obtained using dynamic surface tension measurement, and this suggests a new method for the measurement of kinetic rate constants. © 2006 Cambridge University Press.

Beschreibung: The characteristics of Boussinesq and non-Boussinesq starting forced plumes were investigated in this study. Two distinct periods in the transient plume penetration are identified, namely, the period of flow development (PFD) and period of developed flow (PDF). Similarity solutions are developed in PDF by incorporating the behaviour of an isolated buoyant vortex ring and recent laboratory results on the trailing forced plume, and the temporal variation of the penetration rate is derived during the different phases of jet-like, transitional and plume-like flow. To verify the similarity solutions, experiments were conducted on vertical starting forced plumes using combined particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF) with refractive index matching. The discharge Reynolds number was varied from 3773 to 7403 and the range of excess densities Δ0=(ρ∞ - ρ0)/ ρ∞ are initial plume and ambient density, respectively) from 2.77% to 25.07%. The experimental results revealed distinct differences between plumes having an initial density difference of larger or smaller than 15% due to the non-Boussinesq effects. Thus, the value of 15% was employed as an approximate criterion to divide the plumes into Boussinesq versus non-Boussinesq cases. The measured penetration rates and the mean centreline axial velocity of the Boussinesq starting forced plumes agreed well with the analytical predictions at the fully developed stage. However, the behaviour was substantially more complex for the non-Boussinesq plumes. In the transient records, it was noted that the time scales for the penetration of the starting plumes and the velocity development in the trailing forced plume were similar, but the time scale for the Gaussian profile to become self-similar was somewhat longer. © 2006 Cambridge University Press.

Beschreibung: We use Brownian dynamics to investigate the effect of chain flexibility on the cross-streamline migration of short polymers in a pressure-driven flow between two infinite flat plates. A simulation method is described that models a polymer molecule at the Kuhn step level as a chain of N freely jointed Brownian rods, and includes multibody hydrodynamic interactions between the chain segments and the surrounding channel walls. Our study confirms the existence of shear-induced migration away from the solid boundaries toward the channel centreline as a result of wall hydrodynamic interactions. At a fixed ratio H/Rg of the channel width to the bulk radius of gyration, and at a fixed value of the Weissenberg number Wi, simulations show that migration is not significantly influenced by flexibility for chains of length N ≥ 2. Much weaker migration is observed however for fully rigid chains N = 1), and a mechanism is discussed to explain migration in that case. © 2006 Cambridge University Press.

Beschreibung: The effects of localized periodic blowing on a turbulent boundary layer were investigated by direct numerical simulation. Time-periodic blowing was applied through a spanwise slot by varying the wall-normal velocity in a cyclic manner from 0 to 2A+. Time-periodic blowing was applied at frequencies in the range 0 ≤ f+ ≤ 0.08 at a fixed blowing amplitude of A+ = 0.5. Simulations of a spatially evolving turbulent boundary layer were carried out for two Reynolds numbers, Reθ,in = 300 and 670. Before investigating the effects of periodic blowing, the effects of steady blowing were examined. A new parameter, σ+, was proposed for describing local blowing; the usefulness of this parameter was that the responses of the flow variables at the two Reynolds numbers were the same for the same σ+. The effects of varying the blowing frequency were scrutinized by examining the phase- or time-averaged turbulent statistics. For both Reynolds numbers, application of blowing at a frequency of f+ = 0.035 was found to give the maximum increases in Reynolds shear stress, streamwise vorticity fluctuations and energy redistribution. Analysis of the Reynolds stress budget showed that this effective blowing frequency induced the greatest enhancement of the pressure-strain term, which is closely related to the energy redistribution. Analysis of the phase-averaged stretching and tilting terms revealed that the stretching term is significantly enhanced in the 'downward' motion that is induced by the spanwise vortical motion. The correlation between the streamwise vorticity and the stretching term changed in magnitude and length scale as the blowing phase was varied, whereas the correlation between the streamwise vorticity and the tilting term did not. © 2006 Cambridge University Press.

Beschreibung: We study the temporal stability of the Orr-Sommerfeld and Squire equations in channels with turbulent mean velocity profiles and turbulent eddy viscosities. Friction Reynolds numbers up to Reτ = 2 × 104 are considered. All the eigensolutions of the problem are damped, but initial perturbations with wavelengths λx 〉 λz can grow temporarily before decaying. The most amplified solutions reproduce the organization of turbulent structures in actual channels, including their self-similar spreading in the logarithmic region. The typical widths of the near-wall streaks and of the large-scale structures of the outer layer, λz+ and λz/h = 3, are predicted well. The dynamics of the most amplified solutions is roughly the same regardless of the wavelength of the perturbations and of the Reynolds number. They start with a wall-normal u event which does not grow but which forces streamwise velocity fluctuations by stirring the mean shear (uv 〈 O). The resulting v fluctuations grow significantly and last longer than the v ones, and contain nearly all the kinetic energy at the instant of maximum amplification. © 2006 Cambridge University Press.

Beschreibung: The competition between wind and buoyancy forces acting on a naturally ventilated building with one upwind and one downwind opening and a distributed heat source can lead to multiple steady states. This study considers the impact of a second downwind opening on the existence of these multiple steady states. It is found that if this new opening exceeds a critical area, then the multiple steady states are eliminated, and the transition from buoyancy to wind dominated flow is continuous. This critical area is shown to be a function of the relative heights of the three windows. The predictions of the model are in accord with new laboratory experiments, and the implications for building design are discussed. © 2006 Cambridge University Press.

Beschreibung: The motion of a single Brownian probe particle subjected to a constant external body force and immersed in a dispersion of colloidal particles is studied with a view to providing a simple model for particle tracking microrheology experiments in the active and nonlinear regime. The non-equilibrium configuration of particles induced by the motion of the probe is calculated to first order in the volume fraction of colloidal particles over the entire range of Pe, accounting for hydrodynamic and excluded volume interactions between the probe and dispersion particles. Here, Pe is the dimensionless external force on the probe, or Péclet number, and is a characteristic measure of the degree to which the equilibrium microstructure of the dispersion is distorted. For small Pe, the microstructure (in a reference frame moving with the probe) is primarily dictated by Brownian diffusion and is approximately fore-aft symmetric about the direction of the external force. In the large Pe limit, advection is dominant except in a thin boundary layer in the compressive region of the flow where it is balanced by Brownian diffusion, leading to a highly non-equilibrium microstructure. The computed microstructure is employed to calculate the average translational velocity of the probe, from which the 'microviscosity' of the dispersion may be inferred via application of Stokes drag law. For small departures from equilibrium (Pe), the microviscosity 'force-thins' proportional to Pe2 from its Newtonian low-force plateau. For particles with long-range excluded volume interactions, force-thinning persists until a terminal Newtonian plateau is reached in the limit Pe → ∞. In the case of particles with very short-range excluded volume interactions, the force-thinning ceases at Pe ∼ O (1), at which point the microviscosity attains a minimum value. Beyond Pe ∼ O(1), the microstructural boundary layer coincides with the lubrication range of hydrodynamic interactions causing the microviscosity to enter a continuous 'force-thickening' regime. The qualitative picture of the microviscosity variation with Pe is in good agreement with theoretical and computational investigations on the 'macroviscosity' of sheared colloidal dispersions, and, after appropriate scaling, we are able to make a direct quantitative comparison. This suggests that active tracking microrheology is a valuable tool with which to explore the rich nonlinear rheology of complex fluids. © 2006 Cambridge University Press.

Beschreibung: A fully three-dimensional model is proposed for the generation of tidal sand waves and sand banks from small bottom perturbations of a flat seabed subject to tidal currents. The model predicts the conditions leading to the appearance of both tidal sand waves and sand banks and determines their main geometrical characteristics. A finite wavelength of both sand waves and sand banks is found around the critical conditions, thus opening the possibility of performing a weakly nonlinear stability analysis able to predict the equilibrium amplitude of the bottom forms. As shown by previous works on the subject, the sand wave crests turn out to be orthogonal to the direction of the main tidal current. The present results also show that in the Northern Hemisphere sand bank crests are clockwise or counter-clockwise rotated with respect to the main tidal current depending on the counter-clockwise or clockwise rotation of the velocity vector induced by the tide. Only for unidirectional or quasi-unidirectional tidal currents are sand banks always counter-clockwise rotated. The predictions of the model are supported by comparisons with field data. Finally, the mechanisms leading to the appearance of sand waves and sand banks are discussed in the light of the model findings. In particular, it is shown that the growth of sand banks is not only induced by the depth-averaged residual circulation which is present around the bedforms and is parallel to the crests of the bottom forms: a steady drift of the sediment from the troughs towards the crests is also driven by the steady velocity component orthogonal to the crests which is present close to the bottom and can be quantified only by a three-dimensional model. While the former mechanism appears to trigger the formation of counter-clockwise sand banks only, the latter mechanism can give rise to both counter-clockwise and clockwise rotated sand banks. © 2006 Cambridge University Press.

Beschreibung: We present experimental observations of hole formation in ejecta crowns, when a viscous drop impacts onto a thin film of low-viscosity liquid with significantly lower surface tension than the drop liquid. The holes are promoted by Marangoni-driven flows in the sheet, resulting from a spray of fine droplets ejected from the thin film hitting the inner side of the crown. The puncturing of the sheet takes place in three distinct steps. First a circular patch of the sheet thins by Marangoni-driven flows. Then this thinner film ruptures and a hole quickly opens up spanning the patch. Finally, the hole opens up further at an accelerated rate, driven by the unbalanced surface tension at its edge. The holes grow until they meet adjacent holes, thus leaving a foam-like network of liquid filaments, which then breaks up into a cloud of droplets. © 2006 Cambridge University Press.

Beschreibung: Results are presented of experimental investigations into the motion of a heavy sphere in a rotating cylinder which is completely filled with highly viscous fluid. For a given cylinder rotation rate, the sphere adopts a fixed position and rotates adjacent to the cylinder wall. For the case of a smooth sphere the motion is consistent with that predicted by a Stokes flow model. Artificially roughened spheres exhibit particle-boundary contact caused by impacts of surface asperities with the boundary for low cylinder surface speeds. For higher cylinder surface speeds the behaviour of the roughened spheres crosses smoothly from the particle-boundary contact regime to motion with hydrodynamically lubricated flow. © 2006 Cambridge University Press.

Beschreibung: A theoretical study is made of fully localized solitary waves, commonly referred to as 'lumps', on the interface of a two-layer fluid system in the case that the upper layer is bounded by a rigid lid and lies on top of an infinitely deep fluid. The analysis is based on an extension, that allows for weak transverse variations, of the equation derived by Benjamin (J. Fluid Mech. vol. 245, 1992, p. 401) for the evolution in one spatial dimension of weakly nonlinear long waves in this flow configuration, assuming that interfacial tension is large and the two fluid densities are nearly equal. The phase speed of the Benjamin equation features a minimum at a finite wavenumber where plane solitary waves are known to bifurcate from infinitesimal sinusoidal wavetrains. Using small-amplitude expansions, it is shown that this minimum is also the bifurcation point of lumps akin to the free-surface gravity-capillary lumps recently found on water of finite depth. Numerical continuation of the two symmetric lump-solution branches that bifurcate there reveals that the elevation-wave branch is directly connected to the familiar lump solutions of the Kadomtsev-Petviashvili equation, while the depression-wave branch apparently features a sequence of limit points associated with multi-modal lumps. Plane solitary waves of elevation, although stable in one dimension, are unstable to transverse perturbations, and there is evidence from unsteady numerical simulations that this instability results in the formation of elevation lumps. © 2006 Cambridge University Press.

Beschreibung: The concept of impulse is employed with conformal mapping to yield relatively simple relations for the force exerted on a two-dimensional stationary object by an incompressible irrotational and unsteady flow with moving vortices. An explicit relation for symmetric vortex flows is found, involving the vortex strength and the first and second derivatives of the mapping function evaluated at the vortex position. Furthermore an expression for not-necessarily symmetric vortex flows is derived, containing vortex strength, the first derivative of the mapping function evaluated at the vortex position, and the vortex velocity. © 2006 Cambridge University Press.

Beschreibung: A new third-order solution for bichromatic bi-directional water waves in finite depth is presented. Earlier derivations of steady bichromatic wave theories have been restricted to second-order in finite depth and third-order in infinite depth, while third-order theories in finite depth have been limited to the case of monochromatic short-crested waves. This work generalizes these earlier works. The solution includes explicit expressions for the surface elevation, the amplitude dispersion and the vertical variation of the velocity potential, and it incorporates the effect of an ambient current with the option of specifying zero net volume flux. The nonlinear dispersion relation is generalized to account for many interacting wave components with different frequencies and amplitudes, and it is verified against classical expressions from the literature. Limitations and problems with these classical expressions are identified. Next, third-order resonance curves for finite-amplitude carrier waves and their three-dimensional perturbations are calculated. The influence of nonlinearity on these curves is demonstrated and a comparison is made with the location of dominant class I and class II wave instabilities determined by classical stability analyses. Finally, third-order resonance curves for the interaction of nonlinear waves and an undular sea bottom are calculated. On the basis of these curves, the previously observed downshift/upshift of reflected/transmitted class III Bragg scatter is, for the first time, explained. © 2006 Cambridge University Press.

Beschreibung: The formation of columnar eddies in a rapidly rotating environment is often attributed to nonlinear processes, acting on the nonlinear time scale l/ u . We argue that this is not the whole story, and that linear wave propagation can play an important role, at least on the short time scale of Ω-1. In particular, we consider the initial value problem of a compact blob of vorticity (an eddy) sitting in a rapidly rotating environment. We show that, although the energy of the eddy disperses in all directions through inertial wave propagation, the axial components of its linear impulse and angular momentum disperse along the rotation axis only, remaining confined to the cylinder which circumscribes the initial vortex blob. This confinement has a crucial influence on the manner in which energy disperses from the eddy, with the energy density within the tangent cylinder remaining much higher than that outsid (i.e. decaying as t-1 inside the cylinder and t-3/2 outside). When the initial conditions consist of an array of vortex blobs the situation is more complicated, because the energy density within the tangent cylinder of any one blob is eventually swamped by the radiation released from all the other blobs. Nevertheless, we would expect that a turbulent flow which starts as a collection of blobs of vorticity will, for times of order Ω-1, exhibit columnar vortices, albeit immersed in a random field of inertial waves. Laboratory experiments are described which do indeed show the emergence of columnar eddies through linear mechanisms, though these experiments are restricted to the case of inhomogeneous turbulence. Since the Rossby number in the experiments is of the order of unity, this suggests that linear effects can still influence and shape turbulence when nonlinear processes are also operating. © 2006 Cambridge University Press.

Beschreibung: This work aims at understanding the viscous effects of the outer potential flow on Prandtl's boundary layer. For a body moving with a constant velocity in an otherwise quiescent liquid, the non-zero viscous dissipation of the outer potential flow gives rise to an additional drag, increasing the drag calculated from the boundary layer alone. The drag is considered in three cases here, on a two-dimensional circular gas bubble in a streaming flow, at the edge of the boundary layer around a rapidly rotating cylinder in a uniform flow, and on an airfoil in a streaming flow. The drag may be computed using the dissipation method or the viscous pressure correction of the irrotational pressure. Such a pressure correction can be induced by the discrepancy between the irrotatinal shear stress and the zero shear stress at a fluid-gas interface, or by the discrepancy between the shear stress evaluated from the boundary-layer solution and that evaluated from the outer potential flow solution at the edge of the boundary layer. © 2006 Cambridge University Press.

Beschreibung: We report experimental results for the influence of a tilt angle β relative to gravity on turbulent Rayleigh-Bénard convection of cylindrical samples. The measurements were made at Rayleigh numbers R up to 1011 with two samples of height L equal to the diameter D (aspect ratio Γ ≡ D/L ≃ 1), one with L ≃ 0.5 m (the 'large' sample) and the other with L ≃ 0.25 m (the 'medium' sample). The fluid was water with a Prandtl number σ = 4.38. In contrast to the experiences reported by Chillà et al. (Eur. Phys. J. B, vol. 40, 2004, p. 223) for a similar sample but with Γ ≃ 0.5 (D = 0.5 and L = 1.0 m), we found no long relaxation times. For R = 9.4 × 1010 we measured the Nusselt number N as a function of β and obtained a small β dependence given by N (β) = N 0[1-(3.1 ± 0.1) × 10-2 β ] when β is in radians. This reduction of N is about a factor of 50 smaller than the result found by Chillà et al. (2004) for their Γ ≃ 0.5 sample. We measured sidewall temperatures at eight equally spaced azimuthal locations on the horizontal mid-plane of the sample and used them to obtain cross-correlation functions between opposite azimuthal locations. The correlation functions had Gaussian peaks centred about t1 cc 〉 0 that corresponded to half a turnover time of the large-scale circulation (LSC) and yielded Reynolds numbers Recc of the LSC. For the large sample and R = 9.4 × 1010 we found Recc(β) = Recc(0) × [1 + (1.85 ± 0.21) β - (5.9 ± 1.7) β2]. Similar results were obtained from the auto-correlation functions of individual thermometers. These results are consistent with measurements of the amplitude δ of the azimuthal sidewall temperature variation at the mid-plane that gave δ(β) = δ(0) × [1 + (1.84 ± 0.45) β - (3.1 ± 3.9)β2] for the same R. An important conclusion is that the increase of the speed (i.e. of Re) of the LSC with β does not significantly influence the heat transport. Thus the heat transport must be determined primarily by the instability mechanism operative in the boundary layers, rather than by the rate at which 'plumes' are carried away by the LSC. This mechanism is apparently independent of β. Over the range 109 ≲ R ≲ 1011 the enhancement of Recc at constant β due to the tilt could be described by a power law of R with an exponent of -1/6, consistent with a simple model that balances the additional buoyancy due to the tilt angle by the shear stress across the boundary layers. Even a small tilt angle dramatically suppressed the azimuthal meandering and the sudden reorientations characteristic of the LSC in a sample with β = 0. For large R the azimuthal mean of the temperature at the horizontal mid-plane differed significantly from the average of the top- and bottom-plate temperatures due to non-Boussinesq effects, but within our resolution was independent of β. © 2006 Cambridge University Press.

Beschreibung: We investigate theoretically the first effects of inertia on the orientation dynamics of a torque-free spheroidal particle in simple shear flow when the deviation from sphericity is small. The inertialess motion of any axisymmetric particle in simple shear represents a degenerate limit, the spheroidal geometry being a special case; as originally found by Jeffery (Proc. R. Soc. Lond. A, vol. 102, 1922, p.161), the orientation vector moves indefinitely along any one of a single-parameter family of closed orbits centred around the vorticity axis, the distribution across orbits being determined by initial conditions. We consider both the inertia of the particle and that of the suspending fluid, characterized by the Stokes (St) and Reynolds numbers Re = ρfρpSt, ρp and ρf being the particle and fluid densities), respectively, as mechanisms for breaking the aforementioned degeneracy. The former is defined as St = a2γ̇ρp/μ, where γ̇ is the shear rate, a is the radius of the unperturbed sphere and μ is the fluid viscosity. When the particles are much denser than the suspending fluid, as is the case for aerosols, St ≫ Re (both parameters being much less than unity), inertial forces in the fluid may be neglected. It is then found, in the absence of gravity, that a slightly prolate spheroid drifts toward the shearing plane, while the axis of a slightly oblate spheroid tends toward the vorticity axis, both on a time scale of O( ε St γ̇)-1, where ε(≪ 1) is the deviation from sphericity. For the case of neutrally buoyant particles (St = Re), inertia of both the particle and fluid come into play. In contrast to the small but finite St zero Re case, the orientation vector of a neutrally buoyant prolate spheroid now migrates toward the direction of vorticity, while that of an oblate spheroid drifts towards the shearing plane. The time scale of drift towards the asymptotic state is O( ε Reγ̇)-1 in both cases. Thereafter, we also examine the rotations of prolate and oblate spheroids in the presence of both gravity and shear, the analysis again being restricted to weak inertial effects. A wide range of interesting orientational behaviour arises, and the long-time orientation dynamics of the spheroids are determined as a function of both the density ratio ρp/ρf and a shear parameter N, defined as N = 2aρfg/(9μγ̇). © 2006 Cambridge University Press.

Beschreibung: Direct numerical simulations of thermal convection over grooved plates are presented and discussed, in comparison with the standard flat-plate case, in order to gain a better understanding of the altered near-wall dynamics and of the enhancement of the heat transfer. The simulations are performed in a cylindrical cell of aspect-ratio (diameter over cell height) Γ = 1/2 at fixed Prandtl number Pr = 0.7 with the Rayleigh number Ra ranging from 2 × 106 to 2 × 1011. The results show an increase of heat transfer, or in non-dimensional form the Nusselt number Nu when the mean thermal boundary-layer thickness becomes smaller than the groove height, in agreement with earlier experimental investigations available from the literature. The present increase, however, results in a steeper power law of the Nu vs. Ra law rather than a simple upward shift of the Nu law of the flat plate. This finding agrees with some studies, but it is at variance with others. Possible causes for this difference are discussed with the help of an electrical analogy. © 2006 Cambridge University Press.

Beschreibung: By adding minute concentrations of a high-molecular-weight polymer, liquid jets or bridges collapsing under the action of surface tension develop a characteristic shape of uniform threads connecting spherical fluid drops. In this paper, high-precision measurements of this beads-on-string structure are combined with a theoretical analysis of the limiting case of large polymer relaxation times and high polymer extensibilities, for which the evolution can be divided into two distinct regimes. For times smaller than the polymer relaxation time over which the beads-on-string structure develops, we give a simplified local description, which still retains the essential physics of the problem. At times much larger than the relaxation time, we show that the solution consists of exponentially thinning threads connecting almost spherical drops. Both experiment and theoretical analysis of a one-dimensional model equation reveal a self-similar structure of the corner where a thread is attached to the neighbouring drops. © 2006 Cambridge University Press.

Beschreibung: Viscous fingering in porous media at large Péclet numbers is subject to an unsolved selection problem, not unlike the Saffman-Taylor problem. The mixing zone predicted by the entropy solution is found to spread much faster than is observed experimentally or from fine-scale numerical simulations. In this paper we apply a recent approach by Menon & Otto (Commun. Math. Phys., vol. 257, 2005, p. 303), to develop bounds for the mixing zone. These give growth velocities smaller than the entropy solution result (M - 1/M). In particular, for an exponential viscosity-concentration mixing rule, the mixing zone velocity is bounded by (M - 1)2/(M 1n M), which is smaller than (M - 1/M). An extension to a porous medium with an uncorrelated random heterogeneity is also given. © 2006 Cambridge University Press.

Beschreibung: Prandtl's secondary mean motions of the second kind are driven by the variation of Reynolds stresses near resistive boundaries. In the flows considered here the turbulence is generated away from the boundary in the absence of a mean flow and then impacts onto a rigid surface placed into the flow at t = 0. The initial development of the distorted flow is obtained using the linear approximation and the statistical analysis of rapid distortion theory, following Hunt & Graham (1978) assuming homogeneous stationary high-Reynolds-number turbulence with an integral length scale L∞ and r.m.s. velocity ν′∞. First, the effects of axisymmetric anisotropy and of different forms of the spectra are analysed for turbulence impinging onto a plane surface lying at an angle α to the unit vector e of the axis of symmetry of the energy spectrum tensor Φij(k). R is defined as the ratio of the largest to smallest variances of the velocity components. The surface blocking leads to gradients of Reynolds shear stresses normal to the surface in the source layer B(s) with thickness of order L∞ and thence to a mean velocity U(t)∼-tν′∞2 sin 2α (1 - 1/R)/L∞ along the slope in the opposite direction of the projection of e onto the plane (i.e. in the direction (e Λ n) Λ n where n is the normal into the flow). U is greatest near the surface where y ≪ L∞. As a result of shear stresses being induced by the mean velocity gradient, a steady flow results over a time scale TL = L∞/ ν′∞ - an order of magnitude estimate for the steady-state mean velocity is thence U(t/TL → ∞) ∼ ν′∞ (sin 2α(1 - 1/R)1/2. Secondly, the effect of a curved surface is studied by analysing isotropic turbulence near an undulating surface of wavelength Λ and amplitude H, with a low slope so that H ≪ Λ. The boundary condition of zero normal velocity at the curved surface generates larger irrotational fluctuations in the troughs, smaller fluctuations over the crest, and shear stresses over the slopes. The curl of the gradients of Reynolds normal and shear stresses within B(s) cause the growth of a mean vorticity which induces a mean velocity of order -tν′∞2/L∞ within B(s) and a weaker recirculating velocity of order -tν′∞2/Λ in a deeper wave layer, B(ω), with thickness of order Λ outside B(s). The wavelength of the mean motion is Λ, with downward motions over the troughs and upward motion over the crest. As in the first case, a steady flow is predicted when t/TL ≫ 1. Anisotropic free-stream turbulence also induces mean motions on undulating surfaces with the same wavelength Λ as that of the undulating surface, but the directions of these mean motions can be towards or away from the troughs/crests depending on the orientation of the anisotropy of the free stream. Flow visualization experiments conducted in a mixing box with oscillating anisotropic and isotropic grids demonstrated the existence of these mean flows and that they reach a steady state with an intensity and length scale comparable to those predicted. These results are also consistent with numerical simulation of Krettenauer & Schumann (1992) of convective turbulence over an undulating surface. © 2006 Cambridge University Press.

Beschreibung: We report measurements of the Nusselt number, Nu, in turbulent thermal convection in a cylindrical container of aspect ratio 4. The highest Rayleigh number achieved was Ra = 2 × 1013. Except for the last half a decade or so of Ra, experimental conditions obey the Boussinesq approximation accurately. For these conditions, the data show that the log Nu-log Ra slope saturates at a value close to 1/3, as observed previously by us in experiments with smaller aspect ratios. The increasing slope over the last half a decade of Ra is inconclusive because the corresponding conditions are non-Boussinesq. Finally, we report a modified scaling relation between the plume advection frequency and Ra that collapses data for different aspect ratios. © 2006 Cambridge University Press.

Beschreibung: Ice sheets are susceptible to the formation of ice streams, or narrow bands of fast-flowing ice whose high velocities are caused by rapid sliding at the contact between ice and the underlying bed. Based on recent geophysical work which has shown that the sliding motion of ice streams may be described by a Coulomb friction law, we investigate how the location of ice streams depends on the geometry of an ice sheet and on the mechanical properties of the underlying bed. More generally, this problem is relevant to the flow of thin films with Coulomb (or 'solid') friction laws applied at their base. By analogy with friction problems in elasticity, we construct a variational formulation for the free boundary between ice streams, where bed failure occurs, and the surrounding ice ridges, where there is little or no sliding. This variational problem takes the form of a non-coercive variational inequality, and we show that solutions exist provided a force and moment balance condition is satisfied. In that case, solutions are also unique except under certain specialized circumstances which are unlikely to arise for a real ice sheet. Further, we show how the variational formulation of the ice flow problem can be exploited to calculate numerical solutions, and to simulate the effect of changing ice geometry and bed friction on the location and velocities of streaming flow. Lastly, we study the effect of ice-shelf buttressing on the flow of ice streams whose spatial extent is determined by the yield stress distribution of the bed. In line with previous studies of ice-shelf buttressing, we find that the removal of an ice shelf can cause an ice stream feeding the ice shelf to speed up considerably, which underlines the important role ice shelves may play in controlling the dynamics of marine ice sheets. © 2006 Cambridge University Press.

Beschreibung: We study the streaming flow past a rapidly rotating circular cylinder. The starting point is the full continuity and momentum equations without any approximations. We assume that the solution is a boundary-layer flow near the cylinder surface with the potential flow outside the boundary layer. The order of magnitude of the terms in the continuity and momentum equations can be estimated inside the boundary layer. When terms of the order of δ/a and higher are dropped, where δ is the boundary-layer thickness and a is the radius of the cylinder, the equations used by M. B. Glauert (Proc. R. Soc. Lond. A, vol. 242, 1957, p. 108) are recovered. Glauert's solution ignores the irrotational rotary component of the flow inside the boundary layer, which is consistent with dropping δ/a terms in the governing equations. We propose a new solution to this problem, in which the velocity field is decomposed into two parts. Outside the boundary layer, the flow is irrotational and can be decomposed into a purely rotary flow and a potential flow past a fixed cylinder. Inside the boundary layer, the velocity is decomposed into an irrotational purely rotary flow and a boundary-layer flow. Inserting this decomposition of the velocity field inside the boundary layer into the governing equations, we obtain a new set of equations for the boundary-layer flow, in which we do not drop the terms of the order of δ/a or higher. The pressure can no longer be assumed to be a constant across the boundary layer, and the continuity of shear stress at the outer edge of the boundary layer is enforced. We solve this new set of equations using Glauert's method, i.e. to expand the solutions as a power series of α = 2U0/Q, where U0 is the uniform stream velocity and Q is the circulatory velocity at the outer edge of the boundary layer. The pressure from this boundary-layer solution has two parts, an inertial part and a viscous part. The inertial part comes from the inertia terms in the momentum equations and is in agreement with the irrotational pressure; the viscous part comes from the viscous stress terms in the momentum equations and may be viewed as a viscous pressure correction, which contributes to both drag and lift. Our boundary-layer solution is in reasonable to excellent agreement with the numerical simulation in the companion paper by Padrino & Joseph (2006). © 2006 Cambridge University Press.

Beschreibung: We report on a newly discovered bifurcation that occurs in dry grains flowing down a chute with a wavy bottom. We find that the bifurcation outwardly resembles the long-known fluid analogue of inviscid channel flow over a wavy bottom reported in 1886 by Lord Kelvin; however, in detail, the two situations differ significantly. We compare three distinct states seen in the granular system: a 'regular' flow in phase with the bottom wave; an 'antiregular' flow that is out of phase; and a 'flat' flow in which the surface slides nearly uniformly downhill. Additionally, we discuss evidence that sustained subsurface circulation in the granular bed, accompanied by strong fluctuations in flow velocities, can appear in granular flows over wavy surfaces. © 2006 Cambridge University Press.

Beschreibung: Results from the numerical simulation of the two-dimensional incompressible unsteady Navier-Stokes equations for streaming flow past a rotating circular cylinder are presented in this study. The numerical solution of the equations of motion is conducted with a commercial computational fluid dynamics package which discretizes the equations applying the control volume method. The numerical set-up is validated by comparing results for a Reynolds number based on the free stream of Re = 200 and dimensionless peripheral speed of q̃ = 3, 4 and 5 with results from the literature. After the validation stage, various pairs of Re q̃ are specified in order to carry out the numerical experiments. These values are Re = 200 with q̃ = 4 and 5; Re = 400 with q̃ = 4, 5 and 6, and Re = 1000 with q̃ = 3. In all these cases, gentle convergence to fully developed steady state is reached. From the numerical vorticity distribution, the position of the outer edge of the vortical region is determined as a function of the angular coordinate. This position is found by means of a reasonable criterion set to define the outmost curve around the cylinder where the vorticity magnitude reaches a certain cut-off value. By considering the average value of this profile, a uniform vortical region thickness is specified for every pair of Re and q̃. Next, the theoretical approach of Wang & Joseph (2006a; see the companion paper) and the numerical results are used to determine two different values of the effective vortical region thickness for every pair of Re and q̃. One effective thickness δD/a is obtained from the match between the additional drag on the outer edge of the vortical region according to the viscous correction of viscous potential flow (VCVPF) and the corresponding numerical profile while the other thickness δL/a is determined from the match between the pressure lift on the cylinder obtained from Wang & Joseph (2006a)'s simple modification of the boundary-layer analysis due to Glauert (Proc. R. Soc. Lond. A, vol. 242, 1957, p. 108) and the numerical value of the pressure lift coefficient. The values of δD/a and δL/a are used in the computation of various parameters associated with the flow, namely, the torque on the rotating cylinder, the circulatory velocity at the edge of the vortical region, which links the cylinder's angular velocity with the circulation of the irrotational flow of the viscous fluid outside this region, and the viscous dissipation. Predictions from the approaches of Glauert (1957) and Wang & Joseph (2006a) are also included for comparison. The values of both effective thicknesses, δD/a and δL/a, are found to have the same order of magnitude. Then, we show that choosing δD/ a as a unique effective thickness, the modification of Glauert's boundary-layer analysis and the VCVPF approach as proposed by Wang & Joseph (2006a) produce results which are in better general agreement with the values from numerical simulation than those from Glauert's solution. © 2006 Cambridge University Press.

Beschreibung: Approximations to the scattering of linear surface gravity waves on water of varying quiescent depth are investigated by means of a variational approach. Previous authors have used wave modes associated with the constant depth case to approximate the velocity potential, leading to a system of coupled differential equations. Here it is shown that a transformation of the dependent variables results in a much simplified differential equation system which in turn leads to a new multi-mode 'mild-slope' approximation. Further, the effect of adding a bed mode is examined and clarified. A systematic analytic method is presented for evaluating inner products that arise and numerical experiments for two-dimensional scattering are used to examine the performance of the new approximations. © 2006 Cambridge University Press.

Beschreibung: We study the capillary instability of a liquid film (thickness h0 coating a horizontal cylindrical tube (radius R0). We show experimentally that the instability only occurs if h0/R0 〉 0.3(R0/a)2, where a is the capillary length. If this criterion is not fulfilled, the liquid film does not destabilize into an array of drops, owing to the gravitational drainage. © 2006 Cambridge University Press.

Beschreibung: This paper addresses how the turbulent flow field in submerged wall jets responds to an abrupt change from smooth to rough beds. Experiments were conducted for submerged wall jets having different submergence factors and jet Froude numbers. The bed configurations investigated consisted of different combinations of the lengths of smooth beds and the roughness of rough beds. The vertical profiles of time-averaged velocity components, turbulence intensity components and Reynolds stress were detected by an acoustic Doppler velocimeter at different streamwise distances; and the horizontal distributions of bed shear stress were estimated from the Reynolds stress profiles. The flow field displays the decay of jet velocity due to abrupt changes from smooth to rough beds. The boundary layer grows more quickly with increase in roughness of rough beds. The change in bed roughness induces an increased depression of the free surface over the smooth bed. The Reynolds and bed shear stresses are also computed by solving the Navier-Stokes equations. The response of the turbulent flow characteristics of submerged wall jets to abrupt changes from smooth to rough beds is analysed from the point of view of similarity, growth of the length scale, and decay of the velocity and turbulence characteristics scales. The significant observation is that the flow in the fully developed zone is plausibly self-preserving on both smooth and rough beds. Also, the use of a common length scale makes it possible to collapse all the flow data onto a single band; and there is a gradual variation of flow at the junction of the smooth and rough beds. The equilibrium scour profiles downstream of a smooth apron due to submerged wall jets are computed from the threshold condition of the sediment particles on the scoured bed. Use of the modified bed shear stress for the downstream variation of scoured bed permits the computation of the equilibrium scour profiles. The time-variation of maximum scour depth is computed from the bed shear stress with a modification for the time dependence. The agreement between the results obtained from the model and the experimental data is satisfactory. © 2006 Cambridge University Press.

Beschreibung: The wake of a streamwise oscillating circular cylinder has been experimentally investigated over a range of oscillation amplitude and frequency ratios using laser-induced-fluorescence flow visualization, particle image velocimetry and hot-wire techniques. Five typical flow structures, referred to as S-I, S-II, A-I, A-III and A-IV, are identified. Special attention is given to the S-II mode because this flow structure is observed experimentally for the first time. It consists of two rows of binary vortices symmetrically arranged about the centreline of the wake. Each binary vortex contains two counter-rotating vortices shed from the same side of the cylinder. This flow structure corresponds to zero mean and fluctuating lift on the cylinder, which could be of engineering significance. A theoretical analysis for this flow has been conducted based on the governing equations. The solution to the two-dimensional vorticity equation suggests that the flow may be considered to be the superposition of two components, i.e. that due to a stationary cylinder in a steady uniform cross-flow and to a cylinder oscillating in fluid at rest, which are characterized by alternate and symmetric vortex shedding, respectively. The solution provides insight into the formation of the various modes of the flow structure. A semi-empirical prediction of the S-II mode structure is developed, which is in excellent agreement with experimental data as well as with previous numerical results. © 2006 Cambridge University Press.

Beschreibung: The shape of the interface between two superimposed layers in a two-dimensional channel confined between a planar and a corrugated or indented wall is investigated in the limit of Stokes flow. A perturbation analysis for walls with small-amplitude sinusoidal corrugations reveals that an insoluble surfactant amplifies the deformation of the interface and causes a negative drift in the phase shift under most conditions. The effect is most significant at moderate capillary numbers and for corrugations whose wavelength is large compared to the thickness of the adjacent layer lining the wavy wall. The precise effect of the surfactant depends on the ratio of the fluid viscosities, proximity of the interface to the planar wall, capillary number, and wavelength of the corrugations. When the interface is near the plane wall, introducing surfactant reduces the interfacial amplitude and causes a positive phase shift with respect to the wavy wall. As the interface further approaches the plane wall, the interfacial wave tends to become in phase with the wavy wall, reflecting its unshifted topography. In the second part of this study, a boundary integral method is implemented to compute Stokes flow over a wall with an arbitrary periodic profile, and results are presented for sinusoidal walls and planar walls containing a periodic sequence of square and circular depressions or projections. The numerical results reveal that the linear perturbation theory overestimates the deformation of the interface over a wavy wall, and illustrate the nature of shear-driven film flow over a planar wall with indented topography. © 2006 Cambridge University Press.

Beschreibung: Drag-reduction experiments with combined injection of high-molecular-weight long-chained polymers and microbubbles were conducted on a 3.1 m long flat plate model in the 1.22 m diameter water tunnel at the Applied Research Laboratory of the Pennsylvania State University. Combined gas injection upstream of polymer injection produced, over a wide range of test conditions, higher levels of drag reduction than those obtained from the independent injection of polymer or microbubbles alone. These increased levels of drag reduction with combined injection were often greater than the product of the drag reductions obtained by the independent constituents, defined as synergy. We speculate that the synergy is a result of the gas-layer-induced extension of the polymer-alone initial diffusion zone in combination with the increased drag reduction by microbubbles. This increased length of the initial zone layer, consistent with high drag reduction, can significantly increase the persistence of the drag reduction and may improve the outlook for practical application. © 2006 Cambridge University Press.

Beschreibung: We study the time-independent free-surface flow which forms when a fluid drains out of a container, a so-called bathtub vortex. We focus on the bathtub vortex in a rotating container and describe the free-surface shape and the complex flow structure using photographs of the free surface, flow visualizations, and velocity measurements. We find that the velocity field in the bulk of the fluid agrees with predictions from linear Ekman theory for the boundary layer at the bottom, and we discuss the limitations of linear Ekman theory for the source-sink flow in the experiment. We introduce a radial expansion approximation of the central vortex core and reduce the model to a single first-order equation. We solve the equation numerically and find that the axial velocity depends linearly on height whereas the azimuthal velocity is almost independent of height. We discuss the model of the bathtub vortex introduced by Lundgren (J. Fluid Mech. vol. 155, 1985, p. 381) and compare it with our experiment. We find that the measured velocities and surface profiles are described well by the model when Ekman upflow and surface tension effects are included. © 2006 Cambridge University Press.

Beschreibung: The nonlinear stability of falling film flow down an inclined flat plane is investigated when an electric field acts normal to the plane. A systematic asymptotic expansion is used to derive a fully nonlinear long-wave model equation for the scaled interface, where higher-order terms must be retained to make the long-wave approximation valid for long times. The effect of the electric field is to introduce a non-local term which comes from the potential region above the liquid film. This term is always linearly destabilizing and produces growth rates proportional to the cubic power of the wavenumber - surface tension is included and provides a short wavelength cutoff. Even in the absence of an electric field, the fully nonlinear equation can produce singular solutions after a finite time. This difficulty is avoided at smaller amplitudes where the weakly nonlinear evolution is governed by an extension of the Kuramoto-Sivashinsky equation. This equation has solutions which exist for all time and allows for a complete study of the nonlinear behaviour of competing physical mechanisms: long-wave instability above a critical Reynolds number, short-wave damping due to surface tension and intermediate growth due to the electric field. Through a combination of analysis and extensive numerical experiments, we find parameter ranges that support non-uniform travelling waves, time-periodic travelling waves and complex nonlinear dynamics including chaotic interfacial oscillations. It is established that a sufficiently high electric field will drive the system to chaotic oscillations, even when the Reynolds number is smaller than the critical value below which the non-electrified problem is linearly stable. A particular case of this is Stokes flow. © 2006 Cambridge University Press.

Beschreibung: This paper presents analytical and numerical results for separated stratified inviscid flow over and around an isolated mountain in the limit of small Froude number. The vertical density profile consists of a lower strongly stratified layer whose depth is just less than that of the mountain. It is separated from a semi-infinite upper stably stratified layer by a thin, highly stable, inversion layer. The paper aims to provide, for this particular profile, a thorough analysis of the three-dimensional separated flow over a mountain top with strong stratification. The Froude numbers F and F1 of the lower layer and the interface are small with F1 ≪ F ≪ 1 but the upper-layer Froude number is arbitrary. The flow at each height in the lower layer is governed by the two-dimensional Euler equations and moves horizontally around the mountain. It is given by a modification of a previous model using Kirchhoff free-streamline theory for the separated flow region downstream of the mountain. The pressure variations associated with the lower-layer flow are of the same order as the dynamic head and induce significant displacements of the inversion layer. When the inversion is near the top of the mountain these deflections are of the same order as the height of the projecting part of the mountain top and combine with the flow over the mountain top to excite vertically propagating internal waves in the upper layer. The resultant pressure field, vertical stream surface displacements, and surface streamlines in the upper layer are described consistently in the hydrostatic limit. Many of the features of the upper flow, including the perturbations of the critical dividing streamlines, are similar to those in flows with uniform stable stratification at low Froude number. Comparisons are made with experiments and approximate models for these summit flows based on the assumption that the dividing streamlines have small vertical displacement. © 2006 Cambridge University Press.

Beschreibung: In a recent paper, Segur et al. (J. Fluid Mech. vol. 539, p. 229, 2005, hereafter referred to as L showed, based on a damped version of the nonlinear Schrodinger equation (NLS), that any amount of dissipation (of a certain type) stabilizes the Benjamin-Feir instability of a modulated Stokes wave train. Their theoretical predictions are confirmed by laboratory experiments for waves of small or moderate amplitude, but not for waves of large amplitude or with relatively large perturbations. L left open questions regarding the validity of their theoretical results for these large-amplitude waves, and possibly the validity of the NLS assumptions of weak nonlinearity and narrow-bandedness. We investigate these issues using direct simulations of the primitive equations, incorporating constant and wavenumber-dependent dissipation models. For small or moderate amplitudes, our full simulations agree with the theory and experiments of L. For large amplitudes, we find that it is primarily the form of the dissipation model, rather than the assumptions of NLS, that is responsible for the failure of L's theoretical predictions. Indeed, with an appropriate wavenumber-dependent dissipation model, both the full simulations and NLS obtain the correct evolution behaviour for large-amplitude waves. Finally, using direct and NLS simulations, we confirm the general conclusion of L for stabilization of the Benjamin-Feir instability over long-time wave train evolution. © 2006 Cambridge University Press.

Beschreibung: Optimal perturbations in compressible, non-parallel boundary layers are considered here. The flows past a flat plate and past a sphere are analysed. The governing equations are derived from the linearized Navier-Stokes equations by employing a scaling that relies on the presence of streamwise vortices, which are well-known for being responsible for the 'lift-up' effect. Consequently, the energy norm of the inlet perturbation encompasses the wall-normal and spanwise velocity components only. The effect of different choices of the energy norm at the outlet is studied, testing full (all velocity components and temperature) and partial (streamwise velocity and temperature only) norms. Optimal perturbations are computed via an iterative algorithm completely derived in the discrete framework. The latter simplifies the derivation of the adjoint equations and the coupling conditions at the inlet and outlet. Results for the flat plate show that when the Reynolds number is of the order of 103, a significant difference in the energy growth is found between the cases of full and partial energy norms at the outlet. The effect of the wall temperature is in agreement with previous parallel-flow results, with cooling being a destabilizing factor for both flat plate and sphere. Flow divergence, which characterizes the boundary layer past the sphere, has significant effects on the transient growth phenomenon. In particular, an increase of the sphere radius leads to a larger transient growth, with stronger effects in the vicinity of the stagnation point. In the range of interesting values of the Reynolds number that are typical of wind tunnel tests and flight conditions for a sphere, no significant role is played by the wall-normal and streamwise velocity components at the outlet. © 2006 Cambridge University Press.

Beschreibung: The oscillatory convection for a real system of fluids under the joint action of buoyancy and thermocapillary effect is investigated. The nonlinear development of the oscillatory instability is studied. Two types of boundary condition are considered. In the case of periodic boundary conditions, regimes of either travelling waves or standing oscillations have been found, depending on the period of the flow. For rigid heat-insulated lateral walls, various types of symmetric and asymmetric standing waves are obtained. Transitions between the motions with different spatial structures are investigated. It is shown that in the case of rigid heat-insulated lateral walls the period of oscillations changes non-monotonically. The nonlinear oscillations exist in a finite interval of the Grashof number values, between the stability regions of a quiescent state and stationary convection. © 2006 Cambridge University Press.

Beschreibung: The formation of vortex rings generated by an impulsively started jet in the presence of uniform background co-flow is studied experimentally to extend previous results. A piston-cylinder mechanism is used to generate the vortex rings and the co-flow is supplied through a transparent shroud surrounding the cylinder. Digital particle image velocimetry (DPIV) is used to measure the development of the ring vorticity and its eventual pinch off from the generating jet for ratios of the co-flow to jet velocity (Rv in the range 0 - 0.85. The formation time scale for the ring to obtain maximal circulation and pinch off from the generating jet, called the formation number (F), is determined as a function of Rv using DPIV measurements of circulation and a generalized definition of dimensionless discharge time or 'formation time'. Both simultaneous initiation and delayed initiation of co-flow are considered. In all cases, a sharp drop in F (taking place over a range of 0.1 in Rv) is centred around a critical velocity ratio (Rcrit). As the initiation of co-flow was delayed, the magnitude of the drop in F and the value of Rcrit decreased. A kinematic model based on the relative velocities of the forming ring and jet shear layer is formulated and correctly predicts vortex ring pinch off for Rv 〉 Rcrit. The results of the model indicate the reduction in F at large Rv is directly related to the increased convective velocity provided to the ring by the co-flow. © 2006 Cambridge University Press.

Beschreibung: Wide-field particle image velocimetry measurements were performed in a Mach 2 turbulent boundary layer to study the characteristics of large-scale coherence at two wall-normal locations (y/δ = 0.16 and 0.45). Instantaneous velocity fields at both locations indicate the presence of elongated streamwise strips of uniform low- and high-speed fluid (length 〉 8δ). These long coherent structures exhibit strong similarities to those that have been found in incompressible boundary layers, which suggests an underlying similarity between the incompressible and supersonic regimes. Two-point correlations of streamwise velocity fluctuations show coherence over a longer streamwise distance at y/δ = 0.45 than at y/δ = 0.16, which indicates an increasing trend in the streamwise length scale with wall-normal location. The spanwise scale of these uniform-velocity strips increases with increasing wall-normal distance as found in subsonic boundary layers. The large-scale coherence observed is consistent with the very large-scale motion (VLSM) model proposed by Kim & Adrian (Phys. Fluids, vol. 11, 1999, p. 417) for incompressible boundary layers. © 2006 Cambridge University Press.

Beschreibung: The high-Reynolds-number axisymmetric wake behind a disk has been studied from x/D = 30 to x/D = 150 using the proper orthogonal decomposition (POD) applied to measurements of the streamwise fluctuating velocity. It was found that the energetic structure of the axisymmetric wake can very efficiently be described in terms of POD modes. The first radial (or lowest-order) POD mode has 56 % of the energy. Two major features dominate the eigenspectra, manifested as two major peaks. The first peak is an azimuthal mode-1 peak at a frequency corresponding to the Strouhal number of the near wake. The second is an azimuthal mode-2 peak at near-zero frequency. The mode-1 peak dies out faster than the mode-2 peak, so that the far wake is dominated by the latter. This evolution from azimuthal mode-1 dominance in the near wake to mode-2 dominance in the far wake corresponds closely to the approach to equilibrium similarity. Once azimuthal mode-2 becomes equally important as azimuthal mode-1 (after x/D = 30 or x/θ = 110, the ratio of turbulence intensity to centreline velocity deficit is constant, the mean deficit and turbulence intensity collapse in similarity variables, and the wake grows as x1/3. © 2006 Cambridge University Press.

Beschreibung: The receptivity phenomenon, which is the process of environmental disturbances initially entering the boundary layers and generating disturbance waves, is one of the important but not well understood mechanisms involving laminar-turbulent transition of hypersonic flows. This paper presents a numerical simulation study of the receptivity to weak free-stream fast acoustic waves for a Mach 7.99 axisymmetric flow over a 7° half-angle blunt cone. In hypersonic boundary-layer flow over a blunt cone, the process of receptivity to free-stream disturbances is altered considerably by the presence of a bow shock and an entropy layer. In the present study, both steady and unsteady flow solutions are obtained by computing the full Navier-Stokes equations with a fifth-order shock-fitting finite-difference scheme, which is able to account for the effects of bow-shock/free-stream-disturbance interaction accurately. The current numerical results for the steady base flow are compared with previous experimental and numerical results. In addition, a normal-mode linear stability analysis is used to identify the main components of boundary-layer disturbances generated by forcing free-stream fast acoustic waves. It is found that neither the first mode nor the second-mode instability waves are excited by free-stream fast acoustic waves in the early region along the cone surface, although the Mack modes can be unstable there. Instead, the second mode is excited downstream of the second-mode Branch I neutral stability point. The delay of the second-mode excitation is because the hypersonic boundary-layer receptivity is governed by a two-step resonant interaction process: (i) resonant interactions between the forcing waves and a stable boundary-layer wave mode I near the leading-edge region; and (ii) resonant interactions between the induced stable mode I and the unstable second Mack mode downstream. The same receptivity mechanism also explains the results that no first Mack mode components are generated by the current receptivity process because there is no resonant interaction between fast acoustic waves and the first Mack mode. © 2006 Cambridge University Press.

Beschreibung: We present a parametric experimental study of convective electrokinetic instability (EKI) in an isotropically etched, cross-shaped microchannel using quantitative epifluorescence imaging. The base state is a three-inlet, one-outlet electrokinetic focusing flow configuration where the centre sample stream and sheath flows have mismatched ionic conductivities. Electrokinetic flows with conductivity gradients become unstable when the electroviscous stretching and folding of conductivity interfaces grows faster than the dissipative effect of molecular diffusion. Scalar images, critical applied fields required for instability, and temporal and spatial scalar energy are presented for flows with a wide range of applied d.c. electric field and centre-to-sheath conductivity ratios. These parameters impose variations of the electric Rayleigh number across four orders of magnitude. We introduce a scaling for charge density in the bulk fluid as a function of local maximum conductivity gradients in the flow. This scaling shows that the flow becomes unstable at a critical electric Rayleigh number (Rae,ℓ = 205) and applies to a wide range of applied field and centre-to-sheath conductivity ratios. This work is relevant to on-chip electrokinetic flows with conductivity gradients such as field amplified sample stacking, flow at the intersections of multi-dimensional assays, electrokinetic control and separation of sample streams with poorly specified chemistry, and low-Reynolds number micromixing. © 2006 Cambridge University Press.

Beschreibung: This paper presents data on turbulent-spot propagation in the hypersonic boundary-layer flow over a blunted cylindrical body. Data are based on the measurement of time-dependent surface heat transfer rates using gauges positioned as arrays in either the axial or transverse directions. These are used to provide data on individual spots, including sectional profiles, characteristic spot planform geometries, propagation speeds, growth rates and some information on the development of an internal thermal cell structure and corresponding thermal streaks in the base or calm region of the spot. © 2006 Cambridge University Press.

Beschreibung: Time-averaged two-point measurements of the fluctuating wall pressure and instantaneous measurements of the full fluctuating wall pressure field were performed in incompressible turbulent impinging jets with nozzle-to-plate spacings of 2 and 4 diameters, Reynolds numbers of 23 300, and Mach numbers of 0.03. An azimuthal Fourier decomposition of the fluctuating wall pressure revealed that the fluctuations in the stagnation region were dominated by azimuthal mode 1 to 3, and the contributions from these modes were larger for the jet with H/D=4. Azimuthal modes 0 and 1 made significant contributions to the pressure fluctuations in the wall jet region of both jets, indicating that the large-scale ring structures formed in the jet shear-layer play a prominent role in this region. The contributions from modes 0 and 1 in the wall jet were smaller for the jet with H/D=4 indicating that the ring structures play a less prominent role in the wall jet region as the nozzle-to-plate distance increased. A wavelet analysis of the transient fluctuations indicated that azimuthal mode 1 had dominant high-frequency and low-frequency components, while azimuthal mode 0 had only the higher-frequency oscillations. The higher-frequency components of azimuthal modes 0 and 1 occurred in both the stagnation and the wall jet regions and are attributed to the asymmetric evolution of the ring structures in the jet. The low-frequency oscillations were primarily associated with azimuthal mode 1 and were evident only in the stagnation region. These oscillations became more prominent as the nozzle-to-plate distance was increased. © 2006 Cambridge University Press.

Beschreibung: The linear stability of the Stokes layers generated between a pair of synchronously oscillating parallel plates is investigated. The disturbance equations were studied using Floquet theory and pseudospectral numerical methods used to solve the resulting system. Neutral curves for an extensive range of plate separations were obtained and when the plate separation is large compared to the Stokes layer thickness the linear stability properties of the Stokes layer in a semi-infinite fluid were recovered. A detailed analysis of the damping rates of disturbances to the basic flow provides a plausible explanation of why several previous studies of the problem have failed to detect any linear instability of the flow. To compare more faithfully with experimental work the techniques used for the channel problem were modified to allow the determination of neutral curves for axisymmetric disturbances to purely oscillatory flow in a circular pipe. Critical Reynolds numbers for the pipe flow tended to be smaller than their counterparts for the channel case but the smallest critical value was still almost twice the experimentally reported result. © 2006 Cambridge University Press.

Beschreibung: The high-Reynolds-number axisymmetric wake behind a disk has been studied for 10 ≤ x/D ≤ 150 (36 ≤ x/θ ≤ 552) using a rake of 15 hot wires. The disk had a diameter of 20 mm, and the Reynolds number based on the free-stream velocity was 26 400. Mean velocity profiles, root-mean-square profiles, and power spectra are presented. By using regression techniques to fit the velocity profiles it was possible to obtain accurate velocity centreline deficits and transverse length scales to even the last downstream position. Beyond the initial region which extends to x/D=30, the data are in excellent agreement with the high-Reynolds-number equilibrium similarity solution. © 2006 Cambridge University Press.

Beschreibung: We consider the release from a point source of relatively heavy fluid into a porous saturated medium above an impermeable slope. We consider the case where the volume of the resulting gravity current increases with time like tα and show that for α 〈 3 at short times the current spreads axisymmetrically, with radius r ∼ t(α+1)/4, while at long times it spreads predominantly downslope. In particular, for long times the downslope position of the current scales like t while the current extends a distance tα/3 across the slope. For α 〉 3, this situation is reversed with spreading occurring predominantly downslope for short times. The governing equations admit similarity solutions whose scaling behaviour we determine, with the full similarity form being evaluated by numerical computations of the governing partial differential equation. We find that the results of these analyses are in good quantitative agreement with a series of laboratory experiments. Finally, we discuss the implications of our work for the sequestration of carbon dioxide in aquifers with a sloping, impermeable cap. © 2006 Cambridge University Press.

Beschreibung: Valveless pumping can be achieved through the periodic compression of a pliant tube asymmetrically from its interfaces to different tubing or reservoirs. A mismatch of characteristic impedance between the flow channels is necessary for creating wave reflection sites. Previous experimental studies of the behaviour of such a pump were continued in order to demonstrate the wave mechanics necessary for the build-up of pressure and net flow. Specific measurements of the transient and resonant properties were used to relate the bulk responses to the pump mechanics. Ultrasound imaging through the tube wall allowed visualization of the wall motion concurrently with pressure and flow measurements. For analysis, a one-dimensional wave model was constructed which predicted many of the characteristics exhibited by the experiments. © 2006 Cambridge University Press.

Beschreibung: The surface flow, pressure distributions, and vortex-shedding properties of the circular cylinder flow in the subcritical regime modulated by a self-excited vibrating rod were experimentally studied in a closed-circuit wind tunnel for Reynolds numbers between 2 × 104 and 1.8 × 105. The principle of galloping was employed to induce self-vibration of an elastic rod. The natural (uncontrolled) boundary layer showed significantly different flow patterns in two subranges of Reynolds number: ReD 〈 0.55 × 105 and ReD 〉 0.55 × 105. In the low-Reynolds-number subrange, the laminar separation mode, which was similar to the result reported by previous investigators, was observed. While in the high-Reynolds-number subrange, the separation bubble mode, which was rarely discussed previously, was found. The term separation bubble mode was used to denote the existence of secondary recirculation bubbles induced by the reattachment of separated boundary layers. The surface flow modulated by the vibrating rod presented complex variations in these two subranges. Depending on the position of the control rod, the separation bubble mode or the turbulent separation mode might appear because of the increase of the turbulence kinetic energy. Modulating the surface flow patterns could significantly influence the surface pressure distributions on the main cylinder and the vortex shedding in the wake. Forcing the boundary layer at the positions upstream of the natural separation point would drastically lower the values of the minimum pressure coefficient and the base pressure coefficient, and therefore increase the lift. The drag coefficient, however, would not be apparently decreased. The frequency of the vortex shedding in the wake could 'lock' to the rod vibration frequency if the position of the vibrating rod was properly adjusted. © 2006 Cambridge University Press.

Beschreibung: The interactions of vortices shed from two coaxially joined cylinders with a diameter ratio of 0.51 have been studied in a water channel, at Reynolds numbers, based on the large cylinder diameter, between 63 and 1100. Spectral and wavelet analyses of streamwise velocity measurements have identified the formation of three distinct spanwise vortex-shedding cells away from the far ends of the two cylinders, including a low-frequency cell, which appeared in a cyclic manner near the step and behind the large cylinder. Analysis of flow-visualization images has identified two distinct types of vortex connection at cell boundaries: some vortices in a cell of lower frequency connected across the boundary to counterparts in the cell of higher frequency, while others formed a half-loop to connect to a vortex shed from the opposite side of the cylinder in the same cell. Additional cross-boundary vortex connections balanced the total vortex strengths. The interactions of two types of streamwise vortices, identified as edge vortices and junction vortices, with spanwise vortices have also been documented. © 2006 Cambridge University Press.

Beschreibung: A framework is developed to describe the two-point statistics of potential vorticity in rotating and stratified turbulence as described by the Boussinesq equations. The Kármán-Howarth equation for the dynamics of the two-point correlation function of potential vorticity reveals the possibility of inertial-range dynamics in certain regimes in the Rossby, Froude, Prandtl and Reynolds number parameters. For the case of large Rossby and Froude numbers, and for the case of quasi-geostrophic dynamics, a linear scaling law with 2/3 prefactor is derived for the third-order mixed correlation between potential vorticity and velocity, a result that is analogous to the Kolmogorov 4/5-law for the third-order velocity structure function in turbulence theory. © 2006 Cambridge University Press.