ALBERT

Description: The stability of steady isothermal flow of one-dimensional Newtonian fibres is considered. Bifurcation theory yields a stable supercritical Hopf bifurcation, with frequency decreasing for increasing winder speeds near the critical winder speed. A new Chebyshev expansion procedure is used with time-marching to obtain accurate numerical solutions valid far from the critical point. Our numerical solution agrees well with our analytical solution near the critical winder speed, but differs significantly from those of previous numerical models. There is qualitative agreement with a previous isothermal experiment for oscillation amplitude but not for oscillation frequency. These comparisons are discussed. © 1984, Cambridge University Press 1984. All rights reserved.

Description: A class of compressible laminar boundary-layer flows subject to adverse pressure gradients of different magnitude is studied using a finite-element—differential method in which the assumed solutions are represented by classical cubic spline functions. The numerical integration process for the reduced initial-value problem has been carried out directly to at least one integration step upstream of the separation point, and very accurate numerical results have been obtained for a large number of integration steps extremely close to separation. The skin-friction and heat-transfer coefficients for nearly zero-heat-transfer, cooled-wall and heated-wall cases, computed under the assumption of constant Prandtl number Pr = 1.0 as well as Pr = 0.72, have clearly exhibited the same distinctive behaviour near separation. It is deduced that Buckmaster's series expansions for the solution near separation, derived on the assumptions of cooled wall and Pr — 1.0, are valid for all the cases considered. By matching the numerical results with Buckmaster's expansions, accurate distributions of skin friction and heat transfer have been obtained up to the separation point. Moreover, the importance of Prandtl number on the solution is evidenced from the numerical results presented. © 1984, Cambridge University Press 1984. All rights reserved.

Description: A linearized potential-flow analysis is presented for predicting the unsteady airloads produced by the vibrations of turbomachinery blades operating at transonic Mach numbers. The unsteady aerodynamic model includes the effects of blade geometry, non-zero mean-pressure variation across the blade row, high-frequency blade motion, and shock motion within the framework of a linearized frequency-domain formulation. The unsteady equations are solved using an implicit least-squares finite-difference approximation which is applicable on arbitrary grids. A numerical solution for the entire unsteady flow field is determined by matching a solution determined on a rectilinear-type cascade mesh, which covers an extended blade-passage region, to a solution determined on a detailed polar-type local mesh, which covers and extends well beyond the supersonic region(s) adjacent to a blade surface. Results are presented for cascades of double-circular-arc and flat-plate blades to demonstrate the unsteady analysis and to partially illustrate the effects of blade geometry, inlet Mach number, blade-vibration frequency and shock motion on unsteady response. © 1984, Cambridge University Press 1984. All rights reserved.

Description: This paper describes the results of experiments conducted on a circular jet simultaneously excited by two different acoustic tones. By varying the phase between two signals at harmonically related frequencies, control can be exercised on the process of harmonic generation-sometimes the process being virtually destroyed. This is shown to be so for both harmonic and subharmonic generation, but the latter is more difficult to control. © 1984, Cambridge University Press 1984. All rights reserved.

Description: We present experimental results on the modified Stokes force F exerted on a sphere in magnetic levitation whose position is kept fixed by an optical feedback system. A Newtonian liquid moves at a constant velocity U relative to the sphere. We consider the motion in two different situations. (i) When the sphere approaches a wall perpendicular to U, the increase in IFl due to lubrication agrees quantitatively with theoretical results such as those of Brenner (1961) and Maude (1961), obtained neglecting the unsteadiness of the flow field. (ii) In the complementary situation of a sphere moving along the axis of a cylindrical tube, our results expressed as a function of the eccentricity of the trajectory and of the ratio of the two radii confirm and extend previous theoretical analyses. They show in particular the existence of a minimum of |F| away from the axis of the cylinder and a sharp increase in | F| when the sphere approaches the sidewall. By comparing with the results for a sphere moving parallel to a flat wall, we analyse the effect of the curvature of the cylindrical tube. © 1984, Cambridge University Press. All rights reserved.

Description: The transition from diffusion-dominated to inertia-dominated behaviour in the transport of condensable heavy molecules carried in a continuum subsonic He jet that impinges on a solid surface is studied experimentally. The Stokes number S, or ratio between the heavy-molecule relaxation time and the fluid-dynamic time, is varied in the interval 0 ≲S ≲ 1 by changing the jet Mach number at a constant value of the Reynolds number. Although the heavy species departs considerably from equilibrium at all but the smallest values of S, the helium jet is always near equilibrium conditions. At values of S of order unity the observed rate of deposition at the stagnation point asymptotes to a value some six times greater than in the diffusion region (where S →0), implying that the process is governed by the large inertia of the heavy species, very much like in aerosol impactors. As a result, it is argued that the concept of pressure diffusion is unsuitable to explain the observed behaviour. An approximate theoretical description of the transport process is given for the region S ≪ 1 where the kinetic problem is amenable to a hydrodynamic treatment. Finally, the analogy with the inertia-dominated behaviour of aerosols is used to assess the relative merits of various aerodynamics schemes aiming at separating isotopes. © 1984, Cambridge University Press. All rights reserved.

Description: The ionization relaxation and radiative cooling of weakly unsteady shock waves in krypton and xenon is examined. We find that, besides radiation energy loss, the shock-tube boundary layers and shock attenuation strongly influence the radiative-cooling region. Calculations taking these effects into account are in excellent agreement with experimental values of electron densities. The contribution of line radiation to total radiation energy loss is obtained, and amounts to about 54% at temperatures of 10000 K in krypton. For xenon, first comparisons indicate a similar result. © 1984, Cambridge University Press 1984. All rights reserved.

Description: The vortex loop observed in flow-visualization studies of boundary-layer transition has been investigated by mapping the instantaneous velocity and vorticity fields. All three velocity components have been measured with hot-film anemometers at numerous grid points in a measuring volume centred on the location where the vortex loop appears in flow-visualizaton studies. The instantaneous vorticity field has been computed from the velocity field, and the vortex loop is revealed in the longitudinal component of vorticity. The loop propagates downstream at approximately the primary disturbance wavespeed. The fluid in the outer part of the boundary layer travels faster, and flows over the loop. This forms the inflexional high-shear layer, which breaks down into the hairpin vortices. The magnitude of the vorticity in the high-shear layer is actually about three times larger than that in the loop. These two regions of vorticity are distinguished by the direction of the instantaneous vorticity vectors, i.e. the vectors in the high-shear layer run in the spanwise direction, while the vectors in the vortex loop run primarily in the downstream direction. This also explains why the loop cannot be detected with simple Əu/Əy measurements. © 1984, Cambridge University Press. All rights reserved.

Description: This paper we investigate some effects of a boundary forcing on 2-dimensional cellular patterns in instabilities above threshold. Boundary forcing is modelled as an inhomogeneous boundary condition on the slowly varying amplitude A, i.e. A = λ eiϕ0on boundaries. The relevant range is A—0(ε1/2), where e is the relative distance to the linear-instability threshold. A wavenumber-selection mechanism then occurs, resulting in a band of selected wavenumbers of width proportional to λ A. For large values of λε-1/2 it is shown that no stationary solution exists outside the band of Eckhaus-stable wavenumbers (Eckhaus 1965). For finite geometries of size L, a nonlinear analogue of 'quantization' of modes is investigated. The amplitude equation (equivalent to a space-dependent Ginzburg-Landau model) is analysed by an expansion in powers of exp (—L/£), where £ is the coherence length. The range A = 0(e) is also investigated. A correction to previous theories of wavenumber selection through boundaries (Cross, Daniels, Hohenberg & Siggia 1983a; Pomeau & Zaleski 1981) is calculated. The latter results are general and assume only the existence of a higher-order stationary amplitude equation, which is recast in a form consistent with its boundary conditions. © 1984, Cambridge University Press. All rights reserved.

Description: This paper reports an experimental study of a meandering water stream upon an inclined smooth hydrophobic surface. It was found that the sinuosity (ratio of the total stream length to the length of the projection of the stream on the line of maximum slope of the surface) increases with both increasing discharge rate and surface slope. It was observed that the meandering pattern is not always stable: once the discharge rate exceeds the upper critical value, the meandering pattern becomes unstable, whereas, when the discharge rate is smaller than the lower critical value, the water stream becomes discontinuous, and normally forms droplets, sliding successively down the sloping surface. It was found that, with increasing surface slope, the upper critical value decreases exponentially, while the lower critical value decreases only gradually. It was found that, when a system of stable meanders is formed on the surface, the meander loops are smoothly curved, swinging gradually from left-handed to right-handed deflections from the line of fastest descent, and vice versa, with an almpst constant amplitude and wavelength. The stable meandering pattern migrates gradually down the sloping surface. The observations showed that the central axis of the meandering stream does not coincide with the locus of the highest points of the stream, the highest points being displaced towards the outside of each bend: the cross-sectional profile of the stream is thus usually asymmetrical. It was found that the cross-sectional area of the stream varies cyclically, with one increase and one decrease associated with each bend of the stream. This cyclic variation is repeated many times along the length of the stream, with each point of maximum cross-sectional area located close to a bend. A secondary reversing spiral flow was observed in the stream, and it was found that the sense of rotation of the flow is reversed at each bend. A plausible mechanism of these stream meanders is proposed on the basis of the present results, involving the existence of hysteresis of the contact angle between water and Plexiglas, the presence of asymmetrical surface-tension forces on the stream, and the acceleration and deceleration of the stream as it swings from loop to loop. © 1984, Cambridge University Press. All rights reserved.

Description: The hydrodynamics and heat/mass transport associated with condensation on a moving drop have been investigated for the intermediate Reynolds-number range of drop motion (Re = 0(100)). The drop environment is a mixture of saturated vapour and a non-condensable. The formulation entails a simultaneous solution of the quasi-steady elliptic partial differential equations that describe the flow field and transport in the gaseous phase, and the motion inside the liquid drop. The heat transport inside the drop is treated as a transient process. Results are reported for the interfacial velocities, drag, external and internal flow structure, heat flux, drop growth rate and temperature—time history inside the drop. The results obtained here have been compared with experimental data where available, and these show excellent agreement. The results reveal several novel features. The surface-shear stress increases with condensation. The pressure level in the rear of the drop is higher. As a consequence, the friction drag is higher and the pressure drag is lower. The total drag coefficient increases with condensation rate for small values of drop size or temperature differential, and it decreases for large values of these parameters. The volume of the separated-flow region in the rear of the drop decreases with condensation. At very high rates of condensation, the recirculatory wake is completely suppressed. Condensation also delays the appearance of the weak secondary internal vortex motion in the drop. The heat and mass fluxes are significantly affected by the presence of the non-condensable in the gaseous phase and by the circulation inside the drop. © 1984, Cambridge University Press. All rights reserved.

Description: Some new exact relations are derived between integral properties of a progressive irrotational gravity wave of finite amplitude in deep water. In particular it is shown that the Eulerian-mean angular momentum AEis directly proportional to the Lagrangian T—V, through the relation Ae= 2C(T-V)/g, where c is the phase speed and g denotes the acceleration due to gravity. Moreover, for waves of constant length, the differential relation dAB= 2(3T-V)dc/g also holds. In a wave of limiting steepness it was shown previously that the level of action yais very nearly equal to the crest level ymax-This is further discussed, and is shown to be probably a numerical coincidence. © 1984, Cambridge University Press. All rights reserved.

Description: Turbulent spots formed artificially in a Blasius boundary layer have been investigated over a finite width extending across the plane of symmetry of the spots. Hot wires were used to measure the local mean and fluctuating parts of the downstream and spanwise velocity components, and the third component was computed. The results are presented in contour diagrams, and are compared with previous published work. The values of energy thickness in the spots are computed from the contours of downstream velocity. The spots are found to consist of an upper part containing most of the turbulence, moving over a lower layer whose contribution to the energy thickness is small. When, near the rear of the spot, the energy thickness decreases to the value in Blasius flow, the two parts recombine, and the flow slowly regains the Blasius velocity profile. The spots grow by entrainment of laminar fluid, and the physical principles governing this process are discussed. © 1984, Cambridge University Press 1984. All rights reserved.

Description: We consider the motion of a sphere or a slender body in the presence of a plane fluid-fluid interface with an arbitrary viscosity ratio, when the fluids undergo a linear undisturbed flow. First, the hydrodynamic relationships for the force and torque on the particle at rest in the undisturbed flow field are determined, using the method of reflections, from the spatial distribution of Stokeslets, rotlets and higher-order singularities in Stokes flow. These fundamental relationships are then applied, in combination with the corresponding solutions obtained in earlier publications for the translation and rotation through a quiescent fluid, to determine the motion of a neutrally buoyant particle freely suspended in the flow. The theory yields general trajectory equations for an arbitrary viscosity ratio which are in good agreement with both exact-solution results and experimental data for sphere motions near a rigid plane wall. Among the most interesting results for motion of slender bodies is the generalization of the Jeffrey orbit equations for linear simple shear flow. © 1984, Cambridge University Press 1984. All rights reserved.

Description: Longitudinal and transverse components of the velocity were simultaneously measured for various vertical locations at 20 off-centreline positions in turbulent spots artificially generated in a zero-pressure-gradient laminar boundary layer. Global ensemble-averaged velocity diagrams and vertical vorticity contours were computed in similarity coordinates ξ = (x—x0)/(U∞ (t-t0)) and ξ =z /(U∞(t—t0)) for different heights η = y/δ above the plate. This global averaging technique inadequately describes the spot, which is not a single large vortex structure. A discriminative averaging technique was developed to construct a statistically most-probable spot with sufficient resolution to include some of the largest substructures detected in visual studies. Four eddies were identified in vertical slices of the central region of the spot, while several rows appeared in the plan view. These features of the velocity and vorticity contours of the statistically most-probable spot exhibit similarities with structures observed in flow visualizations. © 1984, Cambridge University Press. All rights reserved.

Description: This paper extends previous theoretical work on inextensible sails in two ways. First, the asymptotic expansion of sail camber in terms of the small angle of attack a is continued to include terms of order a3because only at this order can one obtain information about the longitudinal static stability of a sail aerofoil. Secondly, to describe aerofoils such as those found in pterodactyl or bat wings, we also consider pretensioned membranes which acquire camber by stretching the surface material, or bending the supporting structure. Approximate formulae are derived for the aerodynamic coefficients in the limits of large and small tension, and the effect of sail and structural flexibility on these coefficients is discussed. © 1984, Cambridge University Press. All rights reserved.

Description: Turbulent airflow over a Stokes water-wave train of small amplitude is studied numerically based on the two-equation closure model of Saffman & Wilcox (1974) together with appropriate boundary conditions on the wave surface. The model calculates, instead of assuming, the viscous sublayer flow, and it is found that the energy transfer between wind and waves depends significantly on the flow being hydraulically rough, transitional or smooth. Systematic computations have yielded a simple approximate formula for the fractional rate of growth per radian, with δi= 0.04 for transitional or smooth flow and δi= 0.06 for rough flow, where p is density of airwthat of water, UAwind speed at one wavelength height and c the wave phase velocity. This formula is in good agreement with most existing data from field experiments and from wave-tank experiments. In the case of waves travelling against wind, the corresponding values are δt— —0.024 for transitional and smooth flow, and δt= —0.04 for rough flow. © 1984, Cambridge University Press. All rights reserved.

Description: This paper involves a numerical simulation of the final stages of transition to turbulence in plane channel flow at a Reynolds number of 1500. Three-dimensional incompressible Navier-Stokes equations are numerically integrated to obtain the time evolution of two-and three-dimensional finite-amplitude disturbances. Computations are performed on the CYBER-203 vector processor for a 32 x 51 x 32 grid. Solutions indicate the existence of structures similar to those observed in the laboratory and characteristic of the various stages of transition that lead to final breakdown. In particular, evidence points to the formation of a A-shaped vortex and the subsequent system of horsehoe vortices inclined to the main flow direction as the primary elements of transition. Details of the resulting flow field after breakdown indicate the evolution of streaklike formations found in turbulent flows. Although the flow field does approach a steady state (turbulent channel flow), the introduction of subgrid-scale terms seems necessary to obtain fully developed turbulence statistics. © 1984, Cambridge University Press. All rights reserved.

Description: High-speed schlieren cinéphotography of the firing of a high-energy plasma-jet igniter reveal turbulent structures similar in appearance to laboratory models of thermals or turbulent puffs. Measurements of the growth rates of these features together with those of their impulse and thermal energy confirm this similarity. A simple model based on the entrainment assumption gives a good description of the motion of the element and also of the decay of the internal temperature. © 1984, Cambridge University Press. All rights reserved.

Description: A geometrical condition sufficient for uniqueness in two-dimensional time-periodic linear water-wave problems is derived, and some examples are given. The technique can be seen as a generalization of work by John (1950), who established uniqueness for surface-piercing bodies that have the property that vertical lines down from the free surface do not intersect the body. The paper is in two parts. Part 1 provides a review of current knowledge on the topic of uniqueness, and gives a simple form of John’s proof. Part 2 describes the recent progress, in which the ideas of John’s proof are extended so that uniqueness can be demonstrated for surface-piercing bodies that do not satisfy John’s geometrical criterion. In fact the new technique proves uniqueness for a large class of problems involving floating bodies, submerged bodies and multiple-body systems. However, the present work still does not constitute a general proof of uniqueness for all configurations. © 1984, Cambridge University Press. All rights reserved.

Description: Spectral models for turbulent pressure fluctuations are developed by directly Fourier transforming the integral solution to the Poisson equation for a homogeneous constant-mean-shear flow. The turbulence-turbulence interaction is seen to possess the well-known k-7/3inertial subrange and to dominate the high-wavenumber region. The turbulence-mean-shear contribution is seen to be dominant in the energy-containing range and falls off as k-11/3the inertial subrange. The subrange constants and the mean-square pressure fluctuation are evaluated using a spectral model for the velocity. A spectral analysis of the velocity contamination of a pressure probe is also presented. Results are compared with spectral measurements with a static-pressure probe in the mixing layer of an axisymmetric jet. © 1984, Cambridge University Press. All rights reserved.

Description: Numerical solutions are presented of the governing equations for three plane flows: the laminar free jet; the developing turbulent free jet; and the turbulent impinging jet for different ratios h/b of the nozzle height h above the plate to the nozzle width b. The accuracy of the numerical procedure is demonstrated by comparing the solution of the Navier-Stokes equations for the laminar-flow case with their analytical boundary-layer solution. For turbulent flows these equations are solved after Reynolds averaging. Closure is achieved by a two-equation turbulence model in conjunction with three alternative algebraic expressions for the turbulent stresses. The capabilities of such an approach are illustrated by the extent and consistency of the predictions and the satisfactory agreement of the measurable quantities with the more reliable experimental data in the literature. The limitations of the models employed, evident from their lack of universality, are discussed in the light of their derivation from more complex ‘single-point’ closures. Features of the flows studied of interest include: the near-nozzle behaviour of a ‘finite’ laminar free jet; the potential core and transition regions of a turbulent free jet, along with the fully developed similarity profiles; the enhanced heat-transfer characteristics of impinging jet flows; and the similarity of the developing wall jet after impingement to the standard wall-jet configuration. © 1984, Cambridge University Press. All rights reserved.

Description: Head-on collision of two (KdV) solitary waves at the interface of an inviscid two-fluid system of rigid upper and lower boundaries is investigated by a perturbation method. We obtain the third-order solution and find a dispersive wavetrain trailing behind each emerging solitary wave. The wavetrain is of the same polarity (depression/ elevation) as the main wave. Furthermore, the energy and amplitude of the wave train are decreasing in time as long as it is still attached to the main wave. This implies an increase in energy of the main wave. Up to the third order of accuracy the solitary wave emerging from a head-on collision retains its initial profile save for a phase shift. This phase shift is found to be amplitude dependent to the second order. The transfer of energy from the wavetrain to the main wave explains the slow recovery of the incident profiles in existing numerical results on the head-on collision of two solitary waves at the surface of an infinite channel. © 1984, Cambridge University Press. All rights reserved.

Description: Two-and three-dimensional non-stationary viscous-fluid flows in a plane channel are considered. By means of efficient computational algorithms for direct integration of the incompressible Navier-Stokes equations the evolution of these flows over large time intervals is simulated. Classes of two-and three-dimensional non-stationary flows with stationary integral characteristics (the flow rate, mean pressure gradient, total energy of pulsations etc.) were found. Such flows are called secondary flows. Two-dimensional secondary flows have only qualitative similarity to turbulent flows observed in experiments. Three-dimensional secondary flows agree very well, even quantitatively, with turbulent flows. The principal characteristics of turbulent flows such as drag coefficient, mean-velocity profile, the distributions of the pulsation velocity components and some others are reproduced in three-dimensional secondary flows with good accuracy. © 1984, Cambridge University Press. All rights reserved.

Description: Moderate-amplitude axisymmetric oscillations of charged inviscid drops held together by surface tension are calculated by a multiple-timescale expansion. The corrections to the drop shape and velocity caused by mode coupling at second order in amplitude are predicted for two-, three-and four-lobed motions of drops with net charge up to the Rayleigh limit Qc= 4π1/2. Resonant oscillations between four-and six-lobed motions occur for total charge values near Qr= (32/3π)1/2and are analysed. Both frequency and amplitude modulation of the oscillation are predicted for drop motions starting from general initial deformations. © 1984, Cambridge University Press. All rights reserved.

Description: The process of three-dimensional distortion of previously two-dimensional disturbances was investigated in a rectangular channel. For the first time the three-dimensional structures at the breakdown station of the two-dimensional wave were studied by flow visualization. It was shown that the structures have forms identical with A-shaped vortices in a boundary layer of the flat plate. The spanwise spacing of the A-shaped vortices is quite independent of the mean-flow velocity and of the frequency of artificial disturbances. © 1984, Cambridge University Press. All rights reserved.

Description: We consider the time evolution of a layer of fresh water placed on top of a layer of salt water in a laboratory tank when denser salt water is supplied to a nozzle at the free surface. The inflow is carried out slowly so as to form a pure plume, which at first does not penetrate through the interface. The two basic processes that govern the time evolution of the initially fresh-water layer are the filling-box process (Baines & Turner 1969) and the entrainment through the end of the plume which impinges upon the density interface. A theoretical model that takes these two processes into account is presented, with the numerical solution of the asymptotic state, valid at large times. The asymptotic solution and experiment are in good agreement; the theory describes well the vertical buoyancy profile, the change in buoyancy difference across the interface with time, and the time when the plume begins to penetrate through the interface. The entrainment rate obtained from changes in thickness of the upper layer with time can be expressed as a function of the Froude number. The functional dependence is close to Fr3at small values of Fr, and it approaches a finite limit as Fr increases. The buoyancy flux across the interface, which is non-dimensionalized by the rate of buoyancy input, also changes as a function of Fr, taking a maximum value of 0.168 at Fr = 0.46 and decreasing sharply at larger and smaller Froude numbers. These values agree well with those found from field observations and experiments on the entrainment at the boundary of convectively mixed layers. It is pointed out that some earlier results of Baines (1975) are not consistent with the model presented here. © 1984, Cambridge University Press. All rights reserved.

Description: We use a numerical method that was described in Part 1 (Marcus 1984a) to solve the time-dependent Navier-Stokes equation and boundary conditions that govern Taylor-Couette flow. We compute several stable axisymmetric Taylor-vortex equilibria and several stable non-axisymmetric wavy-vortex flows that correspond to one travelling wave. For each flow we compute the energy, angular momentum, torque, wave speed, energy dissipation rate, enstrophy, and energy and enstrophy spectra. We also plot several 2-dimensional projections of the velocity field. Using the results of the numerical calculations, we conjecture that the travelling waves are a secondary instability caused by the strong radial motion in the outflow boundaries of the Taylor vortices and are not shear instabilities associated with inflection points of the azimuthal flow. We demonstrate numerically that, at the critical Reynolds number where Taylor-vortex flow becomes unstable to wavy-vortex flow, the speed of the travelling wave is equal to the azimuthal angular velocity of the fluid at the centre of the Taylor vortices. For Reynolds numbers larger than the critical value, the travelling waves have their maximum amplitude at the comoving surface, where the comoving surface is defined to be the surface of fluid that has the same azimuthal velocity as the velocity of the travelling wave. We propose a model that explains the numerically discovered fact that both Taylor-vortex flow and the one-travelling-wave flow have exponential energy spectra such that In [E(k)] ∝ k1where k is the Fourier harmonic number in the axial direction. © 1984, Cambridge University Press. All rights reserved.

Description: A study is made of some numerical calculations of two-dimensional and geostrophic turbulent flows. The primary result is that, under a broad range of circumstances, the flow structure has its vorticity concentrated in a small fraction of the spatial domain, and these concentrations typically have lifetimes long compared with the characteristic time for nonlinear interactions in turbulent flow (i.e. an eddy turnaround time). When such vorticity concentrations occur, they tend to assume an axisymmetric shape and persist under passive advection by the large-scale flow, except for relatively rare encounters with other centres of concentration. These structures can arise from random initial conditions without vorticity concentration, evolving in the midst of what has been traditionally characterized as the cascade of isotropic, homogeneous, large-Reynolds-number turbulence: the systematic elongation of isolines of vorticity associated with the transfer of vorticity to smaller scales, eventually to dissipation scales, and the transfer of energy to larger scales. When the vorticity concentrations are a sufficiently dominant component of the total vorticity field, the cascade processes are suppressed. The demonstration of persistent vorticity concentrations on intermediate scales smaller than the scale of the peak of the energy spectrum and larger than the dissipation scales does not invalidate many of the traditional characterizations of two-dimensional and geostrophic turbulence, but I believe it shows them to be substantially incomplete with respect to a fundamental phenomenon in such flows. © 1984, Cambridge University Press. All rights reserved.

Description: Oblique wave groups consist of waves whose straight parallel lines of constant phase are oblique to the straight parallel lines of constant group phase. Numerical solutions for periodic oblique wave groups with envelopes of permanent shape are calculated from the equations for irrotational three-dimensional deep-water motion with nonlinear upper free-surface conditions. Two distinct families of periodic wave groups are found, one in which the waves in each group are in phase with those in all other groups, and the other in which there is a phase difference of π between the waves in consecutive groups. It is shown that some analytical solutions for oblique wave groups calculated from the nonlinear Schrodinger equation are in error because they ignore the resonant forcing of certain harmonics in two dimensions. Particular attention is given to oblique wave groups whose group-to-wave angle is in the neighbourhood of the critical angle tan1√1/2, corresponding to waves on the boundary wedge of the Kelvin ship-wave pattern. © 1984, Cambridge University Press. All rights reserved.

Description: A nonlinear analysis of Bénard-Marangoni convection in a horizontal fluid layer of infinite extent is proposed. The nonlinear equations describing the fields of temperature and velocity are solved by using the Gorkov-Malkus-Veronis technique, which consists of developing the steady solution in terms of a small parameter measuring the deviation from the marginal state. This work generalizes an earlier paper by Sehluter, Lortz & Busse wherein only buoyancy-driven instabilities were handled. In the present work both buoyancy and temperature-dependent surface-tension effects are considered. The band of allowed steady states of convection near the onset of convection is determined as a function of the Marangoni number and the wavenumber. The influence of various dimensionless quantities like Rayleigh, Prandtl and Biot numbers is examined. Supercritical as well as subcritical zones of instability are displayed. It is found that hexagons are allowable flow patterns. © 1984, Cambridge University Press. All rights reserved.

Description: The inviscid compressible instability of columnar-vortex flows to three-dimensional perturbations with large wavenumbers is considered. The sufficient conditions for instability obtained are compared with recently published results for incompressible fluids. © 1984, Cambridge University Press. All rights reserved.

Description: Results are presented of an experimental study on the transition to geostrophic turbulence, and the detailed behaviour within the turbulence regime, in a rotating, laterally heated annulus of fluid. Both spatial and temporal characteristics are examined, and the results are presented in the form of wavenumber and frequency spectra as a function of a single external parameter, the rotation rate. The transition to turbulence proceeds in a sequence of steps from azimuthally symmetric (no waves present) to chaotic flow. The sequence includes doubly periodic flow (amplitude vacillation), semiperiodic flow (structural vacillation), and a transition zone where the characteristics undergo a gradual change to chaotic behaviour. The spectra in the transition zone are characterized by a gradual merging of the background signal with the spectral peaks defining regular wave flow as the rotation rate is increased. Within the geostrophic turbulence regime, the wavenumber spectra are characterized by a broad peak at the baroclinic scale and a power dependence of energy density on wavenumber at the high-wavenumber end of the spectrum. Our data reveal a significant dependence of the slope on the thermal Rossby number, ranging from — 4.8 at Rot = 0.17 to —2.4 at RoT= 0.02. The frequency spectra also show a power dependence of the energy density on frequency at the high-frequency end of the spectrum. We find a nominal —4 power which does not appear to be sensitive to changes in Rossby or Taylor number. © 1984, Cambridge University Press. All rights reserved.

Description: In this paper we apply a formalism introduced in a previous paper to write down a self-consistent set of equations for the functions that describe the near-equilibrium time behaviour of random oceanic internal waves. These equations are based on the direct-interaction approximation. The self-consistent equations are solved numerically (using the Garrett-Munk spectrum as input) and the results are compared to parameters obtained in the weak-interaction approximation (WIA). The formalism points out that an extra parameter that is implicitly vanishingly small in the WIA has a significant effect on decay rates when computed self-consistently. We end by mentioning possible future self-consistent calculations that would improve upon our own. © 1984, Cambridge University Press. All rights reserved.

Description: Local measurements have been carried out in a mercury-nitrogen two-phase flow using the hot-film anemometric technique, in a cylindrical pipe with electrically insulated walls. The flow was turbulent (Re = 63000) and in the bubbly regime (〈a〉 ≈ 0.03). The maximum intensity of the magnetic field was 0.94 T. Processing of the hot-film signal provided in this medium, for the first time, simultaneous quantitative data for the local time-averaged velocity of the liquid-phase turbulent fluctuations, as well as local void fractions. These data were checked against those obtained, for the same conditions, using a double conductivity probe. The latter also provided information on the bubble velocity and average bubble size. Turbulence spectra were also measured. © 1984, Cambridge University Press. All rights reserved.

Description: A cylinder containing liquid with a free surface is subjected to a vertical oscillation of amplitude εg/ω2and frequency 2ω, where ω is within 0(εω) of the natural frequency of a particular (primary) mode in the surface-wave spectrum and 0 〈 ε ≪1. A Lagrangian formulation, which includes terms of second and fourth order in the primary mode and second order in the secondary modes (which are excited by the primary mode), together with the method of averaging, leads to a Hamiltonian system for the slowly varying amplitudes of the primary mode. The fixed points (which correspond to harmonic motions) and phase-plane trajectories and their perturbations due to linear damping are determined. It is shown that ε 〉 δ, where δ is the damping ratio (actual/critical) of the primary mode, is a necessary condition for subharmonic response of that mode. Explicit results are given for the dominant axisymmetric and antisymmetric modes in a circular cylinder. Internal resonance, in which a pair of modes have frequencies that approximate ω and 2ω, is discussed separately, and the fixed points and their stability for the special case ω2= 2ω1are determined. Internal resonance for ω2 = ω1 is discussed in an appendix. © 1984, Cambridge University Press. All rights reserved.

Description: Experiments on shock-wave attenuation in a porous tube have shown that attenuation is a function of distance from the origin and the rate of cross-mass flow per unit area. It is a linear function of distance if the cross-mass flow rate per unit area is held constant. In a tube with solid walls the relationship between attenuation, mass extraction rate per unit area and distance is similar to that in a proous tube. The ratio of the local attenuation to the local cross-mass flow, or mass extraction rate, per unit area is the same linear function of distance in both sets of experiments. The mechanism of attenuation is therefore also identical. © 1984, Cambridge University Press. All rights reserved.

Description: The stability properties of steady two-dimensional solutions describing convection in a horizontal fluid layer heated from below with stress-free boundaries are investigated in the neighbourhood of the critical Rayleigh number. The region of stable convection rolls as a function of the wavenumber a and the Rayleigh number R is bounded towards higher a by the monotonic skewed varicose instability, while towards low wavenumbers stability is limited by the zigzag instability or by the oscillatory skewed varicose instability. Only for a limited range of Prandtl numbers, 0.543 〈 P 〈 ∞, does a finite domain of stability exist. In particular, convection rolls with the critical wavenumber ∝care always unstable. © 1984, Cambridge University Press. All rights reserved.

Description: This report presents a numerical study of the two-dimensional, steady and inviscid flow of a perfect gas past wedge profiles with detached shock waves for free-stream Mach numbers between 1.05 and 1.44. Utilizing the hodograph transformation, a boundary-value problem for the mixed flow is formulated in the hodograph plane and subsequently solved by a finite-difference scheme, iterating respectively between the elliptic and hyperbolic regions. The use of boundary-fitted coordinates and a graded lattice failed to achieve satisfactory results, owing to either convergence difficulties or numerical inaccuracies introduced through the coordinate generator. On the other hand, Cartesian coordinates presented no convergence problems and yielded accurate results. After transforming the solution back to the physical plane, the flow field between the shock wave and the limiting Mach wave is determined. A comparison of the results with experiments and other theories shows a good agreement both for the pressure distribution on the wedge and for the shock stand-off distance. Also of special interest is a quantitative comparison of the results with the small-disturbance theory (solution of the Tricomi equation) and the limiting case of the free-stream Mach number 1. Moreover, an example of the flow past round-nosed wedges, with and without an angle of attack, is treated using the inverse method. © 1984, Cambridge University Press. All rights reserved.

Description: Experiments were conducted to investigate the response of a rigid two-dimensional elastically mounted smooth circular cylinder, with oscillations restricted to a plane normal to the incident flow, as influenced by the vicinity of an identical fixed body placed inside the wake. The static lift and drag coefficients, as well as the vibration amplitude and frequency of the upstream cylinder as functions of relative position of the pair of cylinders are given. Most measurements were carried out under two conditions of free-stream turbulence. Whilst turbulence decreased the magnitude of drag coefficients, it had no appreciable effect on lift coefficients. The forces on the upstream body were found to be influenced by the proximity to the downstream one in a significant way only when the streamwise spacing is less than two diameters. In the dynamic tests, two kinds of instability, namely a vortex-resonance and galloping, were observed, with the latter only occurring when the downstream cylinder was well submerged in the near wake of the upstream one. The vortex-shedding frequency was always found to lock to oscillation frequency. Whereas the vibration characteristics remained essentially unaffected with changing turbulence intensity, the galloping amplitudes were observed to be sensitive to cylinders aspect ratio. A quasi-steady theory was developed to predict the galloping behaviour. © 1984, Cambridge University Press. All rights reserved.

Description: Observations of the flow of a two-layer fluid resulting from the motion of a towed streamlined two-dimensional obstacle are described in some detail. The experiments were designed to further our understanding of the factors governing the nature and magnitude of upstream disturbances in the general flow of stratified fluid over two-dimensional topography, and predictions for arbitrary two-dimensional flows are made from the results of these experiments. In particular, the relationship between uniformly stratified flow and single-layer flow over topography is suggested. Most of the observed features of interest in these experiments are nonlinear in character. Relatively complete descriptions of the observed flows are presented over a wide range of parameter values, and the phenomena observed include upstream undular and turbulent bores, bores with zero energy loss, rarefactions (in which the interface height changes monotonically over a transition region of continuously increasing length), and downstream hydraulic drops and jumps. Their properties are shown to be broadly consistent with predictions from a two-layer hydrostatic model based on continuity and momentum considerations, which employs jump criteria and rarefaction equations where appropriate. Bores occur because of nonlinear steepening when the layer containing the obstacle is thinner than the other, and rarefactions occur when this layer thickness is comparable with or greater than that of the other layer. The speed and amplitude of the upstream bores are governed by nonlinear effects, but their character is determined by a balance between nonlinear steepening, wave dispersion and interfacial friction when the bore is non-turbulent. Experimental evidence is presented for two types of hysteresis or multiple equilibria situations where two different flow states may exist for the same external steady conditions. In the first of these hysteresis types, the upstream flow may be supercritical or consist of an upstream bore state. It is analogous to the type anticipated for single-layer flow by Baines & Davies (1980) and described numerically by Pratt (1983), but it is only found experimentally for part of the expected parameter range, apparently because of interfacial stress effects. The second hysteresis type is new, and involves the presence or absence of a downstream hydraulic drop and following jump. © 1984, Cambridge University Press. All rights reserved.

Description: The stability of the two-dimensional flow induced by the transverse oscillation of a cylinder in a viscous fluid is investigated in both the linear and weakly nonlinear regimes. The major assumption that is made to simplify the problem is that the oscillation frequency is large, in which case an unsteady boundary layer is set up on the cylinder. The basic flow induced by the motion of the cylinder depends on two spatial variables, and is periodic in time. The stability analysis of this flow to axially periodic disturbances therefore leads to a partial differential system dependent on three variables. In the high-frequency limit the linear stability problem can be reduced to a system dependent only on a radial variable and time. Furthermore, the coefficients of the differential operators in this system are periodic in time, so that Floquet theory can be used to reduce this system further to a coupled infinite system of ordinary differential equations together with uncoupled homogeneous boundary conditions. The eigenvalues of this system are found numerically and predict instability entirely consistent with the experiments with circular cylinders performed by Honji (1981). Results are given for cylinders of elliptic cross-section, and it is found that for any given eccentricity the most dangerous configuration is when the cylinder oscillates parallel to its minor axis. Some discussion of nonlinear effects is also given, and for the circular cylinder it is shown that the steady-streaming boundary layer of the basic flow is significantly altered by the instability. © 1984, Cambridge University Press. All rights reserved.

Description: The bottom boundary layer under a progressive water wave is studied using Saffman's turbulence model. Saffman's equations are analysed asymptotically for the case Re≫ 1, where Re is a Reynolds number based on a characteristic magnitude of the orbital velocity and a characteristic orbital displacement. Approximate solutions for the mass-transport velocity at the edge of the boundary layer and for the bottom stress are obtained, and Taylor's formula for the rate of energy dissipation is verified. The theoretical results are found to agree well with observations for sufficiently large Reynolds numbers. © 1984, Cambridge University Press. All rights reserved.

Description: Flows occurring between parallel rotating disks have recently been generalized by Parter & Rajagopal (1984) to include solutions that are not axisymmetric. They prove existence, whereas in the present paper we report, for the first time, numerical results for two cases: (i) rotation about a common axis, and (ii) rotation about distinct axes. Calculations were performed for two values of the Ekman number E = v /d2ω at the relative disk rotations of s= 0.8, s= 0 and s= 0.25, where s= ω2/ω1. © 1984, Cambridge University Press. All rights reserved.

Description: The problem of thermoacoustic heating at the closed end of a tube, in which small gas oscillations are maintained, leads in the case of adiabatic walls, and within the framework of a linear theory of the oscillations and a second order theory of the heating effect, to singular behaviour of the equilibrium temperature at the tube end. Two cases are discussed: one with vanishing viscosity and one with viscosity tending to infinity. The singularities turn out to be similar in character and integrable in both cases. © 1984, Cambridge University Press. All rights reserved.

Description: Experiments have been made on quasi two dimensional sails of small camber and at small incidence. Four excess length ratios have been tested at a Reynolds number of 1.2 × 105. The results for lift, tension, centre of lift, maximum camber and its position, and leading and trailingedge membrane angles have been compared with existing inviscid theories and show poor agreement in general. This is attributed to leading and trailingedge flow separations as indicated by supplementary flow visualization experiments. The optimum incidences in particular are much greater than the theoretical value of 0°. Luffing occurs at slightly negative incidences and appears to be a dynamic instability. The highest lift-to-drag ratio obtained was 16.5 on a membrane with an excess length ratio of 0.03. © 1984, Cambridge University Press. All rights reserved.

Description: The interference of passive thermal fields produced by two (and more) line sources in decaying grid turbulence is studied by using the inference method described by Warhaft (1981) to determine the cross correlation coefficient p between the temperature fluctuations produced by the sources. The evolution of p as a function of downstream distance, for 0.075 〈 d/l 〈 10, where d is the wire spacing and l is the integral lengthscale of the turbulence, is determined for a pair of sources located at various distances from the grid. It is found that p may be positive or negative (thereby enhancing or diminishing the total temperature variance) depending on the line source spacing, their location from the grid and the position of measurement. It is also shown that the effects of a mandoline (Warhaft & Lumley 1978) may be idealized as the interference of thermal fields produced by a number of line sources. Thus new light is shed on the rate of decay of scalar variance dissipation. The thermal field of a single line source is also examined in detail, and these results are compared with other recent measurements. © 1984, Cambridge University Press. All rights reserved.

Description: A stability theory for the steady swirling flow above an infinite rotating disk immersed in an otherwise unbounded rigidly rotating fluid is developed in order to corroborate the various numerical computations considered for this problem. An analysis of the initial value problem for linearized time dependent perturbations on the steady state similarity solutions shows that the disturbance equations have a stable continuum spectrum which, under certain conditions, exhibits only algebraic decay in time. In addition, a numerical analysis on the discrete spectrum shows that there are unstable eigenvalues for certain rotational rates of the disk relative to the fluid at infinity. The results obtained are in good agreement with the large time behaviour of the corresponding solutions of the unsteady similarity equations. © 1984, Cambridge University Press. All rights reserved.

Description: The three dimensional laminar flow past a junction formed by a thin wing protruding normally from a locally flat body surface is considered for wings of finite span but short or long chord. The Reynolds number is taken to be large. The leading edge interaction for a long wing has the triple deck form, with the pressure due to the wing thickness forcing a three dimensional flow response on the body surface alone. The same interaction describes the flow past an entire short wing. Linearized solutions are presented and discussed for long and short two dimensional wings and for certain three dimensional wings of interest. The trailing edge interaction for a long wing is different, however, in that the three dimensional motions on the wing and on the body are coupled together and in general the coupling is nonlinear. Linearized properties are retrieved only for reduced chord lengths. The overall flow structure for a long wing is also discussed, including the traditional three dimensional corner layer, which is shown to have an unusual singular starting form near the leading edge. Qualitative comparisons with experiments are made. © 1984, Cambridge University Press. All rights reserved.

Description: Surface waves travelling in water of finite depth may be scattered by a region of undulating bottom topography. The present study is concerned with the idealized two-dimensional situation in which long-crested surface waves are incident upon a patch of long-crested regular bottom ripples. The principal question examined concerns the amount of incident wave energy that is reflected by the ripple patch. Linear perturbation theory is used to show that the reflection coefficient is both oscillatory in the quotient of the length of the patch and the surface wavelength, and also strongly dependent upon the quotient of the surface and bed wavelengths. In particular, there is a Bragg resonance between the surface waves and the ripples, which is associated with the reflection of incident wave energy. A secondary question concerns the nature of the wave field in the immediate vicinity of the ripple patch. In resonant cases, it is shown how the partially standing wave on the upwave side of the ripple patch gives way, in an almost linear manner over the patch itself, to a progressive transmitted wave on the downwave side. The theoretical predictions are compared with an extensive set of laboratory observations made in a wave tank. Comparisons relating both to the reflection coefficient, and also to the wave field over the ripple patch, are shown to give consistently good agreement. Finally, the implications of the results for sediment transport on an erodible bed are examined. © 1984, Cambridge University Press. All rights reserved.

Description: A linear stability analysis is presented of both hydraulically smooth and transitional flows over an erodible bed. The present theory is developed to account for the formation of ripples. It is essentially an extension of the theory of Richards (1980) to include the effect of viscosity upon the bed wave stability. The theory takes into consideration that the formation of ripples does not depend on flow depths, and that only the bed-load transport is involved in the formation of ripples. The effect of gravity is included in the analysis through the local inclination of the wavy bed surface. The results show that the bed is unstable (i.e. ripples exist) when the grain Reynolds number is less than a certain value. The limiting values of the grain Reynolds number for ripple existence obtained through present analysis are found to be in good agreement with observations. © 1984, Cambridge University Press. All rights reserved.

Description: A thermal creep flow of a slightly rarefied gas induced axisymmetrically around two unequal spheres is studied on the basis of kinetic theory. The spheres, whose thermal conductivities are assumed to be identical with that of the gas, for simplicity, are placed in an infinite expanse of the gas at rest with a uniform temperature gradient at a far distance. Owing to the poor thermal conductivities of the spheres, a tangential temperature gradient is established on the surfaces, and this causes a thermal creep flow in its direction. Consequently, the spheres experience forces in the opposite direction. The flow considered here is a low-Reynolds-number flow in the ordinary fluid dynamic sense (except for the Knudsen layer), and the solution is obtained in terms of bispherical coordinates, with respect to which the system of equations of Stokes type is well developed. The velocity field around the spheres and the forces acting on them are given explicitly. The results show the interesting feature that the smaller sphere experiences the minimum force at a value of the separation distance that depends on the radius ratio. This is in contrast with the case of the axisymmetric motion of two spheres treated by Stimson & Jeffery (1926) in ordinary fluid dynamics at low Reynolds number. The ultimate velocities that the spheres would have under the action of the present thermal force when they are freely suspended are also obtained by utilizing the results for the forces of axisymmetric translational problems of two spheres at low Reynolds number. For a given temperature gradient in the gas, both spheres acquire larger velocities than those they would have if they were alone, and the smaller sphere tends to move faster than the larger one in the direction opposite to the temperature gradient. Also presented, for completeness, are the results for the sphere plane case and for the case of eccentric spheres, the solutions for which are derived as special cases of the preceding problem of two unequal spheres. © 1984, Cambridge University Press. All rights reserved.

Description: A third order regular perturbation solution is developed for laminar flow through a straight pipe that is rotating about an axis not aligned with the pipe axis. Coriolis accelerations produce transverse secondary velocities (similar to those in flow through coiled tubes) and modify the axial velocity profile. The effects of rotation on the velocity fields are shown to depend on two parameters: (i) the product of axial and rotational Reynolds numbers, and (ii) the square of the rotational Reynolds number itself. Even though their strength increases with increases in parameter magnitudes, transverse circulations are qualitatively insensitive to parametric values. The axial profile, on the other hand, can be significantly modified by the rotation; the zeroth order parabolic axial profile can be skewed toward the outside, dimpled in the centre with maximums on either side of the centreline, or both, depending on the values of the two parameters. The modification of the axial velocity profile has important ramifications in the design of heat/mass-transfer devices. © 1984, Cambridge University Press. All rights reserved.

Description: A laboratory experiment is used to study the transient flow in an initially isothermal cavity at temperature T0 following the rapid change of the two vertical endwalls to temperatures T0± ΔT respectively. Individual temperature records are taken and the transient flow in the entire cavity is visualized with the aid of a tracer technique. It is shown that an oscillatory approach to final steady state conditions exists for certain flow regimes, although the form of the oscillatory response is different to that suggested by previous work. It is argued that this oscillatory behaviour is due to the inertia of the flow entering the interior of the cavity from the sidewall boundary layers, which may lead to a form of internal hydraulic jump if the Rayleigh number is sufficiently large. © 1984, Cambridge University Press. All rights reserved.

Description: A large (3.05m long x 0.32m diameter) heated-surface, axisymmetric body, designed for transition research in a 1.22m diameter water tunnel is described. Boundary layer transition data are presented as functions of the heating power supplied to the body and the total concentration of free stream particulate matter in the water. Body surface temperatures range from 0 to 25 °C over the ambient water temperature, and the total heat supplied ranges from 0 to 93.3 kW. Transition arclength Reynolds numbers are found to vary from 4.5x106 for the body operating cold to 3.64x107 for the maximum heat level considered. The concentration of free stream particles is shown to affect the transition Reynolds number. These particles range in diameter from 10 to 70 μm and their concentration ranges from less than 5 to 198 particles per cm3. The decrease in transition Reynolds number due to to the higher concentration of particles is of order 30 %. © 1984, Cambridge University Press. All rights reserved.

Description: A magnetic field is shown to be asymptotically (t→∞) decaying in a flow of finite conductivity with v = Cr, where C = Cξ(t) is a random matrix. The decay is exponential, and its rate does not depend on the conductivity. However, the magnetic energy increases exponentially owing to growth of the domain occupied by the field. The spatial distribution of the magnetic field is a set of thin ropes and (or) layers. © 1984, Cambridge University Press. All rights reserved.

Description: A method for the Monte Carlo simulation, by digital computer, of the evolution of a colliding and coagulating population of suspended particles is described. Collision mechanisms studied both separately and in combination are: Brownian motion of the particles, and laminar and isotropic turbulent shearing motions of the suspending fluid. Steady state distributions are obtained by adding unit size particles at a constant rate and removing all particles once they reach a preset maximum volume. The resulting size distributions are found to agree with those obtained by dimensional analysis (Hunt 1982). © 1984, Cambridge University Press. All rights reserved.

Description: Numerical solutions are presented for steady, axisymmetric, laminar, isothermal, source—sink flow in a rotating cylindrical cavity. These results, which are in good agreement with previously published experimental work, have been used to give a fresh insight into the nature of the flow and to investigate the validity of other theoretical solutions. When the fluid enters the cavity through a central uniform radial source and leaves through an outer sink, it is shown that the flow near the disks can be approximated by two known analytical solutions. If the radial source is replaced by an axial inlet the flow becomes more complex, with a wall jet forming on the downstream disk at sufficiently high flow rates. © 1984, Cambridge University Press. All rights reserved.

Description: The shock wave structure close to a wall in pure argon and binary mixtures of noble gases (argon-helium, xenon—helium) is investigated experimentally and numerically in the shock wave Machnumber range 2.24 ≤ Ms≤ 9.21. Measured and calculated density profiles are compared, and some conclusions are drawn about the accommodation at the wall and the intermolecular force potential. For binary gas mixtures only a few results are presented. Weak argon signals of the electron-beam-luminescence method on the experimental side and the computer time needed for the numerical simulation allowed the treatment of a few parameter combinations only. © 1984, Cambridge University Press. All rights reserved.

Description: Measurements were taken of a developing complex turbulent flow formed by the merging of two far turbulent wakes of equal cylinders. The lower wake only was slightly heated, permitting the use of the conditional-sampling technique to study the interaction of the two wakes in detail. A special four-wire probe (Fabris 1978) enabled simultaneous uncontaminated measurement of all three instantaneous velocity components and temperature. The single-wake data of Fabris (1979) served as a reference. The interaction of the two single turbulent wakes resulted in a striking enhancement of the lateral transfer of heat. Undulations of the thermal interface are significantly wider laterally, but shorter stream wise than in the basic single wake. Lateral velocities of the heated and the unheated intermittent lumps are amplified two-to threefold by the interaction process. Levels of all three components of the kinetic energy of turbulence reach their highest relative maxima in the heated zones as they cross the upper cold wake. These maxima are higher than appropriate conventional or conditional maxima in the single wake. In addition to physical insights into the phenomena of turbulent flow, the data should be useful in refining and validating predictive methods, possibly spurring their further development. © 1984, Cambridge University Press. All rights reserved.

Description: Rotationally symmetric vortex flows between concentric cylinders with the inner one rotating and the outer one at rest have been investigated by numerical simulation and by laser-Doppler velocimetry for an annulus of aspect ratio r—1.05 with a radius ratio η = 0.5066. Stationary states and relaxation towards them were explored close to the transition from the primary flow, which is mirror symmetric with respect to the midplane of the annulus, to a flow which gradually loses the symmetry. Detailed comparison of numerically simulated and measured velocity fields is made. © 1984, Cambridge University Press. All rights reserved.

Description: The establishment of an upstream intrusion of a buoyant fluid discharged into an open-channel flow of uniform density and finite depth is studied numerically using the full Navier-Stokes and diffusion equations. The problem is posed as an initial-boundary-value problem for the laminar motions of a Boussinesq fluid. The equations are integrated numerically by finite-difference methods. The flow patterns produced are controlled by the influx of buoyancy; therefore they are characterized by an inflow densimetric Froude number. A comparison with available experimental data provides favourable support to the theoretical predictions. The critical value of densimetric Froude number of the source of a vertically downward inflow at the free surface of a channel is determined. For densimetric Froude number less than critical, an intrusion is established on the upstream side of the source. Because dissipative mechanisms associated with viscosity take a finite time to intervene, the intrusion starts as an inviscid gravity current with a propagation speed greater than the surface velocity of the stream. The front speed is proportional to the phase velocity of long internal waves. Subsequently, the front decelerates as the interfacial friction, and, if applicable, the boundary frictional forces increase simultaneously with mass entrainment across the interface. The current slows down towards a two-zone equilibrium: (1) the zone encompassing the current behind the frontal zone, where a steady state is approached with respect to the inertial frame of reference; (2) the frontal zone, where the upstream speed approaches a steady speed of frontal advance, albeit small. The upstream intrusion alters the flow pattern of the ambient stream dramatically. A significant feature of both the upstream and downstream currents is the presence of surface convergence with concomitant downwelling near the fronts. As the upstream front decelerates, wavelike disturbances are excited just behind the front at frequencies characteristic of internal waves. As the front approaches steady state, these disturbances appear to be damped. This problem has practical implications in the design of once-through cooling-water systems for power plants taking their cooling water from rivers. © 1984, Cambridge University Press. All rights reserved.

Description: The time-dependent Navier-Stokes equations are integrated numerically for a finite-length concentric-cylinder geometry. The motion is initiated by an impulsive start of the inner cylinder from a state of rest. The transient development of a Taylor-vortex structure is discussed from the standpoint of the amplitude history, the onset time and vortex-front propagation; steady-state results are compared with previously published experimental results. © 1984, Cambridge University Press. All rights reserved.

Description: The interactions of compliant coatings with laminar, transitional and turbulent boundary layers are investigated. A 2 m long flat plate is towed in the range of speeds of 20–140 cm/s in an 18m water channel using a carriage riding on an oil film. Isotropic and anistropic compliant coatings are used to cover about 20% of the working Plexiglas surface. The compliant material used is a viscoelastic plastisol gel produced by heating a mixture of polyvinyl chloride resin, a plasticizer and a stabilizer, and allowing them to gel. The shear modulus of rigidity of the plastisol was varied by changing the percentage of PVC in the mix. Anisotropy is introduced by placing the plastisol on a rubber surface having longitudinal grooves scaled with the low-speed streaks in the turbulent boundary layer. The most pronounced effect of the surface compliance in a turbulent boundary layer is a hydroelastic instability in the form of a spanwise wave structure on the compliant surface. The compliant-surface deformation was measured using a novel remote optical technique. The onset speed of the hydroelastic instability waves depends on the thickness and the modulus of rigidity of the plastisol. Their wavelength, wave speed and amplitude are found to depend on these plastisol parameters as well as on the towing speed. In a laminar boundary layer with freestream speeds of over twice the corresponding onset velocity for the turbulent case, no similar instability is observed. © 1984, Cambridge University Press. All rights reserved.

Description: The problem of transient natural convection in a cavity of aspect ratio A 〈 1 driven by internal buoyancy sources and sinks distributed linearly in the horizontal and uniformly in the vertical is considered. Scaling analysis is used to show that a number of possible transient flow regions are possible, collapsing ultimately onto one of conductive, transitional, or convective steady-state flow regimes. A number of numerical solutions are obtained, and their relationships to the scaling analysis are discussed. © 1984, Archives Européenes de Sociology. All rights reserved.

Description: A horizontal layer is heated from below and cooled from above so that the enclosed single component liquid is frozen in the upper part of the layer. When the imposed temperature difference is such that the Rayleigh number across the liquid is supercritical, there is Benard convection coupled with the dynamics of the solidification interface. An experiment is presented which shows that the interfacial corrugations that result are two dimensional when this solid is thin but hexagonal when the solid is thick. A weakly nonlinear convective instability theory is presented which explains this behaviour, and isolates this ‘purely thermal’ mechanism of pattern selection. Jump behaviour is seen in the liquid layer thickness at the onset of hexagonal convection. © 1984, Cambridge University Press. All rights reserved.

Description: Smith & Townsend's (1982) experimental data on circular Couette flow are re examined in the framework of surface layer similarity theory. Surface layer similarity of horizontally stratified shear flow is shown to have its counterpart in a narrow gap Couette flow between concentric cylinders. Smith & Townsend's data of mean angular momentum and mean velocity profiles in a region near a cylinder lend support to the applicability of Monin Obukhov similarity to circular Couette flow. Only for flows of very high Reynolds numbers is a region of logarithmic variation of mean profiles found close to the cylinder wall. Because of curvature effects on the flow, the mean profiles deviate from the logarithmic profile as distance from the cylinder wall increases. For flows of sufficiently low Reynolds number, but still very high Taylor number, no logarithmic profile seems to exist; instead, profiles in the viscous region and in the outer region are connected to each other by a ‘ free convection (rotation) ’ profile. From Smith & Townsend’s data the velocity field is not observed to follow the prediction of ‘free-convection’ similarity; however, the ‘free-convection’ profile is found in the distribution of mean angular momentum. © 1984, Cambridge University Press. All rights reserved.

Description: A new system of approximating equations is derived for three dimensional steady viscous compressible flows in which a primary flow direction is present, but in which both transverse velocity components can be large. If the transverse velocity vector which corrects a given potential flow is first decomposed into ‘potential’ and ‘ rotational ’ vector components, then a re examination of three dimensional boundary layer theory shows that both components (vϕwϕ) of the potential velocity vector may be assumed small, whereas both components (vψ, wψ) of the rotational velocity vector and hence of the composite secondary flow (v, w) can remain of order unity. An assumption of small scalar potential then leads to a system of governing equations whose characteristic polynomial has a non elliptic form for arbitrary Mach number, without introducing any direct approximation of either streamwise or transverse pressure gradient terms. These non elliptic equations can be solved very economically as a well posed initial/boundary-value problem. Computed results for laminar subsonic flow in a curved square duct confirm the small scalar potential approximation for both large (R/d = 100) and small (R/d = 2) radius of curvature. Other computations for R/d = 2.3 are in good agreement with the measurements of Taylor, Whitelaw & Yianneskis (1980). © 1984, Cambridge University Press. All rights reserved.

Description: In the Lagrangian representation, the problem of advection of a passive marker particle by a prescribed flow defines a dynamical system. For two dimensional incompressible flow this system is Hamiltonian and has just one degree of freedom. For unsteady flow the system is non autonomous and one must in general expect to observe chaotic particle motion. These ideas are developed and subsequently corroborated through the study of a very simple model which provides an idealization of a stirred tank. In the model the fluid is assumed incompressible and inviscid and its motion wholly two-dimensional. The agitator is modelled as a point vortex, which, together with its image(s) in the bounding contour, provides a source of unsteady potential flow. The motion of a particle in this model device is computed numerically. It is shown that the deciding factor for integrable or chaotic particle motion is the nature of the motion of the agitator. With the agitator held at a fixed position, integrable marker motion ensues, and the model device does not stir very efficiently. If, on the other hand, the agitator is moved in such a way that the potential flow is unsteady, chaotic marker motion can be produced. This leads to efficient stirring. A certain case of the general model, for which the differential equations can be integrated for a finite time to produce an explicitly given, invertible, area preserving mapping, is used for the calculations. The paper contains discussion of several issues that put this regime of chaotic advection in perspective relative to both the subject of turbulent advection and to recent work on critical points in the advection patterns of steady laminar flows. Extensions of the model, and the notion of chaotic advection, to more realistic flow situations are commented upon. © 1984, Cambridge University Press. All rights reserved.

Description: Hunt (1982) and Friedlander (1960a, b) used dimensional analysis to derive expressions for the steady state particle size distribution in aerosols and hydrosols. Their results were supported by the Monte Carlo simulation of a non interacting coagulating population of suspended spherical particles developed by Pearson, Valioulis & List (1984). Here the realism of the Monte Carlo simulation is improved by accounting for the modification to the coagulation rate caused by van der Waals', electrostatic and hydrodynamic forces acting between particles. The results indicate that the major hypothesis underlying the dimensional reasoning, that is, collisions between particles of similar size are most important in determining the shape of the particle size distribution, is valid only for shear induced coagulation. It is shown that dimensional analysis cannot, in general, be used to predict equilibrium particle size distributions, mainly because of the strong dependence of the interparticle force on the absolute and relative size of the interacting particles. © 1984, Cambridge University Press. All rights reserved.

Description: An experimental study of a high-Reynolds-number turbulent wake in supersonic flow is performed using space and space–time correlation measurements by means of hot-wire anemometry. The correlations for the streamwise component of the mass-flux fluctuations are given for six stations starting from the trailing edge down to the asymptotic part. The validity of the Taylor's hypothesis is tested, the convection velocities are determined and the downstream evolution of the optimum space–time correlation is given; the frequency spectra are discussed and the integral lengths are analysed. Finally, the three-dimensional isocorrelation surfaces are given at the six test stations and discussed in relation to classical incompressible-flow results. The downstream evolution of the correlations shows that the two sides of the wake are statistically independent near the trailing edge, and a statistical link is gradually established during the wake development. A three-zonal description of wakes generated by fully developed turbulent boundary layers applies as well for mean quantities (velocity, width) as for turbulence correlations. In the near-wake region the overall structure of the isocorrelation curves is close to that observed in turbulent boundary layers in incompressible flows; some low-frequency phenomena are observed in this region. In the latest part of the wake, an asymptotic state is reached for all the correlation characteristics; the final state reached is not explained by the double-roller-eddy model established for lower-Reynolds-number wakes; it appears that wakes generated by fully turbulent boundary layers behave quite differently from initially laminar wakes, and new turbulent structure models for high-Reynolds-number wakes are to be devised. © 1984, Cambridge University Press. All rights reserved.

Description: The particle trajectories of nonlinear capillary waves are derived. The properties of the surface and subsurface particles are presented in exact analytic form, up to and including the highest wave. It is found that the orbits of the steeper waves are neither circular nor closed. For the highest wave, a particle moves through a distance [X] equal to 7.99556λ in one orbit, where λ is the wavelength. It moves with an average horizontal drift velocity U equal to 0.88883c, where c is the phase speed of the wave. In addition, the subsurface particles (at depths nearly three quarters that of the wavelength) move at speeds up to one tenth that of surface particles. © 1984, Cambridge University Press. All rights reserved.

Description: The prevalence in a turbulent mixing layer of dynamical events with a coherent history over substantial times suggests that it is profitable to study in detail entirely deterministic versions of this flow and to attempt to use a simplified synthesis of these solutions as the fundamental representation in a stochastic treatment of the layer. It is proposed that the deterministic representation of the flow be achieved by the embedding of a short hierarchy of motions which are studied in detail, though not exhaustively, in Parts 1, 2 and 3. Part 1 deals with the fundamental or first-order motion, which is the evolution of a layer constrained to be purely two-dimensional. © 1984, Cambridge University Press. All rights reserved.

Description: Statistical studies of hydrodynamic interactions between many particles in a dilute dispersion raise a problem of divergent integrals. This problem arises in particular when calculating the average velocity of sedimentation of solid spheres in a viscous fluid. The solution to this problem was given by Batchelor (1972) for monodisperse suspensions of spheres, on the basis of an assumption of homogeneity. This assumption is removed here. The problem of divergent integrals is reconsidered. The solution treats as successive steps: (a) the average flow due to random statistically independent point forces; (b) the average flow due to random statistically independent solid spheres, without hydrodynamic interactions; (c) the average sedimentation velocity of random, pairwise-dependent solid spheres with hydrodynamic interactions, in a dilute suspension. Considering the case of identical spheres, and assuming homogeneity in any horizontal plane, an expression is obtained for the average sedimentation velocity of a sphere in an otherwise inhomogeneous dispersion. The formula is written in terms of integrals involving probability distributions. It reduces, when the suspension is homogeneous, to a formula obtained by Batchelor. The probability distributions are not calculated in this paper. In order to evaluate numerically the average velocity of sedimentation, a simple expression for the pair distribution function is assumed, and two different concentration profiles are considered, viz. a sinusoidal variation and a step function. In the case of sinusoidal concentration wave, it is found that the contribution of the inhomogeneity is, for small wavelengths, comparable in magnitude to that calculated for a homogeneous dispersion by Batchelor (1972), i.e. —6.55c. The difference in velocity between the crest and trough of the wave is an increasing function of the wavelength. For a step function in concentration, particles at the top of the cloud start to fall faster, this effect being limited to a top layer about 10 radii thick. For future study of the long-term behaviour of a sedimenting cloud, the evolution of the pair distribution function should be added to the present theory. © 1984, Archives Européenes de Sociology. All rights reserved.

Description: The effects of curvature on the fluid dynamics of rapidly rotating gas centrifuges are studied. A governing system of a linear partial differential equation and boundary conditions is derived based on a linearization of the equations for viscous compressible flow. This system reduces to the Onsager pancake model if the effects of curvature are neglected. Approximations to the solutions of the governing equations with and without curvature terms are obtained via a finite-element method. Two examples are considered: first where the flow is driven by a thermal gradient at the wall of the centrifuge, and then for the flow being driven by the introduction and removal of mass through the ends of the centrifuge. Comparisons of the results obtained show that, especially for the second example, the inclusion of the terms due to curvature in the model can have an appreciable effect on the solution. © 1984, Cambridge University Press. All rights reserved.

Description: A theoretical calculation is made of the decay of turbulence energy in the presence of coherent internal gravity waves of various intensities. The wave-turbulence interaction considered is energy production by wave shear. The production term (stress) is calculated by a second-order closure, with temperature fluctuations accounted for by buoyancy subrange theory. This formalism applies to large or small turbulence Froude number, both extremes of which are often encountered in experimental turbulence decay. The theoretical turbulence decay is shown to be a universal function of the wave shear (strain rate) and wave frequency provided that the energy is expressed in terms of the buoyancy wavenumber &B, and time is expressed in terms of N, the Brunt—Vaisala frequency. With the amplitude of wave shear characterized by a gradient Richardson number Ri0, the turbulence decay is found to undergo a sudden transition from rapid decay to a much slower oscillating decay when Ri0is less than about 0.4. The transition time occurs at about t « 2nN-1. If Ri0exceeds 0.8 the rate of decay exceeds that of a neutral fluid. A transition in turbulence decay was observed in experiments by Dickey & Mellor (1980). It might explain the continued presence of turbulence in dynamically stable regions of oceans or atmosphere. The theory is compared in much detail with the Dickey & Mellor experiment. A briefer comparison is also made with other experiments, and with previous calculations of turbulence maintenance by steady mean shear. A simple explanation is proposed of why a transition is observed in a vertical grid experiment but not in horizontal grid experiments. © 1984, Archives Européenes de Sociology. All rights reserved.

Description: The plane steady flow of a grounded ice sheet is analysed under the assumption that the ice behaves as a nonlinearly viscous fluid with a strongly temperature-dependent rate factor. It is supposed that the accumulation/ablation distribution on the (unknown) free surface is prescribed, and that there is a given basal sliding condition connecting the tangential velocity, tangential traction and normal pressure. The basal boundary is defined as the smooth contour which describes the mean topography viewed on the ice-sheet lengthscale, and is assumed to have small slope. The perturbation analysis which reduces the isothermal or constant rate factor equations to an ordinary differential equation for the leading-order profile is now extended with similar success to the non-isothermal problem when the temperature distribution is prescribed. That is, the thermomechanically coupled energy balance is not solved, but families of temperature distributions qualitatively compatible with observed patterns are adopted to exhibit the effects of significant creep-rate variation with temperature. © 1984, Archives Européenes de Sociology. All rights reserved.

Description: Using the method of matched asymptotic expansions, the interaction between axisymmetrie laminar boundary layers and inviscid supersonic external flows is investigated in the limit of large Reynolds numbers. The resulting triple-deck equations are solved numerically for two different cases of body shapes: a cylinder-cone configuration and a configuration consisting of two concentric cylinders which are connected by a smooth curve. Solutions to the linearized as well as the fully nonlinear equations are presented. © 1984, Cambridge University Press. All rights reserved.

Description: The flow of an idealized granular material consisting of uniform smooth, but inelastic, spherical particles is studied using statistical methods analogous to those used in the kinetic theory of gases. Two theories are developed: one for the Couette flow of particles having arbitrary coefficients of restitution (inelastic particles) and a second for the general flow of particles with coefficients of restitution near 1 (slightly inelastic particles). The study of inelastic particles in Couette flow follows the method of Savage & Jeffrey (1981) and uses an ad hoc distribution function to describe the collisions between particles. The results of this first analysis are compared with other theories of granular flow, with the Chapman-Enskog dense-gas theory, and with experiments. The theory agrees moderately well with experimental data and it is found that the asymptotic analysis of Jenkins & Savage (1983), which was developed for slightly inelastic particles, surprisingly gives results similar to the first theory even for highly inelastic particles. Therefore the ‘ nearly elastic ’ approximation is pursued as a second theory using an approach that is closer to the established methods of Chapman-Enskog gas theory. The new approach which determines the collisional distribution functions by a rational approximation scheme, is applicable to general flowfields, not just simple shear. It incorporates kinetic as well as collisional contributions to the constitutive equations for stress and energy flux and is thus appropriate for dilute as well as dense concentrations of solids. When the collisional contributions are dominant, it predicts stresses similar to the first analysis for the simple shear case. © 1984, Archives Européenes de Sociology. All rights reserved.

Description: Experiments on and calculation methods for flow in straight non-circular ducts involving turbulence-driven secondary motion are reviewed. The origin of the secondary motion and the shortcomings of existing calculation methods are discussed. A more refined model is introduced, in which algebraic expressions are derived for the Reynolds stresses in the momentum equations for the secondary motion by simplifying the modelled Reynolds-stress equations of Launder, Reece & Rodi (1975), while a simple eddy-viscosity model is used for the shear stresses in the axial momentum equation. The kinetic energy k and the dissipation rate ε of the turbulent motion which appear in the algebraic and the eddy-viscosity expressions are determined from transport equations. The resulting set of equations is solved with a forward-marching numerical procedure for three-dimensional shear layers. The model, as well as a version proposed by Naot & Rodi (1982), is tested by application to developing flow in a square duct and to developed flow in a partially roughened rectangular duct investigated experimentally by Hinze (1973). In both cases, the main features of the mean-flow and the turbulence quantities are simulated realistically by both models, but the present model underpredicts the secondary velocity while the Naot-Rodi model tends to overpredict it. © 1984, Cambridge University Press. All rights reserved.

Description: This paper concerns the effects of topographic changes upon the dispersion of contaminants in rivers. Exact analytical results are derived for the time-of-arrival, temporal variance and skewness far downstream of a sudden contaminant release. It is demonstrated that there can exist optimal discharge sites, such that at all positions far downstream the maximum concentrations are minimized. © 1984, Archives Européenes de Sociology. All rights reserved.

Description: Miniature tubular pumps are used to emit droplets from ink-jet matrix heads. This paper deals with the simulation of the behaviour of a viscous and compressible liquid in such pumps. The response of the liquid in the frequency and time domain is analysed. An approximate method is given to determine the droplet speed and size. © 1984, Cambridge University Press. All rights reserved.

Description: A further refinement of the Howard—Kochar—Jain theorem is given which allows the estimation of the range of complex wave velocity for growing perturbations in a stratified shear flow. According to the results obtained, the boundary of this region depends both on the minimum Richardson number and on the wavenumber of the perturbations. The effect of external boundaries on the stability of parallel flows is defined. An estimate of the maximum rate of growth versus dimensionless wavenumber is found. The theoretical results are compared with numerical computations and laboratory experiments of other authors. © 1984, Archives Européenes de Sociology. All rights reserved.

Description: Experimental evidence suggests that in the turbulent mixing layer the fundamental mechanism of growth is two-dimensional and little affected by the presence of vigorous three-dimensional motion. To quantify this apparent property and study the growth of streamwise vorticity, we write for the velocity field V(x, t) = U(x, z, t) + u(x, y, z, t), where U is two-dimensional and u is three-dimensional. In a first version of the problem U is independent of u, while in the second U is the spanwise average of V. In both cases the equation for u is linearized around U. The equations for U and u are solved simultaneously by a finite-difference calculation starting with a slightly disturbed parallel shear layer. The solutions provide a detailed description of the growth of the three-dimensional motion. They show that its characteristics are dictated by the distribution of spanwise vorticity which results from roll-up and pairing. Pairing inhibits its growth. The solutions also demonstrate that even when the three-dimensional flow attains large amplitudes it has a negligible effect on the interaction of spanwise vortices and thus on the growth of the layer. © 1984, Archives Européenes de Sociology. All rights reserved.

Description: We consider the effect of insoluble surfactants on the steady thermocapillary flow in a differentially heated slot treated previously by Sen & Davis (1982). The equation of state for interfacial tension is taken to be linear in both temperature and surfactant concentration. We treat the problem in the limit of shallow slots and low thermal Marangoni numbers so that the effect of surfactants is described by only two parameters : a surface Peclet number Pe and an elasticity parameter denoted by E, the ratio of the compositional elasticity to the tension difference due to the imposed temperature difference. Using lubrication theory and matched asymptotic expansions, we reduce the problem to a single nonlinear integral—algebraic equation (for the outer core variables), which we solve both numerically and in various asymptotic limits by perturbation theory. It is shown that the general effect of surfactants is to retard the strength of the motion, but that this retardation is not necessarily uniform in space. Surprisingly, there are only extreme cases in which condensed surfactant layers will form, these being E 1, Pe 〉 1. Sharp gradients in surfactant concentrations will not form in the general case of E = 0(1). This behaviour is due to the strong coupling between the flow and the interfacial stress, and is contrasted with certain well-known forced-convection problems. © 1984, Archives Européenes de Sociology. All rights reserved.

Description: Measurements of the velocity characteristics and wall pressure are reported for the axisymmetric turbulent flow downstream of three bluff bodies (disks of 25 % and 50 % area blockage and a cone of 25% blockage) confined by a long pipe. The dimensions of the recirculation regions were found from the mean-velocity components, which were determined by a laser-Doppler velocimeter: the corresponding components of Reynolds stress were also recorded. The lengths and maximum widths of the recirculation bubbles (in bluff-body diameters), recirculating mass-flow rates (normal-ized by the average velocity in the plane of the baffle, U0, and the baffle diameter) and maximum turbulent kinetic energy (normalized by U20) were as follows: cone 1.55, 0.55, 0.19, 0.11; disk (25% blockage) 1.75, 0.62, 0.31, 0.19; disk (50% blockage) 2.20, 0.55, 0.26, 0.16. The increase in recirculation length with blockage is opposite to the trend in unconfined, annular jets. The distribution of Reynolds stresses is strongly dependent on blockage: for the smaller blockage both the disk and the cone have the maximum value of kinetic energy near the rear stagnation point. It is proposed that this is because the generation of turbulence by normal stresses is more important in the flow consequent on the smaller blockage. The measurements include profiles of the velocity characteristics at, as well as upstream of, the trailing edges of the baffles for use as boundary conditions in numerical solutions of the equations of motion. © 1984, Archives Européenes de Sociology. All rights reserved.

Description: Convective flow phenomena in slender vertical slots with larger vertical than horizontal dimension, i.e. Hele Shaw slots, heated from below and subject to specified lateral boundary conditions, are investigated experimentally. Temperature fields in the liquid were visualized by holographic interferometry. Power-density spectra of local time-dependent thermocouple signals are calculated. In these slender slots different steady and time-dependent convection patterns develop with increasing Rayleigh number. The range of oscillatory convective flow exhibits periodic, quasiperiodic or non-periodic structures including possible frequency locking, subharmonics and intermittency. Quasiperiodic and periodic oscillations reappear at higher Rayleigh numbers, with non-periodic flows occurring in-between. These time-dependent flows appear to be caused by an instability of thermal boundary layers at the horizontal walls. Finally, at still higher Rayleigh numbers a reverse transition to a steady-state flow pattern is observed. The transitions between steady and non-steady flows are characterized by hysteresis. © 1984, Archives Européenes de Sociology. All rights reserved.