ALBERT

Description: We report here dates on archaeologic and geologic samples. The samples were counted as methane in gas proportional counters. The techniques used have been described earlier (R, 1971, v 13, p 442–449). Dates are expressed in years BP, taking AD 1950 as the reference year. Modern standard was NBS oxalic acid. Quoted errors are based on counting statistics alone and are equivalent to ±1 standard deviation for samples younger than 10,000 years and ± 2 standard deviations for older samples. Descriptions and references regarding the samples have been supplied by the submitters of the samples.

Description: Procedures and equipment used in the University of Wisconsin laboratory have been described in previous date lists (Steventon & Kutzbach 1983; 1984). Except as otherwise indicated, wood, charcoal, and peat samples are pretreated with dilute NaOH-Na4P2O7 and dilute H3PO4 before conversion to the counting gas methane; when noted, marls and lake cores are treated with acid only. Very calcareous materials are treated with HCl instead of H3PO4. Pretreatment of bone varies with the condition of the bone sample; solid bone with little deterioration is first cleaned manually and ultrasonically. The bone is treated with 8% HCl for 15 minutes, then dilute NaOH-Na4P2O7 for 3 hours at room temperature, washed until neutral, and the collagen extracted according to Longin (1971). Charred bone is treated with dilute HCl, NaOH-Na4P2O7, and then dilute HCl again.

Description: It has been suggested that the sunspot cycle modulates the production rate of radionuclides in the atmosphere and that these modulations can be traced in various parts of the earth surface system. On the basis of a theoretical analysis, Damon, Sternberg, and Radnell (1983) have concluded that the effects of the 11-yr cycle of sunspots should be observable in 14C data provided the measurements are done at a 2 permil (sd) level. This conclusion is based on calculations using models discussed by Lingenfelter and Ramaty (1970) and by O'Brien (1979) and on the 14C inventory modified from Damon, Lerman, and Long (1978). In this note we compare the amplitude estimate of Damon, Sternberg, and Radnell (1983), who calculated a representative peak-to-peak variation of 1.7‰ in 14C for the sunspot cycle between 1848 and 1856, with experimental values derived from recently published data. We find the experimental value to be larger by a significant factor from the theoretical calculation.

Description: The purpose of this paper is to present the methodology used for sample preparation at the Woods Hole Oceanographic Institution Radiocarbon Laboratory. The WHOI lab is dedicated to oceanographic research supported by the National Science Foundation (OCE81-11954). We began operation in March 1982. The methods used for the production of samples are based on those developed previously (Barker, 1953; Suess, 1954; Noakes, Kim, & Stipp, 1969; Linick, 1975). Subsequent changes and refinements to these methods are described. This paper will present detailed descriptions of how various samples are collected and sectioned, then converted to CO2 and to C2H2, the primary counting gas for most of our samples.

Description: A series of shell samples has been studied to determine the magnitude and mechanisms of carbon exchange between shells and their environment. Laboratory contamination experiments included the storing of shell samples in acid and calcareous environments of different 14C concentrations as well as studies of carbon exchange in the course of thermal recrystallization in solid state in an atomosphere of carbon dioxide. The applicability of differential thermal analysis to studies of the structure and texture of shells is discussed.

Description: Radiocarbon measurements made by the La Jolla laboratory on tree-ring samples from South German oak chronologies are presented. Several previously separate tree-ring series have been reduced to one absolutely dendro-dated chronology spanning the period from 4066 BC to the present and one still-floating chronology which spans the approximate period 7225 to 4125 BC. Previous estimates of the dendro-years made by the authors are compared with the dendro-years now assigned.

Description: The laboratory was established by University College, Cardiff, in 1974 primarily for research in vegetation history and archaeology in Britain. The laboratory has been supported yearly since 1978 by the Conservation and Land Division of the Welsh Office, Cardiff, which submits archaeologic samples from rescue excavations in Wales which are carried out by the Clwyd-Powys Archaeological Trust Ltd (CPAT), the Dyfed Archaeological Trust Ltd (DAT), the Glamorgan Gwent Archaeological Trust Ltd (GGAT), and the Gwynedd Archaeological Trust Ltd (GAT).

Description: This compilation of radiometric data from Antarctica contains abstracted information from 400 publications, resulting in nearly 2500 separate entries. Each entry, or “date listing”, gives basic information of the sample site as well as the dating method and the age(s) of the sample analysed. The date list differs from those routinely published in Radiocarbon because we included not only radiocarbon but all dating methods.

Description: The trajectories of surface and subsurface particles of nonlinear gravity-capillary waves are calculated. Surface tension is found to have a small effect on the trajectories and drift velocity of pure gravity waves (down to 20 cm in length). On the other hand, pure capillary wave trajectories can be considerably altered even when the influence of gravity is small (waves of up to 2 cm in length). When the restoring forces are of comparable magnitude, some remarkable trajectories are possible, containing one or more subloops. Overall, the influence of increased surface tension is to increase the relative horizontal distance travelled by a particle, as well as the magnitude of the time-averaged drift velocity ratio at the surface and, as far as short waves are concerned, its penetration depth. These results can have implications for steep waves where parasitic capillaries are generated and for observations of the wind-drift current. © 1985, Cambridge University Press. All rights reserved.

Description: Experiments in which a long vertical, heated wire is surrounded by concentric annuli of a melt and its crystalline solid show that the convection state changes from a stable unicell surrounded by a stationary cylindrical solid-liquid interface, to a complex time-dependent flow surrounded by a rotating, helical solid-liquid interface. This transition occurs at a Grashof number of approximately 150, which is an order of magnitude less than the critical Grashof number calculated for a liquid annulus surrounded by rigid walls. A linear stability analysis has been carried out for an infinitely tall vertical annulus. When the deformable nature of the crystal-melt interface is taken into account in the boundary conditions, two new modes of instability arise. The most dangerous mode is asymmetrical and corresponds to helical waves travelling vertically upwards. The critical Grashof number and the scaling properties of the eigenstate agree with experiments. The results clearly demonstrate the coupling of convection with crystal-melt interfacial instabilities. © 1985, Cambridge University Press. All rights reserved.

Description: We consider the flow of two immiscible fluids lying between concentric cylinders when the outer cylinder is fixed and the inner one rotates. The interface is assumed to be concentric with the cylinders, and gravitational effects are neglected. We present a numerical study of the effect of different viscosities, different densities and surface tension on the linear stability of the Couette flow. Our results indicate that, with surface tension, a thin layer of the less-viscous fluid next to either cylinder is linearly stable and that it is possible to have stability with the less dense fluid lying outside. The stable configuration with the less-viscous fluid next to the inner cylinder is more stable than the one with the less-viscous fluid next to the outer cylinder. The onset of Taylor instability for one-fluid flow may be delayed by the addition of a thin layer of less-viscous fluid on the inner wall and promoted by a thin layer of more-viscous fluid on the inner wall. © 1985, Cambridge University Press. All rights reserved.

Description: A systematic study is made of the effect of latitude on the linear, normal mode stability characteristics of the laminar barotropic Ekman layer. The outcome depends upon the direction of the geostrophic flow (in the case of flows modelling the atmospheric Ekman layer) or, alternatively, upon the direction of the applied stress (in the case of flows modelling the oceanic Ekman layer). The minimum critical Reynolds number Rcis a function of latitude. For the atmospheric Ekman layer Rc = 30.8 for all latitudes less than 26.2° and increases monotonically with latitude to 54.2. At a latitude of 45° N, Rc is 33.9 and arises for a geostrophic wind directed towards a compass heading 252° (clockwise from north), corresponding to rolls with axes pointing due west and having wavenumber k (with unit of length taken to be the Ekman layer depth) of 0.594. The minimum Rcfor the oceanic boundary layer is 11.6 for latitudes less than 81.1°, and increases with latitude to 11.8. At 45° N latitude, the critical condition arises for a surface-current compass heading of 345.2°, roll axis of 351° and a wavenumber k = 0.33. The results for Rcare all symmetric about the equator, with roll axes and associated basic flow directions rotated by 180°. As the Reynolds number R increases, the effects of the perturbation Coriolis • acceleration on the instability diminish, as has been previously shown, and the error caused by neglect of the horizontal component of angular velocity therefore decreases. The high Reynolds number limit is systematically explored. It is shown that the lower branch of the neutral curve is not inviscid as R→∞; rather kR→ constant. The upper branch is inviscid in the limit R→∞, and corresponds to a regular or singular neutral mode depending on whether the angle ε between the outer geostrophic flow and the roll axis is greater or less than 15.93°. ' Inflectional ' modes, thought to be relevant by some investigators, do not exist for ε〈 15.93°. Lastly, the most unstable inviscid mode corresponding to zero phase speed, a condition to which certain well-known experiments are sensitive, occurs at e = 11.8° with wavenumber k = 0.6. This is in good agreement with published experimental data. © 1985, Cambridge University Press. All rights reserved.

Description: The subcritical transition in plane Poiseuille flow (generated in a long wind channel of rectangular cross-section) was studied experimentally. Cylinder-generated vortical disturbances were introduced into the parabolic flow (in the test section) or the inlet flow. The parabolic flow was also disturbed by a controlled periodic jet from a wall orifice. On the basis of the three kinds of observations, we come to the conclusion that the minimum transition Reynolds number is about 1000 and the related threshold intensity (of the external disturbance triggering the transition) is comparable to the maximum intensity of u-fluctuations in fully turbulent channel flows. © 1985, Cambridge University Press. All rights reserved.

Description: In the two-dimensional sedimentation process beneath an inclined wall, the mixture of the particulate and liquid phases is separated from the wall by a boundary layer of the clear liquid. This paper contains a simple mathematical model giving waves on the interface between the clear liquid and the mixture. These waves are caused by a discontinuity in the gradient of the tangential velocity of the clear liquid, across the interface. In the limiting case of small concentration of the particulate phase in the mixture, the model gives a dispersive wave running upward along the interface in the direction of the flow in the boundary layer. The effect of finite concentration is to introduce a damping. © 1985, Cambridge University Press. All rights reserved.

Description: Research on the abstract properties of the Navier—Stokes equations in three dimensions has cast a new light on the time-asymptotic approximate solutions of those equations. Here heuristic arguments, based on the rigorous results of that research, are used to show the intimate relationship between the sufficient number of degrees of freedom describing fluid flow and the bound on the fractal dimension of the Navier—Stokes attractor. In particular it is demonstrated how the conventional estimate of the number of degrees of freedom, based on purely physical and dimensional arguments, can be obtained from the properties of the Navier—Stokes equation. Also the Reynolds-number dependence of the sufficient number of degrees of freedom and of the dimension of the attractor in function space is elucidated. © 1985, Cambridge University Press. All rights reserved.

Description: Steady finite-amplitude solutions for two-dimensional convection in a layer heated from below with stress-free boundaries are obtained numerically by a Galerkin method. The stability of the steady convection rolls with respect to arbitrary three-dimensional infinitesimal disturbances is investigated. Stability is found only in a small fraction of the Rayleigh-number-wavenumber space where steady solutions exist. The cross-roll instability and the oscillatory and monotonic skewed varicose instabilities are most important in limiting the stability of steady convection rolls. The Prandtl numbers P = 0.71, 7, 104are emphasized, but the stability boundaries are sufficiently smoothly dependent on the parameters of the problem to permit qualitative extrapolations to other Prandtl numbers. © 1985, Cambridge University Press. All rights reserved.

Description: The incompressible three-dimensional Navier-Stokes equations are solved numerically for a fluid-filled cylindrical cannister that is spinning and nutating. The motion of the cannister is characteristic of that experienced by spin-stabilized artillery projectiles. Equations for the internal fluid motion are derived in a non-inertial aeroballistic coordinate system. Steady-state numerical solutions are obtained by an iterative finite-difference procedure. Flow fields and liquid induced moments have been calculated for viscosities in the range of 0.9 x 104—1 x 109 cSt. The nature of the three-dimensional fluid motion inside the cylinder is discussed, and the moments generated by the fluid are explained. The calculated moments generally agree with experimental measurements. © 1985, Cambridge University Press. All rights reserved.

Description: Synthetic turbulent boundary layers were constructed on a flat plate by generating systematicmoving patterns of turbulent spots in a laminar flow. The experiments were carried out in a wind tunnel at a Reynolds number based on plate length of 1.7 x 10. Spots were generated periodically in space and time near the leading edge to form a regular hexagonal pattern. The disturbancemechanism was a camshaft that displaced small pinsmomentarily into the laminar flow at frequencies up to 80 Hz. Themain instrumentation was a rake of 24 single hot wires placed across the flow in a line parallel to the surface. Themainmeasured variable was local intermittency; i.e. the probability of observing turbulent flow at a particular point in space and time. The results are reported in numerous (x, z, t)-diagrams showing the evolution of various synthetic flows along the plate. The dimensionless celerity or phase velocity of the large eddies was found to be very nearly 0.88, independent of eddy scale. All patterns with sufficiently small scales eventually showed loss of coherence as theymoved downstream. A novel phenomenon called eddy transposition was observed in several flows that contained appreciable laminar regions. The original large eddies were replaced by new eddies at new positions, intermediate to the original ones, while preserving the hexagonal pattern. The present results, together with some empirical properties of a turbulent spot, were used to estimate the best choice of scales for constructing a synthetic boundary layer suitable for detailed study as amodel for a natural flow. The values recommended are: spanwise period/thickness≈2.5, streamwise period/thickness ≈ 8.0. © 1985, Cambridge University Press. All rights reserved.

Description: The Stewartson-Warn-Warn (SWW) solution for the time evolution of an inviscid, nonlinear Rossby-wave critical layer, which predicts that the critical layer will alternate between absorbing and over-reflecting states as time goes on, is shown to be hydrodynamically unstable. The instability is a two-dimensional shear instability, owing its existence to a local reversal of the cross-stream absolute vorticity gradient within the long, thin Kelvin cat's eyes of the SWW streamline pattern. The unstable condition first develops while the critical layer is still an absorber, well before the first over-reflecting stage is reached. The exponentially growingmodes have a two-scale cross-stream structure like that of the basic SWW solution. They are found analytically using themethod ofmatched asymptotic expansions, enabling the problem to be reduced to a transcendental equation for the complex eigenvalue. Growth rates are of the order of the inner vorticity scale δq, i.e. the initial absolute vorticity gradient dq0/dy times the critical-layer width scale. This ismuch faster than the time evolution of the SWW solution itself, albeitmuch slower than the shear rate du0/dy of the basic flow. Nonlinear saturation of the growing instability is expected to take place in a central region of width comparable to the width of the SWW cat's-eye pattern, probably leading to chaoticmotion there, with very large 'eddy-viscosity ' values. Those values correspond to critical-layer Reynolds numbers λ-1≪ 1, suggesting that formost initial conditions the time evolution of the critical layer will depart drastically from that predicted by the SWW solution. A companion paper (Haynes 1985) establishes that the instability can, indeed, grow to large enough amplitudes for this to happen. The simplest way in which the instability could affect the time evolution of the critical layer would be to prevent or reduce the oscillations between over-reflecting and absorbing states which, according to the SWW solution, follow the first onset of perfect reflection. The possibility that absorption (or over-reflection)might be prolonged indefinitely is ruled out, inmany cases of interest (even if the 'eddy viscosity' is large), by the existence of a rigorous, general upper bound on themagnitude of the time-integrated absorptivity α(t). The bound is uniformly valid for all time t. The absorptivity α(t) is defined as the integral over all past t of the jump in the wave-induced Reynolds stress across the critical layer. In typical cases the bound implies that, nomatter how large tmay become, | α(t)| cannot greatly exceed the rate of absorption predicted by linear theorymultiplied by the timescale on which linear theory breaks down, say the time for the cat's-eye flow to twist up the absolute vorticity contours by about half a turn. An alternative statement is that| α(t) | cannot greatly exceed the initial absolute vorticity gradient dq0/dy times the cube of the widthscale of the critical layer. In typical cases, therefore, a brief answer to the question posed in the title is that the critical layer absorbs at first, at a rate ∝ dq0/dy, whereas after linear theory breaks down the critical layer becomes a perfect reflector in the long-time average. If absolute vorticity gradients vanish throughout the critical layer then the bound is zero, implying perfect reflection for all t. The general conditions for the bound to apply are that the wave amplitude and critical-layer width are uniformly bounded for all t, themotion is two-dimensional, and vorticity is neither created nor destroyed within the critical layer, nor transported into or out of it by diffusion, by advection, or by othermeans. Vorticitymay, however, be diffused or turbulently transported within the critical layer, provided that the region within which the transport acts is of bounded width and the range of values of vorticity within that region remains bounded. There are no other restrictions on wave amplitude, none on wavelength, and no assumptions about flow details within the critical layer nor about the initial vorticity profile q0(y), apart from an assumption that q0(y) has singularities no worse than a finite number of jump discontinuities. The proof, in itsmost general form,makes use of a new finite-amplitude conservation theorem for disturbances to parallel shear flows, generalizing the classical results of Taylor, Eliassen & Palm, and others. © 1985, Cambridge University Press. All rights reserved.

Description: The three-dimensional steady laminar-boundary-layer equations have been cast in the appropriate form for semisimilar solutions, and it is shown that in this form they have the same structure as the semisimilar form of the two-dimensional unsteady laminar-boundary-layer equations. This similarity suggests that theremay be a new type of singularity in solutions to the three-dimensional equations: a singularity that is the counterpart of the Stewartson singularity in certain solutions to the unsteady boundary-layer equations. A family of simple three-dimensional laminar boundary-layer flows has been devised and numerical solutions for the development of these flows have been obtained in an effort to discover and investigate the new singularity. The numerical results do indeed indicate the existence of such a singularity. A study of the flow approaching the singularity indicates that the singularity is associated with the domain of influence of the flow for given initial (upstream) conditions as is prescribed by the Raetz influence principle. © 1985, Cambridge University Press. All rights reserved.

Description: Measurements of themean and fluctuating velocities have been obtained with pressure and hot-wire probes in the attached boundary layers and wakes of two airfoilmodels at a lowMach number. The firstmodel is a conventional airfoil at zero incidence and the second an advanced supercritical airfoil at an angle of attack of 4°. Themean-flow and Reynolds-stress data and related quantities are presented with emphasis on the trailing-edge region. The results indicate that the flow around the conventional airfoil is aminor perturbation of a symmetric flat-plate flow with small wake curvature and weak viscous-inviscid interaction. The flow around the supercritical airfoil is in considerable contrast with strong streamwise pressure gradients, non-negligible normal pressure gradients, and large surface and streamline curvatures of the trailing-edge flow. The near wake is strongly curved and intensemixing occurs between the retarded upper-surface boundary layer and strongly accelerated lower-surface boundary layer. © 1985, Cambridge University Press. All rights reserved.

Description: Countercurrent flowmay be induced by opposing buoyancy forces associated with compositional gradients and thermal gradients within a fluid. The occurrence and structure of such flows is investigated by solving the double-diffusive boundary-layer equations for steady laminar convection along a vertical wall of finite height. Non-similar solutions are derived using themethod ofmatched asymptotic expansions, under the restriction that the Lewis and Prandtl numbers are both large. Two sets of asymptotic solutions are constructed, assuming dominance of one or the other of the buoyancy forces. The two sets overlap in the central region of the parameter space; each setmatches up with neighbouring unidirectional similarity solutions at the respective borderlines of incipient counterflow. Interaction between the buoyancymechanisms is controlled by their relative strength R and their relative diffusivity Le. Flow in the outer thermal boundary layer deviates from single-diffusive thermal convection, depending upon themagnitude of the parameter RLe. Flow in the inner compositional boundary layer deviates from single-diffusive compositional convection, depending upon themagnitude of RLe1/3. © 1985, Cambridge University Press. All rights reserved.

Description: In this paper the translatorymotion of a compound drop is examined in detail for low-Reynolds-number flow. The compound drop, consisting of a liquid drop or a gas bubble completely coated by another liquid,moves in a third immiscible fluid. An exact solution for the flow field is found in the limit of small capillary numbers by approximating the two interfaces to be spherical. The solution is found for the general case of eccentric configuration withmotion of the inner sphere relative to the outer together with themotion of the system in the continuous phase. The results show that the viscous forces tend tomove the inner-fluid sphere towards the front stagnation point of the compound drop. For equilibrium of the inner sphere with respect to the outer theremust, therefore, be a body force towards the front. This can only be achieved with the necessary condition that there be a buoyant force on the inner sphere, opposite to that of the compound drop in the continuous phase. For a given set of fluids, two or four equilibrium configurationsmay be found. Of these only one or two, respectively, are stable. The others are unstable. For the special case of concentric configuration, the equilibrium is alwaysmetastable. © 1985, Cambridge University Press. All rights reserved.

Description: The convective behaviour of xenon gas in a vertical thermally conducting cylinder (height/radius 6) heated from below was investigated. Convectively induced temperature fluctuations in the gas were analysed with digital signal-processing techniques over a range of Rayleigh number 0 ≤ Ra ≾ 2300. Quiescent, steady-state, periodic and weakly turbulent convective regimes were characterized. Bistability of steady states (mode switching) was observed in the range 400 ≾Ra ≾ 700. At Ra = 1550 a strictly periodic flow developed. With increasing Ra two additional incommensurate frequencies appeared, leading to 'turbulence' at Ra ≈ 2000. This turbulence, characterized by a broadband power spectrum, intermittently showed periodic flow. A periodic window with a period-doubling sequence appeared between 2100 ≾ Ra ≾ 2200. The spectral features of this sequence can be followed into the broad band noise at higher Ra. Although these experiments were conducted quasistatically, a strong hysteresis was observed with decreasing Ra. Furthermore, it was demonstrated that the sequence of convective regimes can be fundamentally altered byminor perturbations (self-heating) from the flow sensors. © 1985, Cambridge University Press. All rights reserved.

Description: The influence of weak periodic wall undulations on the structure of turbulent pipe flow has been studied in three ways: measurements in air flow using pressure probes and hot-wire techniques, visualizations in water flow and numerical predictions based on a turbulence (k-ε) model. The flows at Reynolds numbers of 30000 and 115000 have been particularly investigated. The flow characteristics proved to be very different from those observed in a straight pipe. Calculations and experiments agree well for the mean-and turbulent-energy fields; however the detailed behaviour of some local quantities such as anisotropy of the Reynolds stress is not well predicted particularly in the crest region. So the performances and the limitations of classical closure have been appraised. The existence of an unsteady reverse-flow region downstream of every crest suggested by measurements and calculations has been clearly confirmed by visualizations in water flow. © 1985, Cambridge University Press. All rights reserved.

Description: A rapidly scanning one-velocity-component directionally sensitive fringe-type laser-Doppler anemometer which scans the measurement volume perpendicular to the optical axis of the transmitting optics was used to investigate the flow structure of the steady freestream separated turbulent boundary layer of Simpson, Chew & Shivaprasad (1981a). Space-time correlations were obtained for the first time in a separated turbulent boundary layer and showed that the integral lengthscale Lyfor the large eddies grows in size towards detachment, although the ratio of this lengthscale to the boundary-layer thickness remains constant. Results also indicate local dependence of the backflow on the middle and outer regions of the boundary layer at a given instant in time. © 1985, Cambridge University Press. All rights reserved.

Description: A stratified two-layer fluid is brought to solid-body counterclockwise rotation inside a cylindrical tank having a conical bottom with a radial topographic ridge. A stress is then applied to the top surface by means of a clockwise differentially rotating disk. The resulting Ekman-layer flux causes the top layer to spin-down and the interface to rise near the wall and to descend at the centre of the tank. As this process continues, the interface (front) between the two layers intersects the disk surface, and after that migrates away from the wall and allows the bottom fluid to contact the disk directly. The migration of the front continues until a steady state is reached, the front becomes stationary and the system is in geostrophic balance. The first sign of upwelled flow at the surface always occurs as a high-speed jet-like plume at the bottom topography, and only at a later time does a uniform upwelled flow appear at the surface upstream of the topography. This plume, which always forms near the downstream edge of the topography, migrates in advance of the upstream front to produce an upwelling maximum at the bottom topography. The final width of the upstream flow in steady-state conditions is estimated by a simple theoretical model, which is in good agreement with the experimental results. We have an experimental criterion to predict the occurrence of travelling baroclinic waves on the upstream front. On the downstream side of the ridge, large standing waves are observed, with significant upwelling within them. Under some circumstances cyclones pinch-off from the upstream front, the plume on the ridge and the crests of the large downstream standing waves. We present criteria to predict the occurrence of these pinch-off processes. © 1985, Cambridge University Press. All rights reserved.

Description: This paper analyses effects of chemical reactions on reflected-shock flow fields in shock tubes. The method of linearized characteristics is applied to analyse gasdynamic disturbances due to chemical reactions. The analysis treats cases where combustible gas is highly diluted in inert gas, and assumes that flows are one-dimensional and that upstream flows in front of the reflected-shock waves are in the frozen state. The perturbed gasdynamic properties in the reflected-shock flow fields are shown to be expressible mainly in terms of a heat-release function for combustion process. In particular, simple relations are obtained between the heat-release function and the physical properties at the end wall of a shock tube. As numerical examples of the analysis, the present formulation is applied to calculate gasdynamic properties in the reflected-shock region in a H2-O2-Ar mixture. Procedures are demonstrated for calculation of the heat-release function by numerically integrating rate equations for chemical species. The analytical results are compared with rigorous solutions obtained numerically by use of a finite-difference method. It is shown that the formulation can afford exact solutions in cases where chemical behaviours are not essentially affected by gasdynamic behaviours. When the induction time of the combustion process is reduced to some extent owing to gasdynamic disturbances, some discrepancies appear between analytical results and rigorous solutions. An estimate is made of the induction-time reduction, and a condition is written down for applicability of the analysis. © 1985, Cambridge University Press. All rights reserved.

Description: A simple model is proposed for the two-dimensional injection of irrotational inviscid fluid from a slot into a free stream. In a certain range of values of the ratio of free-stream to injection total heads, the film thickness satisfies a nonlinear integral equation whose solution enables the mass flow in the film to be found. Some experiments are described which both agree with this theory when it is relevant and indicate its deficiencies at other values of the total head ratio. © 1985, Cambridge University Press. All rights reserved.

Description: Temperature measurements taken in association with the velocity measurements described by Gargett, Osborn & Nasmyth (1984) are examined. With careful noise removal the temperature dissipation spectrum is fully resolved and x, the dissipation rate of temperature-fluctuation variance, is determined directly. With directly measured values of x and ε, the turbulent-kinetic-energy dissipation rate per unit mass, the observed temperature spectra are non-dimensionalized by Oboukov-Corrsin-Batchelor scaling. Shapes and levels of the resulting non-dimensional spectra are then examined as functions of the degree of isotropy (measured) in the underlying velocity field. Two limiting cases are identified: Class A, associated with isotropic velocity fields; and Class B, associated with velocity fields which are anisotropic (owing to buoyancy forces repressing vertical relative to horizontal dimensions of energy-containing ‘eddies’). The present observations suggest that the Corrsin—Oboukov—Batchelor theory does not provide a universal description of the spectrum of temperature fluctuations in water. Class A scalar spectra have neither k-5/3nor K-1subranges: a Batchelor-spectrum fit to the high-wavenumber roll-off region yields a value of 12 for the ‘universal' constant q. In striking contrast, the buoyancy-affected Class B spectra exhibit a clear k-5/3subrange, an approach to a k-1subrange, and a value of q ~ 4 which is in rough agreement with most previous estimates. Previous oceanic and atmospheric measurements are re-examined in the light of the present results. It is suggested that these previous results are also affected by vertical scale limitation. Reasons underlying the discrepancies between theories and observations are discussed: these may be different in the two classes presented. © 1985, Cambridge University Press. All rights reserved.

Description: This paper describes an experimental study of the electromagnetic stirring in a mercury induction furnace. The 200 mm-diameter furnace is supplied with a single-phase electric current of frequency 50-4700 Hz. The flow pattern is measured by means of a special two-wire probe, which tracks the thermal wake behind a hot-film probe. The magnitudes of fluctuating velocities are measured by hot-film anemometry. Attention is focused on the influence on the mean and turbulent motion of the electromagnetic-skin depth, which is determined by the supply frequency. The measurements of the mean motion show that, for a fixed magnetic field, stirring is maximum when the value of the skin depth normalized by the pool radius is about 0.2, in agreement with previous theoretical predictions. Two turbulence regimes may be distinguished for different frequency ranges. At low frequency the various properties of the turbulence, such as the mean-square fluctuations, the integral scales and the turbulent dissipation rate, are almost uniform over the whole bath. However, at high frequency the turbulence is non-uniform; there is an increase in the turbulent fluctuations and dissipation rate and a decrease of the integral scale within the electromagnetic-skin depth near the wall. © 1985, Cambridge University Press. All rights reserved.

Description: A new analytic solution is presented for predicting evaporation rates from plane liquid surfaces into a neutral turbulent boundary layer. Conditions of passive dispersion are assumed. Molecular diffusivity is incorporated into the boundary conditions. Both smooth and rough surfaces are considered. A comparison with a wide variety of experimental data is made; this tends to reveal inadequacies and inconsistencies in the data, rather than test the theory. The effects of a roughness change at the boundary of the liquid surface and of high vapour pressures can be included for practical purposes by simple formulae. A criterion is derived for the validity of the neglect of buoyancy effects. © 1985, Cambridge University Press. All rights reserved.

Description: The reflection and transmission of a gravity wave propagating through a jet-type background flow is studied. Only the linear, non-dissipative case is treated, and the hydrostatic approximation used in a stratified non-rotating medium. The behaviour of the gravity wave in the presence of two or one critical levels is investigated. In the first case, i.e. two critical levels, it is found that for high values of the Richardson number the wave is highly attenuated. For sufficiently low values of the Richardson number overreflection and overtransmission occur. It is demonstrated that a wave generated below the jet and propagating upward takes energy from the mean flow at the upper critical level for all values of the Richardson number. The single critical level has been studied as a limiting case of two merging critical levels. In this approach it is found that the wave is not transmitted and no overreflection can occur. © 1985, Cambridge University Press. All rights reserved.

Description: Cavitation-noise measurements from an axisymmetric body with ‘controlled’ generation of cavitation are reported. The control was achieved by seeding artificial nuclei in the boundary layer by electrolysis. It was possible to alter the number density of nuclei by varying the electrolysis voltage, polarity and the geometry of the electrode. From the observed trend of cavitation-noise data it is postulated that there exists an ‘interference effect’ which influences cavitation noise. When the nucleus-number density is high and cavitation numbers are low this effect is strong. Under these conditions the properties of cavitation noise are found to differ considerably from those expected based on theories concerning noise from single-spherical-bubble cavitation. © 1985, Cambridge University Press. All rights reserved.

Description: This paper describes an experimental study, conducted in the I.M.S.T. air-sea interaction tunnel, of waves excited on a water surface by a periodic train of vortices in the air flow above. The water surface, under some conditions, shows a rapidly developing resonant response, while in the non-resonant case waves propagate both upstream and downstream at speeds different from, but dependent upon, the vortex-convection speed. © 1985, Cambridge University Press. All rights reserved.

Description: The well-known analogy between the Euler equations for steady flow of an inviscid incompressible fluid and the equations of magnetostatic equilibrium in a perfectly conducting fluid is exploited in a discussion of the existence and structure of solutions to both problems that have arbitrarily prescribed topology. A method of magnetic relaxation which conserves the magnetic-field topology is used to demonstrate the existence of magnetostatic equilibria in a domainD that are topologically accessible from a given field BO(x) and hence the existence of analogous steady Euler flows. The magnetostatic equilibria generally contain tangential discontinuities (i.e. current sheets) distributed in some way in the domain, even although the initial field B0(x) may be infinitely differentiable, and particular attention is paid to the manner in which these current sheets can arise. The corresponding Euler flow contains vortex sheets which must be located on streamsurfaces in regions where such surfaces exist. The magnetostatic equilibria are in general stable, and the analogous Euler flows are (probably) in general unstable. The structure of these unstable Euler flows (regarded as fixed points in the function space in which solutions of the unsteady Euler equations evolve) may have some bearing on the problem of the spatial structure of turbulent flow. It is shown that the Euler flow contains blobs of maximal helicity (positive or negative) which may be interpreted as ‘ coherent structures’, separated by regular surfaces on which vortex sheets, the site of strong viscous dissipation, may be located. © 1985, Cambridge University Press. All rights reserved.

Description: Stably stratified viscous fluid in a container with vertical walls is initially at rest with tilted density surfaces, following a rotation of the container from its orientation when being filled. The initial state so generated is not in equilibrium, and the resultant motion will decay under the action of viscosity and of the diffusion of the salt producing the stratification. The timescales for the succession of stages by which equilibrium is attained are identified, and are found to depend on the strengths of the two diffusive processes, separately and interactively. © 1985, Cambridge University Press. All rights reserved.

Description: A numerical simulation of turbulent natural convection (the Rayleigh-Bénard problem) has been conducted using large-eddy-simulation (LES) methods and the results compared with several experiments. The development of the LES equation is outlined and discussed. The modelling of the small-scale turbulent motion (called subgrid modelling) is also discussed. The resulting LES equations are solved and data collected over a short period of time in a similar manner to the direct simulation of the governing conservation equations. An explicit, second-order accurate, finite-difference scheme is used to solve the equations. Various average properties of the resulting flow field are calculated from the data and compared with experimental data in the literature. The use of a subgrid model allows a higher value of Ra to be simulated than was previously possible with a direct simulation. The highest Ra successfully simulated was 2.5 x 106. The problems at higher values of Ra are discussed and suggestions for improvements made. © 1985, Cambridge University Press. All rights reserved.

Description: The results are presented of turbulence measurements on an ‘infinite’ swept wing, simulated by a duct attached to a blower tunnel. The configuration is close to that used at the Netherlands NLR except that the boundary layer does not quite separate. The measurements include triple products, and a balance of the transport equation for turbulent energy is presented. The results confirm the NLR finding of a significant decrease in the magnitude of shear stress compared with an equivalent two-dimensional boundary layer: this is evidently the effect of crossflow on large eddies that have initially developed in a two-dimensional boundary layer. This unexpected effect of three-dimensionality is at least as important in prediction of real-life flows as the better-known lag between the direction of the shear stress and that of the mean-velocity gradient. Tentative suggestions for modelling the reduction in shear-stress magnitude are advanced. © 1985, Cambridge University Press. All rights reserved.

Description: Wave-power absorption by an oscillating water column in a channel is studied within linear theory, and for different boundary conditions regarding the regions between the absorber and the channel walls. Particular attention is given to the effect of placing projecting sidewalls in front of the column. © 1985, Cambridge University Press. All rights reserved.

Description: Part 1 a study is made of the internal solitary wave on the pycnocline of a continuously stratified fluid. A Korteweg-de Vries (KdV) equation for the ‘ interfacial ’ displacement is developed following Benney’s method for long nonlinear waves. Experiments were conducted in a long wave tank with the pycnocline at several different depths below the free surface, while keeping the total depth approximately constant. A step-like pool of light water, trapped behind a sliding gate, served as the initial disturbance condition. The number of solitons generated was verified to satisfy the prediction of inverse-scattering theory. The fully developed soliton was found to satisfy the KdV theory for all ratios of upper-layer thickness to total depth. In Part 2 of this study we investigate experimentally the evolution and breaking of an internal solitary wave as it shoals on a sloping bottom connecting the deeper region where the waves were generated to a shallower shelf region. It is found through quantitative measurements that the onset of wave-breaking was governed by shear instability, which was initiated when the local gradient Richardson number became less than The internal solitary wave of depression was found to steepen at the back of the wave before breaking, in contrast with waves of elevation. Two slopes were used, with ratios 1:16 and 1:9, and the fluid was a Boussinesq fluid with weak stratification using brine solutions. © 1985, Cambridge University Press. All rights reserved.

Description: The deflection of flow around an isolated obstacle in a rotating homogeneous fluid is investigated. Criteria for the onset of closed streamlines over an isolated obstacle are reviewed. In the flow regime where no closed streamlines exist, steady solutions for the stream function are obtained for both quasigeostrophic and finite-Rossby-number flows. A measure is proposed to allow quantitative evaluation of the flow patterns, and the dependence of deflection on obstacle volume and aspect ratio is examined. In the regime where closed streamlines can exist, the presence of a trapped vortex to the right (looking downstream) of the obstacle is investigated by means of time integration of the shallow-water equations. The significance of the trapped vortex for a real fluid is then tested through the addition of the frictional effect of Eckman pumping. © 1985, Cambridge University Press. All rights reserved.

Description: Several means for visualizing large-scale vortex structure in a turbulent mixing layer are proposed. Most of the observations are recorded along the low-speed side of the mixing layer, external to the rotational portion of the flow. Conventional correlation measurements in both the streamwise and spanwise directions indicate that the vortex structure becomes independent of the downstream coordinate in a non-dimensional distance of order λx/θi= 300–400, where λ = ΔU/2U the speed ratio and θiis the initial integral thickness. Simultaneous hot-wire measurements at 12 spanwise positions allow computer reconstruction of the velocity field as a function of span and time. These visualizations show the vortex structures to be primarily aligned across the span of the flow, but to contain irregularities. Spanwise correlation lengths are of the order of 3-5δω (δωis the local vorticity thickness). However, the large vortices typically have lengths of order 20δω when the irregularities along the span are ignored. © 1985, Cambridge University Press. All rights reserved.

Description: Measurements have been made of the pressure distribution and turbulent-boundary-layer development on the afterbody of a model engine nacelle with a jet exhausting from the base and with the jet replaced by a parallel solid sting. It was found that the effect of replacing the jet by a solid body was to increase the pressure recovery over the afterbody and hence give a lower drag than with the jet. These changes in the pressure distribution affected the boundary-layer development and turbulence structure by different methods based on a momentum integral equation and the kinetic equation for the turbulence. Both methods approximately incorporate the effects of convergence and divergence of the flow caused by changes in transverse curvature of the surface. Neither method was completely satisfactory for the prediction of the overall boundary-layer development. It was also found that, near the tail of the model, where the body radius is decreasing rapidly, the Reynolds shear stress was much lower than it would be in a two-dimensional boundary layer with the same pressure gradient. Calculations and analysis based on earlier work show that this reduction is directly related to the rates of strain associated with the convergence of the streamlines over the afterbody. © 1985, Cambridge University Press. All rights reserved.

Description: This is an experimental and theoretical study of the slow translation of a hot sphere through a fluid at rest at infinity. The viscosity depends strongly on temperature, i.e., if AT = T0—2% is the applied temperature difference and y —| (d/dT0) In µ(T0)|, then the parameter 6—y AT is large: it is about 6.5 in the experiments and is taken as infinite in the theory. The flow is determined by two large parameters, namely the Nusselt number N and the modified viscosity ratio ε1= v∝/(voθ3). The qualitative state of the flow is observed to depend on the relation between N and e. If ε-1-〉∝ (N fixed, possibly large) previous analysis (Morris 1982) shows that all the shear occurs in a thin low-viscosity film coating the sphere; this film and the associated thermal layer separate at the equator, and a separation bubble of low-viscosity fluid trails the sphere. (ii) If N-〉∝ (ε1large but fixed) even the most viscous fluid deforms, and both the drag and heat losses are found to be controlled by this highly viscous flow. The present work maps the major asymptotic states which separate these two end-states for small ε. The drag and heat-transfer laws are determined experimentally and theoretically: in addition it is shown that separation of the thermal layer ceases when the drag is controlled by the most viscous fluid, even though the heat transfer in this case can be still controlled by the dynamics of the least-viscous fluid. The heat-transfer and drag laws are also given for a sphere moving in a spherical container of finite radius. This model is shown to give a close estimate of wall effects for a sphere moving in a cylindrical container. For state (i) the theory predicts the heat transfer to within 20% and, for the smallest ε, the drag to within 30%. In the experiments ε is small enough for all limiting states to be evident but, apart from state (i), a design flaw prevents a quantitative test of the theory. For the other states, the theory is compared with numerical results from Daly & Raefsky (1985). Although the values of ε in the calculations are not small enough for the limiting states to be achieved, the theory predicts the drag to within 8% and the heat transfer to within 10%. © 1985, Cambridge University Press. All rights reserved.

Description: The absolute or convective character of inviscid instabilities in parallel shear flows can be determined by examining the branch-point singularities of the dispersion relation for complex frequencies and wavenumbers. According to a criterion developed in the study of plasma instabilities, a flow is convectively unstable when the branch-point singularities are in the lower half complex-frequency plane. These concepts are applied to a family of free shear layers with varying velocity ratio R = ΔU/2U, where ΔU is the velocity difference between the two streams and U their average velocity. It is demonstrated that spatially growing waves can only be observed if the mixing layer is convectively unstable, i.e. when the velocity ratio is smaller than Rt—1.315. When the velocity ratio is larger than Rv the instability develops temporally. Finally, the implications of these concepts are discussed also for wakes and hot jets. © 1985, Cambridge University Press. All rights reserved.

Description: The Taylor-Goldstein problem for stability of stratified shear flows of inviscid Boussinesq fluids is treated. Perturbation of a known neutral curve is used to obtain the stability characteristics in the neighbourhood of the curve. In the cases that are studied Howard's technique for perturbing neutral modes breaks down. This is related to the vanishing of a coefficient in the expansion of the dispersion relation near the neutral curve. In that case instability may occur on either side of the neutral curve. Examples are used to illustrate how unexpected behaviour arises, such as instability on both sides of a neutral curve. © 1985, Cambridge University Press. All rights reserved.

Description: An attempt is made in this paper to tackle the problem of nonlinear wave resistance by formulating it in Fourier space and by deriving a nonlinear integral equation for the wave amplitude by an approach similar to the one leading to the Zakharov equation. The procedure is illustrated for two simple examples of two-and three-dimensional travelling pressure distributions. A regular perturbation solution up to third-order terms in the slenderness parameter shows that the expansion is not uniform for small Froude numbers. A uniform, generalized, expansion is then constructed, with its leading term satisfying a new nonlinear integral equation. This rather simple integral equation, of a Volterra type, is solved numerically. The generalized wave drag is shown to be significantly larger than the one predicted by the regular perturbation expansion at small Froude number. The method adopted here has the advantage of singling out in a systematic manner the terms of the free-surface conditions which cause the small-Froude-number non-uniformity, and it is applicable to both two-and three-dimensional flows. The results are compared with existing approximate methods of computing wave drag at low Froude numbers. It is found that quasilinearized approximations may be quite accurate for the examples considered here. © 1985, Cambridge University Press. All rights reserved.

Description: An aortic-valve model is developed, having a quadratic cross-section, two rigid cusps and two wedge-shaped aortic sinuses. The flow through this valve is assumed to be one-dimensional, just as the flow behind the cusps should be one-dimensional. The resulting model equations are two nonlinear ordinary differential equations of second order for the valve opening area as a function of time in two different ranges. This model allows the size of the aortic sinus to be varied; it also permits a computation of the pressure at both sides of the cusps (unlike previous models of this kind, which consider the flow behind the cusps as stagnant). The computed valve motion due to this pressure difference is in good agreement with experimental results, although no vortex with circular streamlines is postulated in the aortic sinuses. Obviously such vortices trapped in the sinuses are not important for the valve closure, which is controlled solely by the flow deceleration. © 1985, Cambridge University Press. All rights reserved.

Description: A solid sphere falling through a Bingham plastic moves in a small envelope of fluid with shape that depends on the yield stress. A finite-element/Newton method is presented for solving the free-boundary problem composed of the velocity and pressure fields and the yield surfaces for creeping flow. Besides the outer surface, solid occurs as caps at the front and back of the sphere because of the stagnation points in the flow. The accuracy of solutions is ascertained by mesh refinement and by calculation of the integrals corresponding to the maximum and minimum variational principles for the problem. Large differences from the Newtonian values in the flow pattern around the sphere and in the drag coefficient are predicted, depending on the dimensionless value of the critical yield stress Ygbelow which the material acts as a solid. The computed flow fields differ appreciably from Stokes’ solution. The sphere will fall only when Yg is below 0.143. For yield stresses near this value, a plastic boundary layer forms next to the sphere. Boundary-layer scalings give the correct forms of the dependence of the drag coefficient and mass-transfer coefficient on yield stress for values near the critical one. The Stokes limit of zero yield stress is singular in the sense that for any small value of Ygthere is a region of the flow away from the sphere where the plastic portion of the viscosity is at least as important as the Newtonian part. Calculations for the approach of the flow field to the Stokes result are in good agreement with the scalings derived from the matched asymptotic expansion valid in this limit. © 1985, Cambridge University Press. All rights reserved.

Description: The momentum integral of a baroclinic jet of fluid in a rotating frame determines the relative size of two jets which are produced when the jet is split by a wall. Owing to lateral variation of velocity and depth of the jet, the percentage of fluid which goes to the right or left differs from that of the non-rotating jet, which is generally assumed to have no shear. For a northern hemisphere jet of zero or constant potential vorticity, much more fluid flows to the right than to the left; for a jet normal to the wall more than 65% goes to the right and less than 35% to the left. © 1985, Cambridge University Press. All rights reserved.

Description: A numerical study is made of the development with time of the two-dimensional flow of a viscous, incompressible fluid around a circular cylinder which suddenly starts rotating about its axis with constant angular velocity and translating at right angles to this axis with constant speed. The governing partial differential equations in two space variables and time are reduced to sets of time-dependent equations in one space variable by means of Fourier analysis. By truncating the Fourier series to a finite number of terms, a finite set of differential equations is solved to give an approximation to the theoretical flow. The solutions are obtained by numerical methods. Results are given for the initial development with time of the asymmetrical wake at the rear of the cylinder at Reynolds numbers R ≥ 200, based on the diameter of cylinder, and at small rotation rates. The detailed results show the formation of a Kármán vortex street. The time development of this separated flow is compared in detail at R = 200 with recent experimental results. The details of the formation and movement of the vortices behind the cylinder and the velocity profiles in several locations are virtually identical in the experimental and theoretical studies. The variations with time of the lift, drag and moment exerted by the fluid on the cylinder are determined both by calculations and by means of approximate analytical expressions. The agreement between these results at small times is excellent. © 1985, Cambridge University Press. All rights reserved.

Description: The effect of varying the initial concentration distribution is investigated for a sudden contaminant release in a uniform straight channel. Taking the optimal choice to be that which maximizes the variance of the contaminant cloud far downstream, it is found that, unless the topography is very unusual, the largest variance can be generated by splitting the contaminant into two parts, placing the larger part at the bank where the channel bed slopes most gently, and the remainder near to where the channel is deepest. This procedure significantly reduces peak concentrations far downstream when compared with making the entire release at any single point across the flow. Even at distances as large as six times the e-folding distance for cross-sectional mixing, the splitting of the discharge is shown to reduce the peak concentrations by a third. © 1985, Cambridge University Press. All rights reserved.

Description: Vertical forcing of a fluid layer leads to standing waves by means of a subharmonic instability. When the driving amplitude and frequency are chosen to be near the intersection of the stability boundaries of two nearly degenerate modes, we find that they can compete with each other to produce either periodic or chaotic motion on a slow timescale. We utilize digital image-processing methods to determine the time-dependent amplitudes of the competing modes, and local-sampling techniques to study the onset of chaos in some detail. Reconstruction of the attractors in phase space shows that in the chaotic regime the dimension of the attractor is fractional and at least one Lyapunov exponent is positive. The evidence suggests that a theory incorporating four coupled slow variables will be sufficient to account for the mode competition. © 1985, Cambridge University Press. All rights reserved.

Description: this paper the flow behind a pair of bluff bodies placed side by side in a stream is studied using a variety of flow-visualization methods. Above a critical gap size between the bodies, vortex-shedding synchronization occurs, either in phase or in antiphase. It has previously been assumed that such synchronization forms a wake comprising two parallel vortex streets in phase and in antiphase respectively. In the present paper we find that two antiphase streets are indeed formed, although in-phase shedding leads to the development of a single large-scale wake. The vortices which are formed simultaneously at the cylinders rotate around one another downstream, each pair forming a ‘binary vortex’. The combined wake comprises a street of such vortices, which we term a binary vortex street. Below a critical gap size between the bluff bodies the flow becomes asymmetric. We observe in this regime certain harmonic modes of vortex shedding whereby the shedding frequency on one side of the wake is a multiple of that on the other. Again, a large-scale wake is formed downstream. The present observations lead to a new interpretation of hot-wire-frequency data from other studies in terms of the harmonic modes. © 1985, Cambridge University Press. All rights reserved.

Description: A method is described for solving the integral equations governing Stokes flow in arbitrary two-dimensional domains. It is demonstrated that the boundary-integral method provides an accurate, efficient and easy-to-implement strategy for the solution of Stokes-flow problems. Calculations are presented for simple shear flow in a variety of geometries including cylindrical and rectangular, ridges and cavities. A full description of the flow field is presented including streamline patterns, velocity profiles and shear-stress distributions along the solid surfaces. The results are discussed with special relevance to convective transport processes in low-Reynolds-number flows. © 1985, Cambridge University Press. All rights reserved.

Description: Zakharov’s (1968) Hamiltonian formulation of water waves is used to prove analytically Tanaka’s (1983) numerical result that superharmonic disturbances to periodic waves of permanent form exchange stability when the wave energy is an extremum as a function of wave height. Tanaka’s (1985) explanation for the non-appearance of superharmonic bifurcation is also derived, and the non-existence of stability exchange when the wave speed is an extremum is explained. © 1985, Cambridge University Press. All rights reserved.

Description: The ‘stability’ of flows in symmetric curved-walled channels is investigated by essentially combining Fraenkel’s ‘small’ wall-curvature theory with the multiple-scaling (or WKB) method. The basic flow is characterized by the steady-state stream function Ω, which varies ‘ slowly ’ in the streamwise direction. An asymptotic scheme is posed for Ω in such a way that at lowest order Ω represents a class of Jeffery-Hamel solutions. An infinitesimal disturbance is superimposed on the basic flow through a time-dependent stream function Φ, and the resulting linearized disturbance equation suggests that fixed-frequency disturbances with ‘slowly’ varying wavenumber are appropriate. The asymptotic scheme for Φ yields the Orr-Sommerfeld equation at lowest order. Two classes of channels are considered. In the first class the curvature is constant in sign, and under certain conditions they reduce to symmetric divergent straight-walled channels. In the second class of channels the curvature varies in sign, and these may be more suitable for experimentation. A spatially dependent growth rate of the disturbance relative to the basic flow is defined; this forms the basis of the ‘stability’ analysis. Critical Reynolds numbers are deduced, below which the disturbance decays as it travels downstream, and above which the disturbance grows for a limited range in the streamwise direction. For the first class of channels the ‘ stability ’ analysis is carried out locally, and the dependence of the critical Reynolds numbers on curvature and higher-order terms is investigated. For the second class of channels the ‘stability’ analysis is carried out at various positions downstream, and an overall minimum critical Reynolds number is predicted for a range of channels and flows. © 1985, Cambridge University Press. All rights reserved.

Description: We have developed a compact and cost-effective shock tube to simulate the static and dynamic pressures of blast waves. The shock tube is open at both ends and is driven by high explosives distributed over a finite length of the tube near one end. The overall charge length is determined by the simulation time of interest, and the charge-density distribution is tailored to produce the pressure-waveform shape desired. For the shock tube to simulate a typical blast wave, the charge density must be highest at the charge front (closest to the test section) and gradually reduced towards the back. The resulting shock tube is an order of magnitude shorter than a conventional dynamic airblast simulator (DABS) in which concentrated explosives are used to drive the shock. Tailored charges designed using this method were built and tested in a simulation development programme sponsored by the U.S. Defense Nuclear Agency (DNA). The pressures measured for several charge distributions agreed very well with SRI's PUFF hydrocode computations and demonstrated the feasibility of the compact simulator under realistic test conditions. © 1985, Cambridge University Press. All rights reserved.

Description: The dynamics of two-dimensional uniform wavetrains on the interface between a viscoelastic compliant coating and a boundary-layer flow are explored theoretically. The coating is treated as a single-layer isotropic Voigt material of finite thickness that is bonded to a rigid half-space. The flow is modelled first by potential theory and then modified to incorporate pressure phase shifts and magnitudes found in boundary-layer flow over wavy walls. The consideration of viscoelastic effects has led to an important dimensionless damping parameter ϒt= Ctτt/d (where Tt is the strain relaxation time, Ctis the elastic shear-wave speed andd is the layer depth) that seems to have been overlooked by experimentalists. The flow and the damping are found to have dramatic effects on wave propagation. Using flow pressure and material-damping parameters typical of experiments, the results show that both upstream-and downstream-propagating waves exist at low flow speeds. At higher flow speeds, shorter waves can no longer propagate upstream. At still higher velocities, two instabilities, static divergence and ‘flutter’, are found. Static divergence occurs for flow speeds above 2.86Ctand consists of slow waves moving with speeds of about 0.02Ct. These results compare fairly well with published experimental data. Static divergence is found to be a damping instability for these coating systems. When the flow speed is increased further, the flutter instability appears consisting of waves with phase speeds about equal to Ct. © 1985, Cambridge University Press. All rights reserved.

Description: In order to model the fluid dynamics of Korotkoff sound generation when the artery under the cuff is fully collapsed during most of the heart cycle, the characteristics of pressure-wave propagation in a long silicone-rubber tube were studied experimentally. The central portion of this tube was designed to collapse to zero cross-sectional area as a result of high negative transmural pressure, thus simulating a collapsed artery. Propagation of a single half-sinusoidal pressure wave in and around this segment was studied in detail by pressure, velocity and tube-longitudinal-shape measurements. A very steep wave front (shock wave) capable of producing a short tapping sound was formed by an overtaking phenomenon in the fully collapsed tube segment and it propagated into the inflated tube distal to the collapsed segment. An empirical equation relating the flow rate penetrating into the collapsed segment, the incident-wave pressure and the external pressure Pc over the collapsed segment was obtained. This equation predicts that the pressure-wave propagation in a fully collapsed segment depends only on the flow rate into the collapsed segment. The initial internal pressure of the tube distal to the collapsed segment Pdd is one independent variable in the high-cuff-pressure condition. The amplitude of the steep wave front and the shape of the pressure wave in the inflated tube distal to the collapsed segment are governed by Pc - Pdd and the flow rate penetrating the collapsed segment. For the same flow rate, if Pc - Pdd is lower than a critical value, the amplitude of the pressure in the distal tube decreases with increasing Pdd because of positive pressure-wave reflection at the exit of the collapsed segment. On the other had, if Pc — Pdd is higher than that value, no wave reflection occurs and the amplitude of the pressure wave is independent of Pdd. In the latter case a severe constriction exists near the distal end of the collapsed segment, and flow occurs as two thin high-speed jets. © 1985, Cambridge University Press. All rights reserved.

Description: Observed statistics of non-breaking ocean-surface gravity waves shoaling between 4 and 1m depths are compared with the predictions of linear finite-depth theory and a nonlinear model. The linear theory included effects of the directional distribution of energy within each frequency component. The nonlinear model, which does not consider directional effects, is based on Boussinesq-type equations for a sloping bottom (Freilich & Guza 1984). Given initial conditions in 4m depth, the nonlinear model more accurately predicts the evolution of energy spectra, coherence and phase speed between sensors, and lengths of runs of high waves than does the linear theory. In four out of five cases, observed trends in the evolution of sea-surface-elevation skewness are predicted by the nonlinear model, while linear theory predicts zero skewness. Neither model can explain changes in the directional spectra observed between 9 and 4m depths. © 1985, Cambridge University Press. All rights reserved.

Description: The marginal separation of a laminar incompressible boundary layer on the line of symmetry of a three-dimensional body is discussed. The interaction itself is taken to be quasi-two-dimensional but the results differ from those for a two-dimensional boundary layer in that the effect of the gradient of the crossflow is included. Solutions of the resulting integral equation are computed for two values of the additional parameter, and comparisons made with an analytical prediction of the asymptotic form as the length of the separation bubble tends to infinity. The occurrence of the phenomenon is confirmed by an examination of the results of an existing numerical integration of the boundary-layer equations for the line of symmetry of a paraboloid. © 1985, Cambridge University Press. All rights reserved.

Description: The model penetrative-convection problem of ice-water convection is considered. Analytical progress is made through the remarkable simplification that horizontally long convection cells are preferred when the heat flux is fixed on the boundaries (Chapman & Proctor 1980). However, a linear analysis shows that long horizontal scales are preferred only when the convection is mildly penetrative (i.e. the overlying layer of stable fluid is not deep). A straightforward nonlinear asymptotic analysis of the convection only provides the relatively uninteresting information that the convection is subcritical. Using the technique of reconstitution (Roberts 1985) to provide higher-order corrections to the asymptotic theory, flow properties at larger amplitudes are calculated and predictions about the extent of the subcriticality are made. © 1985, Cambridge University Press. All rights reserved.

Description: Results of laboratory experiments are used to determine the morphology and the ascent rate of growing buoyant plumes in a homogeneous, viscous fluid. The plumes were formed by injecting a glucose solution through a small orifice into another glucose solution of different density. Two classes of creeping (low-Reynolds-number) plumes are investigated: (i) diapiric plumes, for which the plume viscosity is approximately equal to the ambient-fluid viscosity, and (ii) cavity plumes, for which the plume fluid is much less viscous than the ambient fluid. Fully developed diapirs consist of a tapered cylindrical stem capped by a mushroom-shaped vortex at its leading edge. Fully developed cavity plumes consist of a nearly spherical chamber connected to the source by a narrow umbilical conduit. It is observed that the ascent velocity of cavity plumes increases with time as t⅖. The ascent velocity of diapirs is found to be proportional to the terminal velocity of a cylinder moving parallel to its axis. The presence of pre-existing conduits alters the morphology of cavity plumes and greatly increases their ascent rate. Fossil conduits act as plume guides by offering low-resistance ascent paths. Finally, a series of experiments have been made on the interaction between cavity plumes and a large-scale background circulation. A low-viscosity plume generated by a source towed steadily through a highly viscous fluid breaks into a chain of regularly spaced, individual cavities, as first demonstrated by Skilbeck & Whitehead. The cavities ascend as an inclined linear array of Stokes droplets. Dimensional analysis is used to derive scaling laws for the cavity volumes and their replication rate in terms of the source parameters and the tow speed. The qualitative results from these experiments generally lend support to the hypothesis that buoyant plumes in the Earth’s mantle are the source of hot-spot volcanism. In particular the experiments suggest an explanation for the observation that hot spots remain nearly fixed in the presence of mantle convection. © 1985, Cambridge University Press. All rights reserved.

Description: The stability of fully developed pipe-Poiseuille flow to finite-amplitude axisymmetric and non-axisymmetric disturbances has been studied using the equilibrium-amplitude method of Reynolds & Potter (1967). In both the cases the least-stable centre-modes were investigated. Also, for the non-axisymmetric case the mode investigated was the one with azimuthal wavenumber equal to one. Many higher-order Landau coefficients were calculated, and the Stuart—Landau series was analysed by the Shanks (1955) method and by using Pade approximants to look for the existence of possible equilibrium states. The results show in both cases that, for each value of the Reynolds number R, there is a preferred band of spatial wavenumbers a in which equilibrium states are likely to exist. Moreover, in both cases it was found that the magnitude of the minimum threshold amplitude for a given R decreases with increasing R. The scales of the various quantities obtained agree very well with those deduced by Davey & Nguyen (1971). © 1985, Cambridge University Press. All rights reserved.

Description: The propagation of flexural waves in floating ice plates is governed by two restoring forces-elastic bending of the plate, and the tendency of gravity to make the upper surface of the supporting water horizontal. This paper studies steady wave patterns generated by a steadily moving source on a water-ice system that is assumed to be homogeneous and of infinite horizontal extent, using asymptotic Fourier analysis to give a simple description of the wave pattern far from the source. Short-wavelength elastic waves propagate ahead, while the long gravity waves appear behind; and, depending on the system parameters, one, two or no caustics may appear. Wavecrest patterns are shown, and the amplitude variation with direction from the source is given. Where the two caustics just merge together, a special mathematical function analogous to the Airy function is introduced to describe wave amplitudes. These waves can be detected by a strainmeter embedded in the ice, and we compare its theoretical response with some experimental measurements. © 1985, Cambridge University Press. All rights reserved.

Description: Two-and three-lobed oscillations of a rotating liquid drop immersed in an immiscible fluid of comparable density and the same angular velocity were studied experimentally. Using acoustically suspended drops, it has been found that the relative change in the resonance frequencies of the axisymmetric drop-shape oscillations Δωl/ω(0)lis proportional to the square of the normalized angular speed (Ω/ωl(0))2when ωl〉 2Ω. This is in agreement with a recent analytical study of the same problem. Some preliminary results regarding the effect of rotation on the free-decay rate of the two-lobed oscillations are also presented. © 1985, Cambridge University Press. All rights reserved.

Description: The transition from steady axisymmetric Taylor vortices to time-dependent wavy vortices is examined. The critical Taylor number and frequency at the transition point are determined in the infinite-cylinder approximation for a wide range of parameters. The results are compared with long-aspect-ratio experiments. The variation with axial wavelength is examined, and is found to be important when the radius ratio η〈0.75. A new spatially subharmonic mode is found to be the most unstable mode in some parameter regimes. This mode is identified with the jet mode recently discovered experimentally by Lorenzen, Pfister & Mullin and by Cole. © 1985, Cambridge University Press. All rights reserved.

Description: A series of melting experiments with a moving horizontal cylindrical heat source at constant surface heat flux have been performed. The heat source was designed in such a way that it could descend under its weight while melting the phase-change material (n-octadecane) surrounding it. The heat-source velocity was measured and the motion and shape of the solid—liquid interface were determined photographically. The effects of the surface heat flux, the density and initial position of the heat source, and the initial subcooling of the solid were investigated and are discussed. Conduction was found to be the dominant heat-transfer mechanism around the lower stagnation point and controlled the terminal velocity of the source. The fluid motion in the melt pool above the heat source was mainly induced by the descent of the source, while natural convection played only a relatively minor role in the motion. © 1985, Cambridge University Press. All rights reserved.

Description: A linear theory is developed in the time domain for vertical motions of an axisymmetric cylinder floating in the free surface. The velocity potential is obtained numerically from a discretized boundary-integral-equation on the body surface, using a Galerkin method. The solution proceeds in time steps, but the coefficient matrix is identical at each step and can be inverted at the outset. Free-surface effects are absent in the limits of zero and infinite time. The added mass is determined in both cases for a broad range of cylinder depths. For a semi-infinite cylinder the added mass is obtained by extrapolation. An impulse-response function is used to describe the free-surface effects in the time domain. An oscillatory error observed for small cylinder depths is related to the irregular frequencies of the solution in the frequency domain. Fourier transforms of the impulse-response function are compared with direct computations of the damping and added-mass coefficients in the frequency domain. The impulse-response function is also used to compute the free motion of an unrestrained cylinder, following an initial displacement or acceleration. © 1985, Cambridge University Press. All rights reserved.

Description: Equilibrium shapes of two-dimensional rotating configurations of uniform vortices are numerically calculated for two to eight corotating vortices. Additionally, a perturbation series is developed which approximately describes the vortex shapes. The equilibrium configurations are subjected to a linear stability analysis. This analysis both confirms existing results regarding point vortices and shows that finite vortices may destabilize via a new form of instability derived from boundary deformations. Finally, we examine the energetics of the equilibrium configurations. We introduce a new energy quantity called ‘excess energy’, which is particularly useful in understanding the constraints on the evolution of unstable near-equilibrium configurations. This theory offers a first glance at nonlinear stability. As an example, the theory explains some features of the merger of two vortices. © 1985, Cambridge University Press. All rights reserved.

Description: The early phase of the establishment of the flow past a circular cylinder started impulsively into rotation and translation is investigated by visualizing the flow patterns with solid tracers and by analysing qualitatively (flow topology) and quantitatively (velocity distributions and singular-point trajectories) the corresponding photographs. The range considered corresponds to moderate Reynolds numbers (Re 1000). The rotating-to-translating-speed ratio a increases from 0 to 3.25 and the motion covers a period during which the cylinder translates 4.5 or even 7 times its diameter. The details of the mechanisms of the near-wake formation are considered in particular and the increase of the flow asymmetry with increase in rotation is pointed out. Thus the existence of two regimes has been confirmed with the creation or non-creation of alternate eddies after an initial one E1. Furthermore, the new phenomena of saddle-point transposition and intermediate-eddy coalescence have been identified in the formation or shedding of respectively the odd and even subsequent eddies Ei(i = 2,3,.) when they exist. The very good agreement between these experimental data and the numerical results of Badr & Dennis (1985), obtained by solving the Navier-Stokes equations and presented in a parallel paper, confirms their respective validity and permits the determination of the flow characteristics not accessible, or accessible only with difficulty, to the present experiments. These flow properties such as drag and vorticity are capable of providing information on the Magnus effect for the former property and on unsteady separated flows for the latter. © 1985, Cambridge University Press. All rights reserved.

Description: A two-dimensional model of flow and bed topography in sinuous channels with erodible boundaries is developed and applied in order to investigate the mechanism of meander initiation. By reexamining the problem recently tackled by Ikeda, Parker & Sawai (1981), a previously undiscovered ‘resonance’ phenomenon is detected which occurs when the values of the relevant parameters fall within a neighbourhood of certain critical values. It is suggested that the above resonance controls the bend growth, and it is shown that it is connected in some sense with bar instability. In fact, by performing a linear stability analysis of flow in straight erodible channels, resonant flow in sinuous channels is shown to occur when curvature ‘forces’ a ‘natural’ solution represented by approximately steady perturbations of the alternate bar type. A comparison with experimental observations appears to support the idea that resonance is associated with meander formation. © 1985, Cambridge University Press. All rights reserved.

Description: Measurements are presented for low-Reynolds-number turbulent boundary layers developing in a zero pressure gradient on the sidewall of a duct. The effect of rotation on these layers is examined. The mean-velocity profiles affected by rotation are described in terms of a common universal sublayer and modified logarithmic and wake regions. The turbulence quantities follow an inner and outer scaling independent of rotation. The effect appears to be similar to that, of increased or decreased layer development. Streamwise-energy spectra indicate that, for a given non-dimensional wall distance, it is the low-wavenumber spectral components alone that are affected by rotation. Large spatially periodic spanwise variations of skin friction are observed in the destabilized layers. Mean-velocity vectors in the cross-stream plane clearly show an array of vortex-like structures which correlate strongly with the skin-friction pattern. Interesting properties of these mean-flow structures are shown and their effect on Reynolds stresses is revealed. Near the duct centreline, where we have measured detailed profiles, the variations are small and there is a reasonable momentum balance. Large-scale secondary circulations are also observed but the strength of the pattern is weak and it appears to be confined to the top and bottom regions of the duct. The evidence suggests that it has minimally affected the flow near the duct centreline where detailed profiles were measured. © 1985, Cambridge University Press. All rights reserved.

Description: This paper has three main objectives. First, it aims to show that basic general conservation principles for viscous flow can be formulated in terms of diffusion and convection. Secondly, it aims to show that three scalar conservation principles suffice to provide a method for characterizing swirling axisymmetric flows in terms of axial and boundary production of the conserved quantities. Thirdly, it aims to exemplify these two objectives by giving a complete specification of the axial causes for swirl-free conically similar flow in otherwise free space. This series of papers, overall, is concerned with the analysis and characterization of swirling conically similar flows in terms of the singularities that generate the conserved quantities. In conically similar flows there is no natural lengthscale, and the sole parameters governing the flow are provided by the strengths of the singularities that cause the flow. These are required to have the same dimensions as a power of the kinematic viscosity v. The axisymmetric flow generated by uniform production of swirl angular momentum per unit mass along a half-axis at a constant rate provides a simple example. In conically similar flow the three conservation principles for axisymmetric flow provide a sixth-order non-autonomous system of two ordinary differential equations governing the flow. Here, in Part 1, these equations are derived for the general case of swirling flow, and are shown to reduce to a fourth-order system when swirl is absent. The two scalar conservation principles describing swirl-free flow are used to classify the basic axial causes for this system. Part 2 analyses these basic exact one-parameter swirl-free families of solutions, and Part 3 extends the analysis to the remaining one-parameter family of swirling flows associated with uniform swirl angular-momentum production on a half-axis. Each of the families is characterized by a single independent cause, and two of them provide new non-trivial solutions of the Navier-Stokes equations. The effects of nonlinear coupling of these basic one-parameter causes and of conically similar distributions over conical boundaries will be examined in later papers. © 1985, Cambridge University Press. All rights reserved.

Description: This paper describes the calculation of the added-mass and damping coefficients of a submerged toroidal body that is undergoing a forced, periodic heaving motion. The velocity potential of the motion is expressed as an infinite sum of toroidal multipole potentials, and the problem is solved in a manner analogous to Ursell's classical solution for a submerged circular cylinder in two dimensions. When the torus is ‘slender’, in the sense that its tubular radius is small compared with its overall diameter, relatively simple closed-form asymptotic approximations for the added-mass and damping coefficients are obtained. This work is motivated by the proposed RS-35 design of ring-hulled semisubmersible platform. © 1985, Cambridge University Press. All rights reserved.

Description: Thermally induced flow instabilities in uniformly heated boiling channels have been studied analytically. The classical homogeneous equilibrium model was used. This distributed model was transformed into an integrodifferential equation for inlet velocity. A linear analysis showed interesting features (i.e. islands of instability) of the marginal stability boundary which appear when the effects of gravity and friction were systematically considered. A quasilinear Hopf-bifurcation analysis, valid near the marginal-stability boundaries, gives the amplitude and frequency of limit-cycle oscillations that can appear on the unstable side of the boundary. The analysis also shows cases where a finite-amplitude perturbation can cause a divergent instability on the stable side of the linear-stability boundary. © 1985, Cambridge University Press. All rights reserved.

Description: The dispersion of fluid particles in a turbulent flow is described by transition-probability density functions. A renormalized expansion is made to establish the evolution equations of these functions. The resulting equations are nonlinear integrodifferential equations written in terms of Eulerian velocity-correlation functions. For the dispersion of a single particle, the equation at the zeroth order is the same as the one obtained by Roberts (1961). For the relative dispersion of a pair of particles, the equation is more convenient for applications than those of other theories. With this equation, Richardson's 4/3-power law for relative diffusion is recovered analytically based upon the Kolmogoroff spectrum and numerically based upon the von Kármán spectrum and a smoothed experimental spectrum. © 1985, Cambridge University Press. All rights reserved.

Description: The problem of slow draining of incompressible fluid from a rotating cylindrical vessel is considered. Transient effects, internal viscosity, boundary friction and finite cylindrical boundaries are included. In addition a tornado model formulated by Turner is solved and compared with some experiments on rotating turbulence of Hopfinger, Browand & Gagne. © 1985, Cambridge University Press. All rights reserved.

Description: It was shown in Part 1 of this series that in swirl-free flow there are three different types of axial causes of steady conically similar viscous flow. The three corresponding swirl-free one-parameter families of exact solutions to the Navier-Stokes equations are presented and analysed here in terms of the basic conservation principles for volume and ring circulation. The simplest is the irrotational flow generated by a uniform distribution of volume sources along a half-axis. A second, independent, one-parameter family of solutions is provided by Landau's (1943) solution, where the second moment of ring circulation about the axis is produced at the origin at a finite constant rate. Fresh insight into the nature of this flow is gained by separating and comparing the roles of the diffusion and convection terms in the flux vector for ring circulation. A similar analysis is applied to the remaining independent one-parameter family caused by an antisymmetric (about the origin) conically similar axial distribution of the singularity in Landau's solution. This simple new family of exact solutions is characterized by opposed jets neighbouring the axis of symmetry. When the axial jets are directed inwards, they always erupt into an emergent axisymmetric jet normal to the axis of symmetry. Solutions fail to exist, however, for sufficiently strong axial jets directed outwards. © 1985, Cambridge University Press. All rights reserved.

Description: In studying head-sea diffraction by a slender body, Haren & Mei (1981) found, at a special frequency, a singularity inherent in the cross-section (inner) mathematical problem. In this note this singularity is interpreted, and it is shown that the head-sea problem is similar to the problem of an acoustic duct being excited at one end by a pressure field. As a consequence, the head sea is not always refracted away from the body, since the solution remains oscillatory for frequencies above that special frequency. © 1985, Cambridge University Press. All rights reserved.

Description: The motions of vortices around single cylinders and around pairs of cylinders in relative sinusoidal flow are investigated in this paper. Using simultaneous flow visualization and force measurements, the vortex motions are related to the fluid-induced lift and in-line forces. For the single cylinder, several repeatable patterns of vortex shedding are identified within particular ranges of flow amplitude. The process of pairing of vortices from a previous half cycle with those in a present half cycle is fundamental to all the patterns. Visualization is shown to be more effective in a reference frame which is fixed with respect to the undisturbed fluid rather than with respect to the cylinders. For this reason, the examples of vortex motions are taken from a rig in which vertical cylinders are oscillated in a tank of fluid. By oscillating a pair of cylinders over a range of gaps, orientations and amplitudes, it is found that the vortex-shedding patterns identified for a single cylinder can synchronize either in phase or in antiphase between the two cylinders. Such observations help to explain how lift and in-line forces are influenced by cylinder proximity and in some cases these forces are significantly magnified. Force coefficients are evaluated for both the single cylinder and the pair of cylinders. © 1985, Cambridge University Press. All rights reserved.

Description: Detailed mean-flow and turbulence measurements have been made in a low-speed turbulent boundary layer in zero pressure gradient with an isolated, artificially generated vortex imbedded in it. The vortex was generated by a half-delta wing on the floor of the wind-tunnel settling chamber, so that the vortex entering the working section had the same circulation as that originally generated, while axial-component velocity variations were very much reduced, relative to the local mean velocity, from values just behind the generator. The measurements show that the circulation around the vortex imbedded in the boundary layer is almost conserved, being reduced only by the spanwise-component surface shear stress. Therefore the region of flow affected by the vortex continues to grow downstream, its cross-sectional dimensions being roughly proportional to the local boundary-layer thickness. The behaviour of the various components of eddy viscosity, deduced from measured Reynolds stresses, and of the various triple products, suggests that the simple empirical correlations for these quantities used in present-day turbulence models are not likely to yield flow predictions which are accurate in detail. © 1985, Cambridge University Press. All rights reserved.

Description: The unsteady two-dimensional heat-transfer problem of melting around a horizontal heated cylinder is studied numerically. The cylinder is heated isothermally. A physical model is introduced which accounts for the effects of density change upon melting and subcooling effect, as well as natural convection. Most previous work has assumed that the density number (ratio of solid density to liquid density) is unity. In practice, all solid materials exhibit some density change upon melting. If the density number is greater than one, this induces a blowing effect at the phase-change boundary. If the density number is less than one, a suction effect is produced. This study indicates that the density-change effect on heat transfer during melting is minor. Subcooling results when the solid is at a temperature below the melting temperature. When the melting process begins, some of the available thermal energy must be used as sensible heat, to raise the solid's temperature to the melting point. As a result, less thermal energy is available for melting. Subcooling effects are found to have a substantial effect on the heat-transfer process. The effects of natural convection have been clearly documented, and indicate that natural convection must be included in any realistic model of the melting process. Detailed predictions of the effects of density change and subcooling on the melting process are given. Information on the temperature and flow fields for representative values of Stefan, Rayleigh, Prandtl, subcooling and density number is given. Further results from the numerical solutions include information on local and average heat-transfer rates and sensible-heat gain as well as melt volume as a function of time. Comparisons are made with earlier numerical and analytical results. © 1985, Cambridge University Press. All rights reserved.

Description: The permeability of a random array of fixed spheres has been calculated over the range of volume fractions from dilute to almost closest packing, by assuming pairwise-additive (low-Reynolds-number) hydrodynamic interactions within an effective medium. Non-convergent pair interactions arising from the long-range decay of the Stokeslet were removed by renormalizing the Stokes equation to determine the permeability of the effective medium, i.e. to include the mean screening effect of the other spheres. Pair interactions in this Brinkman medium were calculated by the method of reflections in the far field and boundary collocation in the near field. The permeability predicted by the theory asymptotes correctly to established results for dilute arrays, and compares favourably (within 15%) with the Carman correlation for volume fractions between 0.3 and 0.5. The magnitude also falls within the range of exact results for periodic arrays at the higher concentrations, but our model does not reproduce the dependence on structure. Use of the Brinkman equation with an effective viscosity leads to an apparent slip velocity at the boundary of a porous medium. Our calculation of the bulk stress via volume averaging determines the effective viscosity and hence the slip coefficient unambiguously for dilute porous media. However, at concentrations corresponding to the available experimental results the lengthscale characterizing pressure or velocity gradients becomes comparable to the interparticle spacing, and the averaging technique fails. Indeed the Brinkman equation itself is no longer valid. © 1985, Cambridge University Press. All rights reserved.

Description: Acoustic emission by vortex–edge interaction is investigated both theoretically and experimentally. The theory of vortex sound enables us to represent the far-field pressure in terms of the vortex motion near the half-plane edge. It is found that the pressure p depends on the product of an angular factor representing directionality and a time factor representing wave profile. The pressure formula leads to the scaling law [formula omitted] for the sound emitted by a vortex ring of velocity U, L being the nearest distance of the vortex path to the edge. The sound intensity is proportional to U5 and shows cardioid directionality pattern. The vortex ring used in the experiment had radius about 4.7 mm and velocity ranging from 29 to 61 m/s. The above scaling law of the pressure and the cardioid directionality of the intensity were reproduced in the experiment with reasonable accuracy. Especially notable is the agreement between the predicted and observed wave profiles. The theoretical profile is determined by the [formula omitted] time derivative of the volume flux (through the vortex ring) of a hypothetical potential flow around the edge. © 1985, Cambridge University Press. All rights reserved.

Description: An extensive set of numerical simulations is performed to synthesize the behaviour of a barotropic flow over isolated topography on an f-plane and on a β-plane. The model is based on the quasi-geostrophic vorticity equation, where the dissipation terms have been retained. The use of open boundary conditions, following the method described by Orlanski (1976), allows detailed simulation of time-dependent flows over long periods. On the f-plane, the ultimate solution is always characterized by a typical vorticity field with an anticyclonic vortex trapped over the topography, but different transient regimes occur, related to the importance of advection versus topography effect: direct advection of the positive vortex for strong flows; eddy interactions and double-vortex-structure appearance for weaker flows; oscillatory regimes with topographic trapped-waves generation for very strong vorticity-interaction cases. On the β-plane, and for prograde flows, the situation is complicated by a Rossby wave pattern extending mainly downstream but also having an upstream component corresponding to zonal waves. For retrograde flows the obstacle does not excite Rossby waves but a transient response with zonal waves whose lifetime depends on the nonlinearity. © 1985, Cambridge University Press. All rights reserved.

Description: The effects of internal circulation in bubbles and droplets have been analysed by means of a semi-analytical series-truncation method. The equations of motion are transformed into a series of coupled, ordinary, nonlinear differential equations by use of orthogonal sets. These infinite-series equations are then truncated adequately and solved numerically. Using this series-truncation method, we have evaluated the effects of different ratios (between the continuous and dispersed phases) of both density and viscosity for the flows of low Reynolds numbers. For all the density ratios investigated, the density difference has almost no effect on the drag coefficient at low Reynolds numbers. The shear stress and the drag coefficient increase with increasing viscosity ratio of droplet to ambience and decrease with increasing Reynolds number. © 1985, Cambridge University Press. All rights reserved.

Description: The Reynolds-averaged Navier-Stokes equations are solved numerically for supersonic flow over a blunt fin mounted on a flat plate. The fin shock causes the boundary layer to separate, which results in a complicated, three-dimensional shock-wave and boundary-layer interaction. The computed results are in good agreement with the mean static pressure measured on the fin and the flat plate. The main features, such as peak pressure on the fin leading edge and a double peak on the plate, are predicted well. The role of the horseshoe vortex is discussed. This vortex leads to the development of high-speed flow and, hence, low-pressure regions on the fin and the plate. Different thicknesses of the incoming boundary layer have been studied. Varying the thicknesses by an order of magnitude shows that the size of the horseshoe vortex and, therefore, the spatial extent of the interaction are dominated by inviscid flow and only weakly dependent on the Reynolds number. Coloured graphics are used to show details of the interaction flow field. © 1985, Cambridge University Press. All rights reserved.

Description: An asymptotic scheme is derived for calculating values of the ‘ reflected ’ Stokeslet-field velocity dyadic V and its gradient ∇V back at the Stokeslet location for situations in which this singular point lies in close proximity to the wall of an infinitely long circular cylinder. The asymptotic formulas furnished by this scheme permit calculations of first-and second-order wall effects in the non-dimensional parameter K = a/R0(a ≡ characteristic particle radius, R0≡ cylinder radius) upon the Stokes resistance of a particle of arbitrary shape, location and orientation when translating and/or rotating near the wall of an otherwise quiescent fluid-filled or fluid-surrounded circular cylinder. This reflection-type calculation is applicable for circumstances in which the inequalities K ≪ 1 and 1-β≪1 1 are each separately satisfied, while simultaneously K/(1-β)≪ 1. (Here β = b/R0is the fractionally eccentric Stokeslet location, or equivalently the centre of reaction of the particle, with b its distance from the tube axis.) The main result of this paper is the development of the pair of asymptotic wall-correction formulas to particle resistance, with W = Wjkand ∇W = Wkl.jrespectively the non-dimensional normalized wall-effect dyadic and its gradient at the Stokeslet location β. The numerical, rational fraction, β-independent,nCjkandnDjklcoefficients (n = 0, 1, 2) appearing above are evaluated by solving a recursive sequence of Stokes-flow boundary-value problems in the semi-infinite fluid domain bounded by a plane wall. These simple asymptotic formulas are shown to agree excellently in the range near β = 1 with existing values derived from the exact solution of the original circular-cylinder boundary-value problem, involving tedious infinite-series summations of complicated Bessel-function integrands extended over infinite integration domains. Generalizations of the scheme to particle motion in the space external to a circular cylinder is briefly sketched, as too is the case of cylinders of non-circular cross-section. © 1985, Cambridge University Press. All rights reserved.