bluuebunny/crossref_metadata_2025 huggingface dataset:
Numerical study of slightly viscous flow
Authors: Chorin Alexandre Joel
Published: March 2006

A numerical method for solving the time-dependent Navier–Stokes equations in two space dimensions at high Reynolds number is presented. The crux of the method lies in the numerical simulation of the process of vorticity generation and dispersal, using computer-generated pseudo-random numbers. An application to flow past a circular cylinder is presented.
Cnoidal waves and bores in uniform channels of arbitrary cross-section
Authors: Fenton J. D.
Published: March 2006

A steady nonlinear dispersive wave theory is developed in terms of three important invariants of channel flow: discharge, energy, and momentum flux. As such, the work is an extension of Benjamin & Lighthill's approach for rectangular channels.

Considering the differential equation obtained, we examine the behaviour of flows and wave systems in arbitrary channels for changes of energy and momentum. In particular, the bore problem is studied, and previous approaches to this problem, using linear wave theory, are seen to be invalid. The present theory describes several phenomena of open-channel flow, explains a scatter in previously obtained experimental results, and enables simple design recommendations to be made for channels in which stationary or moving bores are expected.

While this work does describe the variation of physical quantities across the channel section, there are some important three-dimensional phenomena, noted experimentally, which remain unexplained.
On the possibility of turbulent thickening of weak shock waves
Authors: Williams J. E. Ffowcs , Howe M. S.
Published: March 2006

This paper examines the possible thickening of an initially sharp sonic boom by the turbulence it encounters in passing to the ground. Three apparently different viewpoints, all indicating substantial thickening, are shown to be actually identical and to give an irrelevant upper bound on wave thickness. All three approaches describe only the apparent mean diffusion induced by random convection of a sharp wave about its nominal position. Although a wave-front folding mechanism ultimately accounts for an apparent thickening as individual rays are weakened and tangled by turbulence, this process is too slow to be effective in the practical boom situation. The paper then considers what linear thickening of a wave packet results from propagation trough atmospheric turbulence and concludes that, in the relevant limit, a wave may be thickened by a factor of about 2 at the most. The conclusion is therefore reached that atmospheric turbulence cannot be the cause of the thousandfold discrepancy between the measured wave fronts and their Taylor thickness.
The critical state: a trapped wave model of vortex breakdown
Authors: Randall J. D. , Leibovich S.
Published: March 2006

A model of vortex breakdown is presented and its predictions compared with the experiments of Sarpkaya (1971). The model is cntred about a theory of long, weakly nonlinear waves propagating on critical flows in tubes of variable cross-section. Although the weakly nonlinear theory must be extended beyond its domain of formal validity, many of the experimentally observed features of vortex breakdown are reproduced by the model. The description of the time evolution of the flow field that is presented requires numerical calculations that are not simple, but some important conclusions may be determined by easy computations. In particular, the axial position of a breakdown may be found from a very simple equation (10).
On the stratified Taylor column
Authors: Hogg Nelson G.
Published: March 2006

We analyse the effects of small, circularly symmetric topography on the slow flow of an inviscid, incompressible, diffusionless, horizontally uniform, baroclinic current and show that the vertical influence depends primarily on three parameters: a stratification measureS(the square of the ratio of buoyancy frequency times height scale to Coriolis parameter times length scale), a topographic parameter β (ratio of scaled topographic height multiplied by scaled bottom current to Rossby number ε) and the scaled upstream shearu′0(z) (the dimensional upstream shear divided by the ratio of the r.m.s. upstream flow speed to height scale).

Investigating a linear stratification model we find that the topographic effect is depth independent ifS[lsim ] ε and a Taylor column, as indicated by the appearance of closed streamlines above the bump, exists when β > 2. Moderate stratification (S∼ 1) causes the flow to be fully three-dimensional and the Taylor column to be a conical vortex whose height depends on βSandu′0). The results are compared with Davies's (1971, 1972) experiments.

Our results tend to support the Taylor column theory of Jupiter's Great Red Spot but effects due to variations in the Coriolis parameter with latitude have been (unjustifiably) ne glected. Using typical values for the earths oceans we find that Taylor columns of significant height could be found there. Some pertinent observations from the ocean are discussed.
On bubbles with small immobile adsorbed films rising in liquids at low Reynolds numbers
Authors: Harper J. F.
Published: March 2006

Surface-active impurities may collect as a stationary film on the lowest part of a bubble rising in liquid while the remainder of the surface moves freely. Numerical approximations for the motion are available if the Reynolds number is low, but they fail for small films. We give the steady-state asymptotic solution for that case, and obtain the perturbation of the drag coefficient from its value for a completely free surface. It depends on the amount by which the surface tension is reduced at the rear stagnation point. This reduction has usually been taken to be the maximum possible for the particular impurity; we consider also the case where dilution is so great that that maximum cannot be reached because the impurity would then be diffusing off the surface at the rear faster than onto it elsewhere.
A numerical method for integrating the unsteady boundary-layer equations when there are regions of backflow
Authors: Phillips J. H. , Ackerberg R. C.
Published: March 2006

A numerical method for integrating the unsteady twodimensional boundarylayer equations using a second-order-accurate implicit method, which allows for arbitrary mesh spacing in the space and time variables, is developed. A unique feature of the method is the use of an asymptotic solution valid at the downstream end of the integration mesh which permits backflow to be taken into account. Newton's iterative technique is used to solve the nonlinear finite-difference equations a t each computation step, using a rapid algorithm for solving the resulting linearized equations. The method is applied to a flow which is periodic in time and contains regions of backflow. The numerical computations are compared with known numerical and asymptotic solutions and the agreement is excellent.
High-order moments of Reynolds shear stress fluctuations in a turbulent boundary layer
Authors: Antonia R. A. , Atkinson J. D.
Published: March 2006

The cumulant-discard approach is used to predict the third- and fourth-order moments and the probability density of turbulent Reynolds shear stress fluctuations uv, the streamwise and normal velocity fluctuations being represented by u and v respectively. Measurements of these quantities in a turbulent boundary layer are presented, with the required statistics of uv obtained by the use of a high-speed digital data-acquisition system. Including correlations between u and u up to the fourth order, the cumulant-discard predictions are in close agreement with the measurements in the inner region of the layer but only qualitatively follow the experimental results in the outer intermittent region. In this latter region, predictions for the third- and fourth-order moments of uv are also obtained by assuming that the properties of both turbulent and irrotational fluctuations are Gaussian and by using some of the available conditional averages of u, v and uv.
On making holes in a sheet of fluid
Authors: Taylor G. I. , Michael D. H.
Published: March 2006

It is suggested in this paper that axisymmetric holes in thin sheets of fluid in which surface tension forces predominate will open out if they are initially large in relation to the thickness of the sheet; but that small holes will close up. No exact criterion has been found for the critical hole size in a free falling sheet, but the behaviour of the sheet may be closely simulated by the suspension of a soap film between coaxial circular rings. Theoretical results and experimental observations on catenoid films so formed are described.

For a hole in a sheet standing under gravity on a horizontal plane an equilibrium configuration exists, which is shown to be unstable. It is suggested that in this case the equilibrium position serves to distinguish between holes which open and those which close. Experiments on the behaviour of holes in a mercury sheet reveal a well-defined critical size which is in good agreement with that predicted by the unstable equilibrium.

A further series of experiments on holes made in a sheet of water standing on paraffin wax gave no sharp distinction between opening and closing holes, and holes of a wide range of sizes could remain stationary. This behaviour is associated with changes in the angle of contact with the plane. Independent meniscus observations similar to those of Ablett for a steadily moving meniscus show that the angle of contact θa, for a meniscus about to advance is greater than the value θr for a meniscus on the point of receding. It is seen that this difference will produce a range of hole diameters within which a hole will be trapped and remain stationary. Observations on the minimum size of hole on a water sheet which will remain open are reported. But it was found that the largest holes which would remain stationary were too large in relation to the size of the sheet for reliable results to be obtained.
On the longitudinal dispersion of dye whose concentration varies harmonically with time
Authors: Chatwin P. C.
Published: March 2006

In recent years many problems concerned with the dispersion of a passive contaminant along pipes and channels have been investigated, and this paper is concerned with one such problem which arises in diverse applications. This is the study of the longitudinal dispersion of a contaminant whose concentration is prescribed as a harmonic function of time at one cross-section. On the basis of physical arguments and of detailed calculations for two laminar flows it is shown that for high frequencies the concentration pattern is transported downstream at the maximum fluid velocity but that for low frequencies it is transported at the discharge velocity, and that the fluctuations in concentration decay to zero in a much shorter downstream distance for high frequencies than for low frequencies. It is shown further that at high frequencies the concentration is exponentially small except near the places where the fluid velocity attains its maximum, whereas for low frequencies the variation in concentration over the cross-section is small. Some of these conclusions are compared with those made by others, and the agreement is in general satisfactory.
Spatially growing wave trails of an inviscid fluid discontinuity
Authors: Freymuth Peter
Published: March 2006

The eigenvalue equation for three-dimensional waves in parallel and cross flows parallel to a fluid discontinuity has been considered for spatially growing waves. The discontinuity plane (x, y plane) is perpendicular to the gravitational acceleration and consists in general of a jump in speed, in flow direction and in density. With the assumption of waves which are periodic in time and periodic in the y direction, the eigenvalue equation is solved for the complex wavenumber α in the x direction. These waves are used to Fourier synthesize the wave trails generated by a time-periodic disturbance with a Gaussian amplitude distribution e−δy2 along the y axis. Lines of constant phase and lines of constant amplitude within the wave trail have been illustrated for some examples.
Shear layers in a rotating stratified fluid with bottom topography
Authors: Desaubies Yves J. F.
Published: March 2006

The structure of shear layers due to bottom topography in a rotating stratified fluid is obtained under the restriction σS [Lt ] E½, where σS = ναgΔT/KΩ2L is a measure of the stratification and E = ν/Ω2L is the Ekman number. The layers are found to be similar to the side-wall layers discussed by Barcilon & Pedlosky (19673) if σS [Gt ] E½ and are Stewartson layers if $\sigma S \ll E^{\frac{2}{3}}$. Some comments are made on the possibility of Taylor column formation in a stratified fluid.
The force on a slender fish-like body
Authors: Newman J. N.
Published: March 2006

The force acting on a fish-like body with combined thickness and lifting effects is analysed on the assumption of inviscid flow. A general expression is developed for the pressure force on the body, which is analogous to the momentum-flux analysis for non-lifting bodies in classical hydrodynamics. For bodies with constant volume, the mean drag (or propulsive) force is expressed in terms of a contour integral around the vortex sheet behind the body. Attention is focused on the case of steady-state motion with constant angle of attack, and the induced drag is analysed for finned axisymmetric bodies using the slender-body approximation developed by Newman & Wu (1973). Unlike earlier results of Lighthill (1970), the lift–drag ratio in this case depends on the body thickness.
On the existence of critical levels, with applications to hydromagnetic waves
Authors: McKenzie James F.
Published: March 2006

It is proved that a critical level, at which a wave packet is neither reflected nor transmitted, can exist only if the wave normal curve, which is formed by taking the cross-section through the wave normal surface in the plane of propagation, possesses an asymptote which is parallel to the direction of variation of the properties of the medium through which the wave packet moves. This condition, when applied to various types of hydromagnetic waves (such as hydromagnetic waves of the inertial or gravity type, or slow magnetoacoustic waves), shows that critical levels for such waves can exist only if the direction of spatial variations of the medium is perpendicular to the ambient magnetic field. Provided that the angle between the gravitational acceleration, or the rotation axis, and the magnetic field is not zero, hydromagnetic critical levels, characteristic of the gravity or inertial type, act like ‘valves’ in the sense that the wave packet can pierce the critical level from one side and is captured from the other side. It is also pointed out that critical-level behaviour is to some extent a consequence of the WKBJ approximation since the other limit, namely when the waves feel an almost discontinuous behaviour in the properties of the medium, gives markedly different results, particularly in the presence of streaming, which can give rise to the phenomenon of wave amplification.
Wave-induced distortions of a slightly stratified shear flow: a nonlinear critical-layer effect
Authors: Haberman Richard
Published: March 2006

A slightly stratified shear flow is considered when the effects of nonlinearity, viscosity and thermal diffusivity are in balance in the critical layer. Finite amplitude essentially non-diffusive neutral waves exist only if the mean temperature, velocity and vorticity profiles are distorted such that small jumps in these quantities occur across the critical layer.
Asymmetric wave-stress tensors and wave spin
Authors: Jones W. L.
Published: March 2006

Linearized wave-stress tensors derived from Hamilton's variational principle may be asymmetric. If interpreted as momentum fluxes, they would lead to lack of conservation of orbital angular momentum. It is shown that changes in internal angular momentum or spin of waves and torque coupling to external fields can adequately provide conservation of total angular momentum in such cases, Examples are given for acoustic, internal gravity, Rossby and plasma waves.
The interaction of a transient exhaust plume with a rarefied atmosphere
Authors: Baum Howard R.
Published: March 2006

The interaction of a gas cloud of specified mass, momentum and energy with an atmosphere in uniform motion is studied using the kinetic theory of gases. The Krook collision model is used to obtain analytically interpretable and numerically tractable results describing the spatial and temporal evolution of the cloud. The cloud originates from a continuum source and expands to a free molecular flow. It then begins to collide with the atmosphere, and is gradually transformed into a continuum flow diffusing through the atmosphere while being convected by the uniform motion.
Identification of turbulent wall eddies through the phase relation of the components of the fluctuating velocity gradient
Authors: Lee Myon Ki , Eckelman Larry D. , Hanratty Thomas J.
Published: March 2006

Simultaneous measurements of the longitudinal (sx) and transverse (sz) components of the turbulent fluctuating velocity gradient at the wall of a pipe are presented for ten locations in the transverse direction. Separate measurements of sx and of sz are also presented for twenty locations. The sz pattern reveals alternating positive and negative values over lengths Λ of the magnitude suggested by the spacing of the streaky wall structure observed in a number of laboratories. Of particular interest is the observation of regular eddies for which the sz pattern is accompanied by a spatial variation of sx out of phase by about 1/4Λ. These regular eddies are associated with intermittent production of Reynolds stress and with the occurrence of large negative values of sx which could be identified with wall bursts previously reported. The time response of the axial flow appears to influence the development of these regular eddies in that the development of an sx pattern lags behind that of an sz pattern. Measurements of spatial correlations of sx and sz with different time delays, as well as direct observations of the temporal variation of sx and sz patterns, support these notions.
The instability of short waves on a vortex ring
Authors: Widnall Sheila E. , Bliss Donald B. , Tsai Chon-Yin
Published: March 2006

A simple model for the experimentally observed instability of the vortex ring to azimuthal bending waves of wavelength comparable with the core size is presented. Short-wave instabilities are discussed for both the vortex ring and the vortex pair. Instability for both the ring and the pair is predicted to occur whenever the self-induced rotation of waves on the filament passes through zero. Although this does not occur for the first radial bending mode of a vortex filament, it is shown to be possible for bending modes with a more complex radial structure with at least one node at some radius within the core. The previous work of Widnall & Sullivan (1973) is discussed and their experimental results are compared with the predictions of the analysis presented here.
Rotational channel flow over small three-dimensional bottom irregularities
Authors: Fredsøe Jørgen
Published: March 2006

Rotational flow of an inviscid fluid over an irregularity in the bottom is investigated. The flow is regarded as a perturbed unidirectional flow, and the shape of the irregularity is described using Fourier transforms. The velocity profile in the unidirectional flow is determined using the eddy-viscosity concept and a finite wall slip velocity.

Two different examples of irregularities are considered: (a) an infinitely long straight irregularity which forms an arbitrary angle with the direction of the basic flow and (b) a hump in a channel with impermeable walls. The influence of rotation on the two- and three-dimensional waves which are formed downstream of these irregularities is analysed and experimentally verified. Further, it is shown that the gradient of the basic velocity profile increases the transverse movement of the fluid particles at the bottom, while at the surface this transverse movement is decreased.
Oscillatory and collective instabilities in large Prandtl number convection
Authors: Busse F. H. , Whitehead J. A.
Published: March 2006

An experimental study of transitions from steady bimodal convection to time-dependent forms of convection is described. Using controlled initial conditions for the onset of bimodal convection two mechanisms of instability can be separated from the effects of random noise. The oscillatory instability of bimodal cells introduces standing waves closely resembling those occurring in low Prandtl number convection. The collective instability introduces spoke-pattern convection which is characteristic for turbulent large Prandtl number convection. Both instabilities originate primarily from the momentum advection terms in the equations of motion, as is evident from the strong Prandtl number dependence of the critical Rayleigh number Rt for the onset of oscillations. The results are discussed in relation to previous experiments and recent theoretical work.
Stability of periodic waves in shallow water
Authors: Bryant P. J.
Published: March 2006

Waves of small but finite amplitude in shallow water can occur as periodic wave trains of permanent shape in two known forms, either as Stokes waves for the shorter wavelengths or as cnoidal waves for the longer wavelengths. Calculations are made here of the periodic wave trains of permanent shape which span uniformly the range of increasing wavelength from Stokes waves to cnoidal waves and beyond. The present investigation is concerned with the stability of such permanent waves to periodic disturbances of greater or equal wavelength travelling in the same direction. The waves are found to be stable to infinitesimal and to small but finite disturbances of wavelength greater than the fundamental, the margin of stability decreasing either as the fundamental wave becomes more nonlinear (i.e. contains more harmonics), or as the wavelength of the periodic disturbance becomes large compared with the fundamental wavelength. The decreasing margin of stability is associated with an increasing loss of spatial periodicity of the wave train, to the extent that small but finite disturbances can cause a form of interaction between consecutive crests of the disturbed wave train. In such a case, a small but finite disturbance of wavelength n times the fundamental wavelength converts the wave train into n interacting wave trains. The amplitude of the disturbance subharmonic is then nearly periodic, the time scale being the time taken for repetitions of the pattern of interactions. When the disturbance is of the same wavelength as the permanent wave, the wave is found to be neutrally stable both to infinitesimal and to small but finite disturbances.
Axisymmetric expansion of a gas from a nozzle into a vacuum
Authors: Tuer Thomas W. , Springer George S.
Published: March 2006

Using a test-particle Monte Carlo method the general features of a gas expanding from a circular nozzle into a vacuum were investigated. Calculations were performed by considering the flow to be uniform and axial at the exit plane of the nozzle with an exit Mach number of 3 and a throat Reynolds number of 25. Results are presented for the density, mean flow velocity and kinetic temperature of the gas. Near the axis of the jet the calculated density distributions were found to agree well with those given by Robertson & Willis. Results are also presented for regions far from the jet's axis where no other solution is available.
Relaxation effects, caused by relative motion, on shock waves in gas-bubble/liquid mixtures
Authors: Noordzij L. , Van Wijngaarden L.
Published: March 2006

We observed a gradual change in the structure of a shock wave passing through a long tube of bubbly liquid, which we attribute to the motion of the bubbles relative to the liquid. We show that the effect of the motion on the structure of a shock wave is like that of thermal relaxation on gasdynamic shock waves: the pertinent relaxation time is the time viscous forces in the fluid take to alter the velocity of a bubble to that of the fluid. Our theory predicts certain changes in the speed of the shock wave and in its structure. We could not verify the prediction as to wave speed: in dilute mixtures it is too small to be measured. But we report experiments on the structure of the wave, which support our theoretical conclusion that the observed changes are due to the relative motion.
On Laplace's tidal equations
Authors: Miles John W.
Published: March 2006

The parametric limit process for Laplace's tidal equations (LTE) is considered, starting from the full equations of motion for a rotating, gravitationally stratified, compressible fluid. The boundary-value problem for free oscillations of angular frequency σ is not well posed if σ2<N2+ 4ω2, whereNis the Väisälä frequency and ω is the rotational speed of the Earth, and the governing partial differential equation is elliptic/hyperbolic on the polar/equatorial sides of the inertial latitudes given by ± σ =f(vertical component of 2ω) if σ < 2ω [Lt ]N. The solution of this ill-posed problem is considered for a global ocean of uniform depth, with the effects of ellipticity, the ‘traditional’ approximation and stratification measured by the small parametersm= ω2a/g, δ =h/aands=hN2/g(g= acceleration due to gravity,h= depth of ocean,a= radius of Earth). LTE represent the joint limitm, δ,s↓ 0 and yield bounded solutions for all latitudes. It is argued that the parametric expansion inmis regular. The joint expansion in δ andswith LTE as the basic approximation is singular at the inertial latitudes if σ < 2ω, which difficulty is traced to the failure of LTE to provide an adequate description of the characteristics in the hyperbolic domain. It is shown that an alternative formulation, in which the buoyancy force is retained in the basic equations in the joint limits↓0, δ↓0 withN[Gt ] 2ω, yields solutions that are uniformly valid in the neighbourhoods of the inertial latitudes. The resulting representation comprises a barotropic mode, which satisfies LTE, and an infinite discrete set of baroclinic modes, each of which has Airy turning points at the inertial latitudes and is trapped between them. The barotropic and baroclinic modes are coupled by the Coriolis acceleration associated with the horizontal component of the Earth's rotation. The relative effects of this coupling are uniformlyO(δ) if σ > 2ω, but it induces currentsO(δ/s1/4) and vertical displacementsO(δ/s3/4) between the inertial latitudes if σ < 2ω [Lt ]N. It appears that resonant amplification of the baroclinic modes forced by the barotropic modes could imply internal displacements that dominate those of the basic motion.
Expansions for the shape of maximum amplitude Stokes waves
Authors: Norman A. C.
Published: March 2006

Grant (1973) showed that the expansion giving the profile of a steady Stokes wave near a 120° corner was more complicated than had previously been assumed. This paper gives further terms in such an expansion, and shows that generating them cannot introduce transcendental quantities beyond those noted by Grant.
Shear-flow stability within the atmosphere of Venus
Authors: Cess R. D. , Harshvardhan
Published: March 2006

Employing a linear stability analysis, Dudis (1973) has recently suggested that shear-flow instability might exist within the upper stratosphere of Venus owing to destabilization by radiative transfer. We have incorporated a more realistic formulation for radiative transfer into his stability analysis and conclude that such an instability is unlikely.
Oscillatory convection in a porous medium heated from below
Authors: Horne R. N. , O'sullivan M. J.
Published: March 2006

The stability of natural convective flow in a porous medium heated both uniformly and non-uniformly from below is studied in order to determine the possibility of oscillatory and other unsteady flows, and to explore the conditions under which they may occur. The results of the numerical work are directly comparable with experiments using a Hele Shaw cell and also, in the uniformly heated case, with the results of Combarnous & Le Fur (1969) and Caltagirone, Cloupeau & Combarnous (1971). It is shown that for the uniformly heated problem there exist, in certain cases, two distinct possible modes of flow, one of which is fluctuating, the other being steady. However in the non-uniformly heated case the boundary conditions force the solution into a unique mode of flow which is regularly oscillatory when there is considerable non-uniformity in the heat input at the lower boundary, provided that the Rayleigh number is sufficiently high.
Decay of two-dimensional homogeneous turbulence
Authors: Herring J. R. , Orszag S. A. , Kraichnan R. H. , Fox D. G.
Published: March 2006

The decay of two-dimensional, homogeneous, isotropic, incompressible turbulence is investigated both by means of numerical simulation (in spectral as well as in grid-point form), and theoretically by use of the direct-interaction approximation and the test-field model. The calculations cover the range of Reynolds numbers 50 ≤ RL ≤ 100. Comparison of spectral methods with finite-difference methods shows that one of the former with a given resolution is equivalent in accuracy to one of the latter with twice the resolution. The numerical simulations at the larger Reynolds numbers suggest that earlier reported simulations cannot be used in testing inertial-range theories. However, the large-scale features of the flow field appear to be remarkably independent of Reynolds number.

The direct-interaction approximation is in satisfactory agreement with simulations in the energy-containing range, but grossly underestimates enstrophy transfer at high wavenumbers. The latter failing is traced to an inability to distinguish between convection and intrinsic distortion of small parcels of fluid. The test-field model on the other hand appears to be in excellent agreement with simulations at all wavenumbers, and for all Reynolds numbers investigated.
Scaling of combustion-generated noise
Authors: Hassan H. A.
Published: March 2006

Using the framework of Lighthill's acoustic analogy, a theory has been developed for combustion-generated noise. The theory is used to derive the scaling laws for combustion-generated noise in open turbulent flames. It is shown that the scaling laws for both power and frequency are in good agreement with experiment.
Line singularities in unbounded stratified flow
Authors: Janowitz G. S.
Published: March 2006

We obtain the solutions, under the Oseen and Boussinesq approximations, for the flow field disturbance due to a line singularity in an otherwise uniform, horizontal, inviscid, incompressible flow of a vertically stratified fluid. The results obtained show no upstream influence for those singularities across which [xdtri ]2ψ + (N/U)2ψ is continuous. Doublet and vortex singularities are examples of these. Uniform flows past doublets and vortices are considered for a range of internal Froude numbers, including the calculation of the pressure distributions and drag for the doublet. An application of the vortex solution to flows in the β-plane is discussed.
The effect of wall cooling on a compressible turbulent boundary layer
Authors: Gran R. L. , Lewis J. E. , Kubota T.
Published: March 2006

Experimental results are presented for two turbulent boundary-layer experiments conducted at a free-stream Mach number of 4 with wall cooling. The first experiment examines a constant-temperature cold-wall boundary layer subjected to adverse and favourable pressure gradients. It is shown that the boundary-layer data display good agreement with Coles’ general composite boundary-layer profile using Van Driest's transformation. Further, the pressuregradient parameter βK found in previous studies to correlate adiabatic highspeed data with low-speed data also correlates the present cooled-wall high-speed data. The second experiment treats the response of a constant-pressure highspeed boundary layer to a near step change in wall temperature. It is found that the growth rate of the thermal boundary layer within the existing turbulent boundary layer varies considerably depending upon the direction of the wall temperature change. For the case of an initially cooled boundary layer flowing onto a wall near the recovery temperature, it is found that δT ∼ x whereas the case of an adiabatic boundary layer flowing onto a cooled wall gives δT ∼ x½. The apparent origin of the thermal boundary layer also changes considerably, which is accounted for by the variation in sublayer thicknesses and growth rates within the sublayer.
Non-Newtonian secretion flow in tubes
Authors: Fitz-Gerald J. M.
Published: March 2006

A model is developed for the phenomenon of non-Newtonian secretion in tubes. The motivation for this study is the problem of glandular secretion, particularly in the pancreas. Power-law fluids are considered in some detail, as being biologically appropriate. It is found that for a power-law fluid whose exponent is less than unity (the biological case) two types of flow occur. For a sufficiently high secretion pressure, all of the tube is used for secretion, and a nonlinear pressure profile results. Numerical solutions are obtained for the pressure and rate of efflux. When the secretion pressure parameter falls below a certain critical value, the upper end of the tube begins to be choked off, only part of the tube being used for secretion. This phenomenon does not occur for exponents greater than or equal to unity. Physiological implications are considered, and a qualitative discussion given for the case of non-power-law fluids.
Free convection effects on steady MHD flow past a vertical porous plate
Authors: Soundalgekar V. M.
Published: March 2006

An analysis of two-dimensional steady flow of an incompressible, viscous, electrically conducting fluid past an infinite vertical porous plate is carried out under the following assumptions: (i) that the suction velocity normal to the plate is constant, (ii) that the plate temperature is constant, (iii) that the difference between the temperatures of the plate and the free stream is moderately large, causing free convection currents, (iv) that the transversely applied magnetic field and magnetic Reynolds number are very small and hence the induced magnetic field is negligible.

Approximate solutions to the coupled nonlinear equations governing the steady velocity and temperature are derived. They are shown graphically. During the course of discussion, the effects of positive and negative G (the Grashof number: G > 0 implies cooling of the plate, G < 0 heating of the plate), of P (the Prandtl number), of positive and negative E (the Eckert number) and of M (the magnetic field parameter) are presented quantitatively.
The vortex-street wakes of vibrating cylinders
Authors: Griffin Owen M. , Ramberg Steven E.
Published: March 2006

The strength (initial circulation) and spacing of vortices in the wake of a circular cylinder have been obtained for conditions under which the body undergoes lateral vibrations. The vibrations of the cylinder were at all times synchronized with those in the wake, thereby suppressing the natural Strouhal frequency in favour of a common synchronized or ‘locked-in’ frequency for the body-wake system. All experiments were performed at a Reynolds number of 144 or 190. An inverse relation between the initial circulation K and the length lF of the vortex formation region was obtained for cylinder oscillations of up to 50% of a diameter, at vibration frequencies both above and below the Strouhal shedding frequency. The initial circulation K of the vortices was increased by as much as 65%, at lF = 1·6 diameters, from the stationary-cylinder value of K corresponding to lF = 3·2d. An increase in the rate A of vorticity generation of 80% from the stationary-cylinder wake value was obtained with the cylinder vibrating at 30% of a diameter and 110% of the Strouhal frequency. Both flow-visualization and hot-wire results show that the lateral spacing of the vortex street decreases as the vibration amplitude of the cylinder is increased, but that the longitudinal vortex spacing is independent of changes in amplitude. The longitudinal spacing, however, varies inversely with the vibration frequency. The street approaches a single line of vortices of alternating sign as the amplitude of vibration approaches values near a full cylinder diameter, and secondary vortex formation at these large amplitudes is associated with the vanishing lateral spacing of the street. Observation of the wake has elucidated the mechanism of vortex formation; the entrainment processes in the formation region have been observed at small intervals over a cycle of the cylinder's motion.
On the stability of extending films: a model for the film casting process
Authors: Yeow Y. L.
Published: March 2006

Isothermal Newtonian film flow is put forward as a simple model of the film casting process. Methods of linear hydrodynamic stability theory are applied to study the stability of the film flow. The relevant eigenvalue problems are formulated and solved numerically. Results are presented in the form of neutral-stability curves in the appropriate parameter space. For the case of two-dimensional disturbances stability results obtained here are compared with those of Pearson & Matovich (1969) and Gelder (1971) for the stability of isothermal Newtonian threadline flow.
Three-dimensional laminar boundary layers in crosswise pressure gradients
Authors: Horlock J. H. , Lewkowicz A. K. , Wordsworth J.
Published: March 2006

Two attempts were made to develop a three-dimensional laminar boundary layer in the flow over a flat plate in a curved duct, establishing a negligible streamwise pressure gradient and, at the same time, an appreciable crosswise pressure gradient.

A first series of measurements was undertaken keeping the free-stream velocity at about 30 ft/s; the boundary layer was expected to be laminar, but appears to have been transitional. As was to be expected, the cross-flow in the boundary layer decreased gradually as the flow became progressively more turbulent.

In a second experiment, at a lower free-stream velocity of approximately 10 ft/s, the boundary layer was laminar. Its streamwise profile resembled closely the Blasius form, but the cross-flow near the edge of the boundary layer appears to have exceeded that predicted theoretically. However, there was a substantial experimental scatter in the measurements of the yaw angle, which in laminar boundary layers is difficult to obtain accurately.
Steady flow in rapidly rotating circular expansions
Authors: Walker J. S.
Published: March 2006

Inertialess incompressible flow through a rapidly rotating, variable-area conduit of circular cross-section is treated. For the practical case of an expansion (or contraction) placed between two pipes, the flow is strongly asymmetrical and involves regions of weak reverse flow in the expansion and downstream pipe, while the disturbance to the fully developed pipe flows persists for large, O(E−½) distances upstream and downstream, where E is the (small) Ekman number. The flow in the two pipes depends only on the ratio of their radii and is independent of the shape and length of the expansion. The startling implication of the disturbance's persistence is that, in practice, fully developed flow will almost never be realized in rapidly rotating pipes.
Source–sink flows in a rotating annulus: a combined laboratory and numerical study
Authors: Bennetts D. A. , Jackson W. D. N.
Published: March 2006

A general characteristic of rapidly rotating fluids is that accurate experimental measurements can only be made of the main (azimuthal) flow. The secondary flow is then usually deduced from theory, although this is often incomplete in the boundary regions where the secondary flow is of most interest.

In this paper we consider the case of source-sink flow between the porous walls of a rapidly rotating annular container and numerically integrate the full equations of motion in order to determine the complete structure of the secondary flow. The results are compared with the (approximate) analytic studies of Hide (1968) and Bennetts & Hocking (1973) to show the differences between the two approaches.

A defect of many previous numerical papers has been the inability to check the solution in the nonlinear case. To overcome this, new experimental measurements of the azimuthal velocity profile for a Rossby number of 0·238 have been obtained and these are compared with the numerical results.
A numerical model of instability in axisymmetric jets
Authors: Grant A. J.
Published: March 2006

The detailed flow fields associated with instability in axisymmetric jets are realized by numerical integration of the time-dependent Navier-Stokes equations.

The mechanism of amplification of small disturbances is shown to be two-dimensional for a thin boundary layer profile and conclusions regarding three-dimensionality which have been inferred from recent models of axisymmetrical systems are clarified.

The computed flow field is shown to be dominated by the large-scale vortex ring structure which has been observed experimentally. Although the wavelength of vortex shedding is found to be slightly variable owing to the randomness of the initial perturbation, the results are shown to agree closely with experiment.
An experimental study of Couette instability of stratified fluids
Authors: Withjack E. M. , Chen C. F.
Published: March 2006

The stability of Couette flow of stratified salt solutions is investigated in an apparatus with both the inner and outer cylinders rotating. The ratio of the radius of the inner cylinder to that of the outer cylinder is 0·2. The flow is visualized by means of shadowgraph and dye-trace methods. Compared with homogeneous fluids, the effect of the stabilizing density gradient is to increase the critical speed of the inner cylinder and to decrease the critical wavelength for a given angular speed of the outer cylinder. When the cylinders are rotating in the same direction, in the critical state, the instabilities appear along the inner cylinder in a spiral wave form which is itself not very stable. With counterrotating cylinders, the instabilities appear as regularly spaced vortices which, for the most part, are neither symmetric Taylor vortices nor simple spirals. In addition, these vortices rotate as a whole at a speed generally smaller than that of the inner cylinder. From shadowgraph observations, stability curves are constructed for three density gradients. The critical wavelength and the rotational periods of the vortices are also determined.
Separation and the Taylor-column problem for a hemisphere
Authors: Walker J. D. A. , Stewartson K.
Published: March 2006

A layer of viscous incompressible fluid is confined between two horizontal plates which rotate rapidly in their own plane with a constant angular velocity. A hemisphere has its plane face joined to the lower plate and when a uniform flow is forced past such an obstacle, a Taylor column bounded by thin detached vertical shear layers forms. The linear theory for this problem, wherein the Rossby number ε is set equal to zero on the assumption that the flow is slow, is examined in detail. The nonlinear modifications of the shear layers are then investigated for the case when ε ∼ E½, where E is the Ekman number. In particular, it is shown that provided that the Rossby number is large enough separation occurs in the free shear layers. The extension of the theory to flow past arbitrary spheroids is indicated.
Sound production at the edge of a steady flow
Authors: Williams J. E. Ffowcs
Published: March 2006

The theory initiated by Lighthill (1952) to describe the sound radiated by turbulence embedded in an uniform fluid at rest is here extended to the case where the turbulence exists on the edge of a uniformly moving stream. An exact analogy is developed between the distant real sound field and that which would be radiated by a particular quadrupole distribution adjacent to a vortex sheet positioned in the linearly disturbed flow. The equivalent sources in this analogy are quadrupoles identical in strength with those in Lighthill's model, but the quadrupoles are now shown to convect with the fluid-particle velocity. There is no amplifying effect of shear. The particular case of a plane shear layer is worked out in detail for sound waves of scale large in comparison with the shear-layer thickness.

A downstream zone of silence is predicted as is the formation of highly directional beams associated with the interference of sound radiated directly and sound reflected from the fluid interface. A distinct structure results in which the variation of sound with flow velocity, density and angle is not easily accounted for by simple power-law scaling. Finally a comparison is made with some features of jet noise; the modelling of the high frequency jet noise problem by a single shear layer yields some features consistent with experiment.
High-intensity light propagation and induced natural laminar flow
Authors: Lehnigk Siegfried H. , Steverding Bernard
Published: March 2006

The objective of this paper is to describe approximately the coupled steady-state processes of light propagation and induced laminar incompressible fluid flow in the case of natural convection.

For the case of a homogeneous fluid and under the assumptions that light energy is instantaneously transformed into heat and that the induced velocities are not too large, it is reasonable to use the boundary-layer equations to describe the induced natural flow. These equations are augmented by the conservation of energy equation. The velocity, temperature and intensity functions are expected to exhibit similarity properties.

A high-intensity light beam with a given rotationally symmetric Gaussian initial intensity distribution is propagating vertically upwards into a fluid initially at rest. The fluid characteristics are assumed to be constant. A stream function is introduced to satisfy the conservation of mass equation. The conservation of momentum equation leads to conditions on the unknown functions involved in the stream function. Additional conditions follow from the conservation of energy equation, which involves the local light intensity as a driving term.

Under the assumptions made, self-defocusing (thermal blooming) will occur. The main results are an exponential increase of the boundary-layer thickness and an exponential decrease of temperature and of light intensity due to the blooming effect in addition to the exponential decrease due to absorption.
Flows with concentrated vorticity: a report on EUROMECH 41
Authors: Riley N.
Published: March 2006

The 41st EUROMECH Colloquium on flows with concentrated vorticity was held in Norwich from 17 to 21 September 1973. There were sixty-five participants from nine countries and the author was the chairman of the organizing committee.