bluuebunny/crossref_metadata_2025 huggingface dataset:
Thermal convection in a horizontal plane Couette flow
Authors: Davies-Jones Robert P.
Published: March 2006

We investigate the behaviour of infinitesimal perturbations introduced into an unstably stratified horizontal Couette flow. We assume that the fluid is Boussinesq and contained in an infinite conducting rectangular channel which is uniformly heated from below. The sidewalls are rigid and the Couette flow is generated by moving them with equal and opposite velocities along the channel. The top and bottom are assumed to be free so that we can separate variables.

Without shear, the preferred modes of convection closely resemble transverse ‘finite rolls’ (Davies-Jones 1970). Shear increases the critical wavelength so that the preferred modes become longitudinally elongated cells, or even longitudinal rolls in some cases. The critical Rayleigh number increases quite rapidly at fist with Reynolds number, but at higher Reynolds numbers it levels off to a constant value (which cannot be greater than the shear-independent Rayleigh number at which longitudinal disturbances fist become unstable).

We also find that the disturbances are tilted in the same direction as the shear, and that the marginally stable ones transfer kinetic energy from the mean flow to the perturbations. Except at low Reynolds numbers, the long wave perturbations gain more energy through the conversion of mean flow kinetic energy than through the release of potential energy, even though the instability is convective in origin.
On sideways diffusive instability
Authors: Hart J. E.
Published: March 2006

We consider the stability of the motion generated in a differentially heated vertical slot filled with a linearly stratified salt solution. The theoretical mean motion field between infinite plates is a function of the Rayleigh number Rs, = gβ(∂S0/∂z) D4/k8ν. If Rs is zero the salinity does not enter the problem and one finds instability in the form of stationary rolls which obtain most of their energy from the basic velocity field. Even at very small Rs of order -1000 these shear instabilities are replaced by diffusively destabilized convective rolls which appear at a thermal Rayleigh number Ra = gαΔTD3/kTν which is two orders of magnitude less than that required for the shear generated modes. The present calculations, which take proper account of both the mean fields and the boundary conditions, give results which compare somewhat more favourably with the experimental results of Thorpe, Hutt & Soulsby (1969) than the theory put forward by these authors. It is shown why their theory, which deals with different boundary conditions from those in the experiment, gives adequate results as Rs tends to negative infinity.
A model for the boundary condition of a porous material. Part 1
Authors: Taylor G. I.
Published: March 2006

In problems where a viscous fluid flows past a porous solid it has frequently been assumed that the tangential component of surface velocity is zero. When the porous solid has an open structure with large pores the external surface stress may produce a tangential flow below the surface. Recently, Beavers & Joseph (1967) have assumed that the surface velocity UB depends on the mean tangential stress $[\mu(d\overline{u}/dy)]_{y=0}$ in the fluid outside the porous solid through the relation
\[
\left[\mu\frac{d\overline{u}}{dy}\right]_{y=0} = \frac{\mu\alpha}{k^{\frac{1}{2}}}(U_B-Q),
\]
where Q is the volume flow rate per unit cross-section within the porous material due to the pressure gradient, k is the Darcy constant and α is a constant which depends only on the nature of the porosity. An artificial mathematical model of a porous medium is proposed for which the flow can be calculated both inside and outside the surface. This conceptual model was materialized and the experimental results agree with the calculations. The calculated values of α so found are not quite independent of the external means of producing the external tangential stress.
A model for the boundary condition of a porous material. Part 2
Authors: Richardson S.
Published: March 2006

The present paper contains an analysis of the model of a porous material proposed in part 1, and carries out calculations which allow comparison between theory and the experiments described therein. The relevant boundary conditions to be applied at an interface between a fluid and such a material are considered.
Rotational temperature profiles of shock waves in diatomic gases
Authors: Macpherson A. K.
Published: March 2006

The variation of the translational temperature, rotational temperature, and density through shock waves in oxygen and nitrogen was studied using classical laws of mechanics and a Monte Carlo scheme. The collision dynamics were calculated using an intermolecular potential by Parker with both a two-dimensional approximation and the full three-dimensional calculations. The rotational velocity frequency distributions were also calculated. The average number of collisions a molecule will experience a t various stages passing through a shock wave were found and plotted with the temperature and density profiles. The nitrogen results were compared with experimental results and good agreement was found. This also provided a method for giving a first approximation to the three-dimensional intermolecular potential.
A ship's waves and its wake
Authors: Peregrine D. H.
Published: March 2006

Waves generated at the stern of a ship must travel through the ship's wake. The effect of the mean flow in the wake refracting the waves is calculated by using a much simplified model. It is found that the waves diverging from the stern of a ship may differ considerably from the bow waves, in qualitative agreement with observation.
On combustion generated noise
Authors: Strahle Warren C.
Published: March 2006

Upon review of past experimental results and theoretical efforts it is apparent that the mechanism by which combustion noise is generated is not well understood. A theory of combustion noise is developed in this paper which follows rigorously from the principles of fluid mechanics. Lighthill's approach, used in his studies of aerodynamic noise, is closely followed in the present work. The sound radiated from open, turbulent flames is found to depend strongly upon the structure of such flames; at present their structure is not well known. However, meaningful bounds and scaling rules for the sound power output and spectral content are derived based upon the present limited knowledge. A framework is developed which explains past experimental work and the origin of combustion noise.
An integral equation for unsteady surface waves and a comment on the Boussinesq equation
Authors: Byatt-Smith J. G. B.
Published: March 2006

An integral equation for unsteady inviscid surface waves has been obtained. Existing known approximations are all derived from the one equation. The Boussinesq equation is obtained and criticized.
Spin-down of a Boussinesq fluid of small Prandtl number in a circular cylinder
Authors: Sakurai Takeo , Clark Alfred , Clark Patricia A.
Published: March 2006

The impulsive linear spin-down of a stably stratified Boussinesq fluid in a circular cylinder is analyzed under the assumption that the Prandtl number P = ν/κ is small (ν is the kinematic viscosity, κ the thermal diffusivity). The nature of the spin-down process depends on the ordering of P with respect to the Ekman number E. For P < E½, the spin-down is similar to that of an unstratified fluid. For P > E½ the process is similar to that for a stratified fluid with P = O(1). The distinctive case P = O(E½) is analyzed in detail. For that case it is shown that for N [Gt ] Ω, the asymptotic state of rigid rotation is reached in a time of the order of (N/Ω)2τ, where N is the Brunt-Väisälä frequency, Ω the angular velocity and τ the thermal diffusion time for the cylinder. We calculate spin-down times for parameter values corresponding to the solar interior. For an angular velocity as large as that suggested by Dicke (5·74 × 10−5 sec −1) the spin-down time is less than the age of the sun. For an angular velocity comparable to the surface value (2middot;87 × 10−6 sec −1), the spin-down time is greater than the age of the sun. These results suggest that a uniformly and rapidly rotating solar interior is not possible, but we cannot rule out a state of non-uniform rotation producing an oblateness as large as that measured by Dicke & Goldenberg (1967).
Generation of fluid motion in a circular cylinder by an unsteady applied magnetic field
Authors: Sneyd Alfred
Published: March 2006

Three problems are considered. In the first, a uniform magnetic field is suddenly switched on outside an infinitely long circular cylinder of incompressible con- ducting fluid. As the field diffuses into the fluid, electric currents are generated and hence a Lorentz force field. Under the assumptions of small magnetic Reynolds number and small magnetic Prandtl number, the initial flow (before it has been modified by convection or viscous diffusion of vorticity) is oalculated. In the second problem an initially uniform field is suddenly switched off outside a similar cylinder of fluid. It is shown that the switching off of the field produces a vorticity distribution identical with that produced by the switching on. The third problem considered is that of a circular cylinder of conducting fluid placed in a rapidly alternating magnetic field. It is shown that the alternating field produces vorticity at a constant rate, and a qualitative description of the resulting flow is given.
Unsteady multicellular viscous vortices
Authors: Bellamy-Knights P. G.
Published: March 2006

The problem of a viscous vortex core embedded in an unsteady outer potential swirling flow is considered. By introducing a suitable similarity variable, the full Navier–Stokes equations for the unsteady axisymmetric flow of an incompressible fluid are reduced to two ordinary differential equations. These are solved numerically. When the radial flux of a particular outer potential flow satisfies certain conditions a family of three-cell core structures is possible. This family is not represented by any known analytical solution.

This work is useful for studying meteorological flow systems such as tornadoes. In particular, it suggests how two- and three-cell structures can develop from a one-cell structure and also shows the sensitivity of the core flow to small changes in the outer potential flow.
Real-gas effects in very weak shock waves in the atmosphere and the structure of sonic bangs
Authors: Hodgson J. P. , Johannesen N. H.
Published: March 2006

An approximate expression is given for the thickness of weak fully dispersed shock waves. Using available data on the thermodynamic properties of air, it is shown that shocks of the strength expected in sonic bangs are fully dispersed. Estimated relaxation times for dry and humid air lead to wide variations in possible thickness, varying from millimetres to metres.
Unsteady viscous flow over a wavy wall
Authors: Lyne W. H.
Published: March 2006

The method of conformal transformation is used to investigate the steady streaming generated by an oscillatory viscous flow over a wavy wall. By assuming that the amplitude of the wall is much smaller than the Stokes layer thickness, the equations are linearized and solved for large and small values of the parameterkR. This parameter is the ratio of the amplitude of oscillation of a fluid particle to the wavelength of the wall. WhenkR[Lt ] 1, the results due to Schlichting (1932) are recovered, and whenkR[Gt ] 1 the equations resemble closely those derived in the theory of stability of plane parallel flows. With the aid of this theory the first-order steady streaming is found.
The near field within the potential cone of subsonic cold jets
Authors: Ko N. W. M. , Davies P. O. A. L.
Published: March 2006

This investigation describes a detailed study of the near pressure field within the potential cone of a subsonic circular turbulent jet.

The components of the near pressure field in the potential cone in which the potential flow condition exists within the fist four and a half diameter downstream appear to be moving with a phase velocity equal to the local speed of sound. The direction of propagation is roughly normal to the shear layer surrounding the cone. Some components of the hot-wire signal can be associated with the jet structure as a simple complex source, while others are related to the local characteristics of turbulence. Differences in the characteristics of the pressure field within the potential cone exist between the vortex generated noise at very low jet velocity and the eddy generated noise at higher velocity.

The power spectra obtained in the potential cone show the peak which is due to the pressure fluctuations and the flat portion due to the turbulence. The frequencies of the dominant components, in terms of the Strouhal number, are functions of both the axial and radial positions.

Microphone measurements were made in the near field outside for detailed comparison with the potential cone results.
An Oseen model of the two-dimensional flow of a stratified fluid over an obstacle
Authors: Trustrum Kathleen
Published: March 2006

The Oseen equations for the two-dimensional flow of a Boussinesq fluid over a thin barrier placed in a channel of finite depth are solved in the double limit ν → 0, t → ∞ under the hypothesis that the velocity at the tip of the barrier is as weakly singular as possible. The predicted flow patterns and drag coefficients are in closer agreement with Davis's experimental observations than those of the Long model.
On the mass and momentum transfer between short gravity waves and larger-scale motions
Authors: Hasselmann K.
Published: March 2006

Interactions between short gravity waves and larger-scale flows are investigated in the two-scale approximation. The effect of the wave field on the mean flow is described by an interaction stress tensor and a surface mass transfer. The results are applied to Phillips’ and Longuet-Higgins’ model of short waves breaking on the crests of long carrier waves. It is found that the work done on the long waves by the interaction stresses (corresponding to Longuet-Higgins’ ‘maser’ mechanism of wave generation) is almost exactly balanced by the loss of potential energy arising from the mass transfer. The residual energy transfer leads to attenuation of the long waves, independent of their propagation direction relative to the short waves. Damping factors are estimated from the upwind–downwind ratios of radar backscatter cross-sections. It is found that interactions with waves shorter than 35cm yield attenuation rates about an order of magnitude smaller than the observed growth rates due to the wind.
Structural features of turbulent flow over smooth and rough boundaries
Authors: Grass A. J.
Published: March 2006

An experimental study of boundary-layer turbulence in a free surface channel flow is described. Attention is concentrated on the effects of different surface roughness conditions on the turbulence structure in the boundary region. Hydrogen bubble flow tracers and medium high-speed motion photography were used to obtain an instantaneous visual and quantitative description of the flow field. In particular it proved possible to record instantaneous longitudinal and vertical velocity profiles from which distributions of the instantaneous Reynolds stress contribution were computed.

Two well-defined intermittent features of the flow structure were visually identified close to the boundary. These consisted of fluid ejection phases, previously reported by Kline et al. (1967) for smooth boundary flow, and fluid inrush phases. Conditional averaging of the instantaneous velocity data yielded quantitative confirmation that ejection phases corresponded with ejection of low momentum fluid outwards from the boundary whilst inrush phases were associated with the transport of high momentum fluid inwards towards the boundary. Inrush and ejection events were present irrespective of the surface roughness condition.

Conditional averaging also indicated that both inrush and ejection sequences correlate with an extremely high contribution to Reynolds stress and hence turbulence production close to the boundary. Indeed the present results, taken with those from previous studies, suggest that turbulence production is dominated by the joint contribution from the inrush and ejection events. It is emphasized that these structural features are intermittent, forming important linked elements of a randomly repeating cycle of wall-region turbulence production which is apparently driven by some violent three-dimensional instability mechanism.

Whilst the most coherent effects of the observed inrush phases appear to be mainly confined to a region close to the boundary, the influence of the ejection phases is far more extensive. The ejected low momentum fluid elements, drawn from the viscous sublayer and from between the interstices of the roughness elements, travel outwards from the boundary into the body of the flow and give rise to very large positive contributions to Reynolds stress at points remote from the boundary. This effect is sufficiently strong to prompt the suggestion that the ejection process could represent a universal and dominant mode of momentum transport outside the immediate wall region and possibly extending across the entire thickness of the boundary layer.

A structural model based on the present observations is seen to exhibit consistency with many commonly visualized features and recorded average properties of turbulent boundary-layer flows in general.
Slender-body analysis of the motion and stability of a vortex filament containing an axial flow
Authors: Widnall Sheila E. , Bliss Donald B.
Published: March 2006

Previous results concerning the effects of axial velocity on the motion of vortex filaments are reviewed. These results suggest that a slender-body force balance between the Kutta–Joukowski lift on the vortex cross-section and the momentum flux within the curved filament will give some insight into the behaviour of the filament. These simple ideas are exploited for both a single vortex filament and a vortex pair, both containing axial flow. The stability of a straight vortex filament containing an axial flow to long wave sinusoidal displacements of its centre-line is investigated and the stability boundary obtained. The effect of axial flow on the stability of a vortex pair is explored. It is shown that to lowest order (in the ratio of vortex core radius to distance between the vortices) the effect of axial flow is to reduce the self-induced rotation of a single filament and that this effect can be considered as a change in effective core radius. To the next order, travelling waves appear in the instability, the instability mode for the vortex pair becomes non-planar but the amplification rate of the instability is not affected.
On the decay of weak shock waves in axisymmetric non-equilibrium flow
Authors: Chou David C. , Chu Boa-Teh
Published: March 2006

The supersonic flight of a slender projectile in a fluid which may undergo internal non-equilibrium transformations is examined by a systematic perturbation scheme. In the frozen limit, the classical results of Whitham and his celebrated ‘rule’ are recovered. Unlike the classical theory, however, the shape of the nose shock can be expressed explicitly in terms of known functions when the relaxation decay length becomes of the same order as a characteristic length scale. The theoretically predicted shock angle, expressed as a function of the radial distance, is found to be in excellent agreement with the experimental measurements of Wegener and Klikoff.
Displacement and curvature effects in a wall jet
Authors: Clark Ann L. , Watson E. J.
Published: March 2006

This paper presents a solution of the second-order boundary-layer equations for the two-dimensional case of a wall jet on a curved surface. The outer flow is obtained by means of a conformal transformation, and general solutions for the displacement and curvature effects are given both as series and as integrals. These solutions are applied to symmetrical flow over a parabolic surface, the wall jet being either outside or inside.
Degeneration of resonantly-excited standing internal gravity waves
Authors: McEwan A. D.
Published: March 2006

The factors bringing about the irreversible distortion or degeneration of a continuously forced standing internal gravity wave in a linearly stratified fluid are studied experimentally and theoretically. For a rectangular container there is strong evidence that the process is initiated by the unstable growth, from a subliminal level, of free wave modes forming triads in second-order resonant interaction with the original wave. These free modes grow by de-energizing the original wave and may collectively induce kinematical conditions sufficiently severe to create localized regions of density discontinuity within the fluid, leading to turbulence.

Although the possible free wave modes are doubly infinite in number, the geometrical constraints greatly reduce the number of possibilities for resonant triads. In many cases this permits critical wave amplitude to be predicted by consideration of one triad only, and the results are in excellent agreement with experiment.

It is speculated that a closely similar process explains observations by Malkus (1968), Aldridge & Toomre (1969), and McEwan (1970) in the analogous context of inertial oscillation of contained rotating fluids.
The determination of the interfacial tension between two liquids
Authors: Milgram Jerome H. , Bradley Robert G.
Published: March 2006

The problems commonly encountered in the measurement of the interfacial tension between two liquids by capillary tube or force measurement are described. In order to avoid such problems, a new method of measurement of the interfacial tension is developed here which is based on the details of axisymmetric capillary waves which can be generated on the interface. Analyses relating these details to the interfacial tension and showing how the details can be measured photographically are given. An apparatus for making these photographic measurements is described and photographs made with such an apparatus are presented. An analysis of these photographs is given which gives the interfacial tensions for the interfaces shown.
Irrotational flow past bodies close to a plane surface
Authors: Tuck E. O.
Published: March 2006

A theroetical analysis is given for potential flow over, around and under a vehicle of general shape moving close to a plane ground surface. Solutions are given both in the form of a small-gap asymptotic expansion and a direct numerical computation, with close agreement between the two for two-dimensional flows with and without circulation. Some results for three-dimensional bodies are discussed.
Spatial structure in the viscous sublayer
Authors: Gupta A. K. , Laufer J. , Kaplan R. E.
Published: March 2006

An experimental investigation was performed to study the spatial coherence of structures in the sublayer of a turbulent boundary layer observed previously by flow visualization. The present work verifies these observations in an Eulerian reference frame and develops a statistical description of the phenomenon. The technique involves simultaneous digital sampling of an array of constant temperature hot-wire anemometers arranged to extract information about a spanwise variation in flow quantities. The quantitative description agrees with dimensionless measures of the structure scales previously published.
Autorotating wings: an experimental investigation
Authors: Smith E. H.
Published: March 2006

The autorotation of a flat plate about its spanwise axis was experimentally studied. Most of the work was done with a wing mounted in the University of Michigan 5 × 7 ft low-speed wind tunnel. The measurements consisted of the unsteady lift, drag, angular acceleration and the wing rotation rate. The flow pattern was studied by means of smoke, tufts and a small model in a water tunnel.

The flow pattern was very different from that over a static wing. The wing did not stall until it was nearly perpendicular to the free stream and the flow did not reattach to the lower surface until the wing had rotated well past zero angle of attack.

The maximum and average lift, drag and angular acceleration were measured for Reynolds numbers from 25 000 to 250 000. At Re = 240 000 the maximum lift coefficient was 4·50 with an average value of 2·20, while the maximum drag coefficient was 4·30 with an average value of 1·60. The angular acceleration was small; the wing rotated at an almost constant angular velocity. The non-dimensional wing rotation rate was measured for Reynolds numbers from 1300 to 280 000 and approached an asymptotic limit of 0·35 for sufficiently high Reynolds numbers.

The effect of applying driving and retarding torques to the wing was studied. As the rotation rate was increased above the free autorotation rate, the lift and drag increased. When the rotation rate was reduced by a retarding torque they both decreased. The power developed by the rotating wing was considerably less than for a windmill of the same frontal area.

A variety of wing configurations were tested, including different airfoils and aspect ratios and spoilers mounted at various locations on the wing. However, except for spoilers that were so large that they prevented autorotation, none of these changes had a major effect on the gross properties of the autorotation phenomenon.

Freely falling wings were also studied. For Reynolds numbers above 4000 the average lift and drag coefficients were comparable to those observed in the fixed axis tests and it appeared that the flow pattern was similar.
A new type of water channel with density stratification
Authors: Odell Garrett M. , Kovasznay Leslie S. G.
Published: March 2006

The novel idea is to use a disk pump to drive each fluid layer independently round a closed-return density-stratified water channel. A small-scale model was built and tested to demonstrate the feasibility of the idea. A hydrogen-bubble technique was used for both flow visualization and velocity measurement. Density measurements were made with an electrical conductivity probe developed by the authors. The tests have demonstrated the usefulness of such a facility, especially for long steady-state experiments in density-stratified flows.
Nearly free-molecular slit flow at finite pressure and temperature ratios
Authors: Wang P. Y. , Yu E. Y.
Published: March 2006

An analytical study is made of nearly free-molecular flow of a noble gas from one reservoir to another through a two-dimensional slit, with finite pressure and temperature ratios across the slit. The fundamental solution of the linear Boltzmann equation is employed in the study. The total mass flow is calculated to the first-order correction terms, of the order of α ln α and α, where α is the inverse Knudsen number. The coefficients of these terms are in general multiple integrals, but they become explicit functions of the pressure and temperature ratios after the multiple integrations are carried out by using Krook collision model. When the general result is simplified to the isothermal case the first-order correction has a negative value, indicating the reduction of the total mass flow due to intermolecular collisions in the counter flows.
The stability of unsteady axisymmetric incompressible pipe flow close to a piston. Part 1. Numerical analysis
Authors: Gerrard J. H.
Published: March 2006

A numerical solution of the Navier-Stokes equations of motion by means of finite-difference forms of the vorticity and continuity equations is presented. This is applied to the study of the flow of an incompressible fluid produced by the motion from rest of a piston in a cylindrical tube of circular cross-section.

Experiments at high Reynolds number indicated the presence in the starting flow of a ring vortex which was not reproduced by computation. Iteration to determine the stream function was not found to be necessary to achieve 1% accuracy. Omitting iteration is equivalent to only slightly disturbing the flow. An additional random disturbance applied to the flow at each time step was found to result in the production of the ring vortex.
The stability of unsteady axisymmetric incompressible pipe flow close to a piston. Part 2. Experimental investigation and comparison with computation
Authors: Hughes M. D. , Gerrard J. H.
Published: March 2006

Flow visualization has been used quantitatively to determine the flow relative to a piston and a free surface started from rest. The discharge of water from a cylindrical reservoir was investigated. Flow with a free surface started from rest was found to have a critical Reynolds number (based on tube diameter and surface speed) of about 450 above which a ring vortex was produced just below the surface.

Measurements at Reynolds numbers of 525 and 1200 were compared with computations made by the methods described in Part 1. The computed drift of tracer particles agreed well with observed values. The largest discrepancies occurred in the radial component of the drift in the early stages of the motion and amounted to 2½% of the tube diameter.
Accurate solution of the Orr–Sommerfeld stability equation
Authors: Orszag Steven A.
Published: March 2006

The Orr-Sommerfeld equation is solved numerically using expansions in Chebyshev polynomials and the QR matrix eigenvalue algorithm. It is shown that results of great accuracy are obtained very economically. The method is applied to the stability of plane Poiseuille flow; it is found that the critical Reynolds number is 5772·22. It is explained why expansions in Chebyshev polynomials are better suited to the solution of hydrodynamic stability problems than expansions in other, seemingly more relevant, sets of orthogonal functions.
A new technique for treating multiparticle slow viscous flow: axisymmetric flow past spheres and spheroids
Authors: Gluckman Michael J. , Pfeffer Robert , Weinbaum Sheldon
Published: March 2006

This paper is the first in a series of investigations having the overall objective of developing a new technique for treating the slow viscous motion past finite assemblages of particles of arbitrary shape. The new method, termed the multi-pole representation technique, is based on the theory that any object conforming to a natural co-ordinate system in a particle assemblage can be approximated by a truncated series of multi-lobular disturbances in which the accuracy of the representation is systematically improved by the addition of higher order multipoles. The essential elements of this theory are illustrated by examining the flows past finite line arrays of axisymmetric bodies such as spheres and spheroids which conform to special natural co-ordinate systems. It is demonstrated that this new procedure converges more rapidly and is simpler to use than the method of reflexions and represents the desired boundaries more precisely than the point-force approximation even when the objects are touching one another. Comparison of these solutions with the exact solutions of Stimson & Jeffery (1926) for the two sphere problem demonstrates the rapidity of convergence of this multipole procedure even when the spheres are touching. Drag results are also presented for flows past chains containing up to 101 spheres as well as for chains containing up to 15 prolate or oblate spheroids. The potential value of the technique is suggested by the rapidity with which the drag calculations were made, the 101 sphere problem requiring about 10 seconds on an IBM 360–65 computer to determine both the fluid flow and the drag coefficient.
The effect of mainflow transverse velocities in linear stability theory
Authors: Chen T. S. , Sparrow E. M. , Tsou F. K.
Published: March 2006

In studying the stability of the boundary layer with surface mass injection, a generalized version of the Orr–Sommerfeld equation was derived which takes account of the transverse velocity component in the mainflow. The new terms in the generalized Orr–Sommerfeld equation are inversely proportional to the Reynolds number. The resulting eigenvalue problem was solved numerically for a wide range of values of the mass injection intensity. It was found that the critical Reynolds number (based on the distance from the leading edge) decreases with increasing mass injection. The deviations between the critical Reynolds numbers from the generalized and conventional Orr–Sommerfeld equations have a different sign at low injection intensities from that at high injection intensities.
The spacing, position and strength of vortices in the wake of slender cylindrical bodies at large incidence
Authors: Thomson K. D. , Morrison D. F.
Published: March 2006

Extensive schlieren studies and yawmeter traverses of the wake behind slender cone-cylinders at large angles of incidence have shown that the flow pattern is generally steady. Under certain flow conditions, however, the wake exhibits an instability which is not understood. For cross-flow Reynolds numbers in the subcritical region the wake can be described in terms of a cross-flow Strouhal number which has a constant value of 0·2 for cross-flow Mach number components (Mc) up to 0·7 and then increases steadily to a value of 0·6 at Mc = 1·6. The strength of the wake vortices varies substantially with Mc, increasing to a maximum at Mc ≈ 0·7 and then decreasing rapidly for higher values of Mc. Schlieren photographs of the wake have been analysed by means of the impulse flow analogy and also by considering the vortices to be part of a yawed infinite vortex street. The impulse flow analogy is shown to be of use in determining the cross-flow Strouhal number but estimates of vortex strength are too high. The Kármán vortex street theory combined with the sweepback principle leads to reliable estimates of vortex strength up to Mc = 1·0.

Information is given on the spacing, path and strength of the vortices shed from the body for flow conditions varying from incompressible speeds up to Mc = 1·0. Finally this information is used to determine the vortex drag of a two-dimensional circular cylinder below Mc = 1·0.
Unsteady viscous flow in a curved pipe
Authors: Lyne W. H.
Published: March 2006

The flow in a pipe of circular cross-section which is coiled in a circle is studied, the pressure gradient along the pipe varying sinusoidally in time with frequency ω. The radius of the pipeais assumed small in relation to the radius of curvature of its axisR. Of special interest is the secondary flow generated by centrifugal effects in the plane of the cross-section of the pipe, and an asymptotic theory is developed for small values of the parameter β = (2ν/ωa2)½, where ν is the kinematic viscosity of the fluid. The secondary flow is found to be governed by a Reynolds number$R_s = \overline{W}^2a/R \omega\nu$, where$\overline{W}$is a typical velocity along the axis of the pipe, and asymptotic theories are developed for both small and large values of this parameter. For sufficiently small values of β it is found that the secondary flow in the interior of the pipe is in the opposite sense to that predicted for a steady pressure gradient, and this is verified qualitatively by an experiment described at the end of the paper.
Mixed convection from long horizontal cylinders
Authors: Gebhart B. , Pera L.
Published: March 2006

This paper is the report of an experimental study of heat transfer from fine horizontal wires of various lengths to fluids having various Prandtl numbers. Transport characteristics were determined for the full spectrum of processes from natural, through mixed, to forced convection. The experimental results are compared with those of past analysis and with correlations. The very high level of accuracy and reproducibility of the data makes possible the detection of very small effects. The influence of cylinder length on transport is shown for both of the asymptotic régimes of natural and of forced convection. Transport in the mixed-convection régime is determined and limits of that régime are estimated.
Measurements of the wave-number/phase velocity spectrum of wall pressure beneath a turbulent boundary layer
Authors: Wills J. A. B.
Published: March 2006

Measurements are presented of the wave-number/frequency and wave-number/phase velocity spectrum of wall pressure for a two-dimensional turbulent boundary layer in zero pressure gradient, obtained from a Fourier transform of experimental filtered spatial correlations. This method allows the results to be corrected for acoustic disturbances in the wind tunnel, and for finite transducer size. An empirical form for the pressure field is proposed, based on the measurements, and is used to predict a frequency spectrum correction for transducer size which agrees well with measured values.
Spin-up of a strongly stratified fluid in a sphere
Authors: Clark Alfred , Clark Patricia A. , Thomas John H. , Lee Nien-Hon
Published: March 2006

A linear theory is developed for the spin-up of a compressible fluid, stratified by a spherical gravity field. Numerical results are obtained for the case of strong stratification (Brunt–Väisälä frequency N much greater than the rotation frequency ω0). The interior flow is solved in terms of a set of angular eigenfunctions which have been obtained numerically. The principal result is that the spin-up is limited to a layer adjacent to the spherical boundary, the thickness δ of the layer being of the order of L(ω0/N), where L is the radius of the boundary. The solution is qualitatively similar to that found by Holton (1965), Walin (1969), and Sakurai (1969a, b) for a stratified fluid in a cylinder. The thickness of the spin-up layer diminishes with latitude ϕ, the variation being described roughly by the formula δ ∼ LΩ0| sin ϕ|/N. For the case of slow continuous spin-up, the Ekman suction velocity has been calculated, and the results show that |ϕ| = 24° is the dividing angle between suction (|ϕ| > 24°) and blowing (|ϕ| < 24°).
On a model representation for certain spatial-resonance phenomena
Authors: Mahony J. J. , Smith Ronald
Published: March 2006

It has been observed that standing surface waves in water may be excited by acoustic fields of very much higher frequency. No special relationship between the two frequencies appears to be required, but there is such a relationship between the spatial variations of the acoustic and surface wave modes. Another requirement is that the lower frequency should be comparable with the resonant and width of the acoustic response of the system. An explanation of such phenomena is proposed and is tested on a somewhat idealized model by the use of techniques which could be extended to deal with more realistic situations. The model serves to explain qualitatively the available experimental observations. It is suggested that the phenomenon of spatial resonance is not confined to the interaction between water waves and acoustic fields, but may occur generally in systems having modes with related spatial patterns but greatly different frequencies.
Observations on a spatial-resonance phenomenon
Authors: Huntley Ian
Published: March 2006

The phenomenon was observed during experiments in which a beaker containing water was vibrated in one of its bell modes (the inextensional flexural vibrations of the wall). For certain combinations of driving force and frequency, a standing water wave of large amplitude was generated whose peripheral wavenumber might be either zero (i.e. the wave was radially symmetric) or twice that of the bell mode. This relationship between the wavenumbers of the bell mode and water wave, and the fact that the driving frequency was many times that of the water wave, indicated that this was an instance of a general mechanism that has been studied theoretically by Mahony & Smith (1972). For a model situation, allowing for dissipative effects and nonlinear coupling between nearly resonant oscillations at greatly differing frequencies, they derived a relation-ship between the driving force and frequency representing conditions of neutrals tability (i.e. such that the rate of energy transfer from the high frequency to the low frequency oscillations is zero). The aim of the experimental observations reported here was to check this relationship and other predictions of their theory.
A ninth-order solution for the solitary wave
Authors: Fenton John
Published: March 2006

Several solutions for the solitary wave have been attempted since the work of Boussinesq in 1871. Of the approximate solutions, most have obtained series expansions in terms of wave amplitude, these being taken as far as the third order by Grimshaw (1971). Exact integral equations for the surface profile have been obtained by Milne-Thomson (1964,1968) and Byatt-Smith (1970), and these have been solved numerically. In the present work an exact operator equation is developed for the surface profile of steady water waves. For the case of a solitary wave, a form of solution is assumed and coefficients are obtained numerically by computer to give a ninth-order solution. This gives results which agree closely with exact numerical results for the surface profile, where these are available. The ninth-order solution, together with convergence improvement techniques, is used to obtain an amplitude of 0.85for the solitary wave of greatest height and to obtain refined approximations to physical quantities associated with the solitary wave, including the surface profile, speed of the wave and the drift of fluid particles.
Kelvin wave attenuation along nearly straight boundaries
Authors: Pinsent H. G.
Published: March 2006

Two related wave problems are considered for a rotating sea of nearly uniform depth bounded by a coastline which is nearly straight. The depth changes are assumed to be independent of the distance from the coastline. The first problem, which is concerned with the origin of Kelvin waves in a coastal wave record, deals with a system of plane waves incident on the coastline and giving rise, in addition to reflected waves, to a Kelvin wave moving along the coast. Linearized theory is used to obtain details of the Kelvin wave for arbitrary perturbations in coastline and depth. Results suggest that the depth changes have their greatest effect in producing Kelvin waves if the incident wave crests are nearly parallel, but not exactly so, to the line of the depth changes. On the other hand when the wave crests are parallel to the coast, Kelvin waves are produced only by changes in the coastal boundary. In the second problem a Kelvin waye is assumed to be the incident wave. To find the energy propagated away from the coastline it is necessary to extend the theory to second order in the perturbations. It is shown that for a fixed wave period less than a pendulum day this energy has a maximum for a perturbation whose length is of comparable magnitude to the incident wavelength. Finally, the theory is applied to Kelvin waves propagating along the Californian coastline. Results obtained tend to confirm the suspicion that coastal irregularities are responsible for certain anomalies detected in tidal wave constituents by Munk, Snodgrass & Wimbush (1970).
Thermal instabilities in two-fluid horizontal layers
Authors: Zeren Richard W. , Reynolds William C.
Published: March 2006

An analytical and experimental study of thermally induced instability in horizontal two-fluid layers is reported. A liner stability analysis for two initially motionless, viscous immiscible fluids confined between horizontal isothermal solid surface and subject to both density (Bénard) and surface-tension-grandient (Marangoni) drving mechanisms is presented. Calculations for the labortory configuaration reported below predict instability for heating from above or below. Response is strongly department on the ratios of the properties of the fluids, the total depth of the layer and the depth fraction of one fluid. Three different response modes occur(interfacial-tension-gradient dominated, buoyancy dominated and surface-deflexion dominated) depending on the fluid depth fractions when the heating is from above, the buoyanvy mechanism is stabilizing for most wavenumbers, including the xritical one. Heating from below lowere the critical Marangoni number and adds a buoyancy driven response mode. Results of experimental measurement of the critical Marangoni number exceeds the predicted critical value by as much as five times. The critical Rayleigh number observe for heating from below fallos between the critical values predicted with and without the Marangoni effect. The presence of surface contamination is belived to be responsible for the apparent lack of convection when heating is from above and for the different between the predicted and measured critical Rayleigh number when heating is from below.
Two-dimensional sink flow of a stratified fluid contained in a duct
Authors: Imberger Jorg
Published: March 2006

A reservoir is assumed to be filled with water which has a linear variation of density with depth. The geometry of the boundaries is simplified to a parallel walled duct with the line sink at the centre of the fluid. The primary focus is on partitioning the flow into distinct flow regimes and predicting the withdrawal-layer thickness as a function of the distance from the sink; the predictions are verified experimentally.

For fluids with a Schmidt number of order unity, the withdrawal layer is shown to be composed of distinct regions in each of which a definite force balance prevails. The outer flow, where inertia forces are neglected, changes from a parallel uniform flow upstream to a symmetric self-similar withdrawal layer near the sink. For distances from the sink smaller than a critical distance, dependent on the flow parameters, inertia forces become of equal importance to buoyancy and viscous forces. The equations valid in this inner region are derived. Using the inner limit of the outer flow as the upstream boundary condition, these inner equations are solved approximately for the withdrawal-layer thickness by an integral method. The inner and outer variations of δ, the withdrawal-layer thickness, are combined to yield a composite solution and it is seen that the inclusion of inertia forces yields layers thicker than those obtained from a strict buoyancy-viscous force balance. In terms of the inner variables the only parameter remaining is the Schmidt number.

Laboratory experiments were carried out to verify the theoretical conclusions. The observed withdrawal-layer thicknesses were shown to be closely predicted by the integral solution. Furthermore, the data could be represented in terms of the inner variables by a single curve dependent only on the Schmidt number.