bluuebunny/crossref_metadata_2025 huggingface dataset:
Effect of tube elasticity on the stability of Poiseuille flow
Authors: Garg Vijay K.
Published: April 2006

The effect of tube elasticity on the stability of Poiseuille flow to infinitesimal axisymmetric disturbances is investigated. The disturbance equations for the fluid are solved numerically while those for the arbitrarily thick tube are solved analytically in terms of Bessel functions of complex argument. It is shown that an elastic tube can cause instability of Poiseuille flow, unlike a rigid tube, in which the flow is always stable. Neutral curves are presented for various values of the tube parameters. It is found that the critical Reynolds number varies almost as the square root of the Young's modulus of the tube material while the critical dimensionless frequency is almost invariant, being about 1·1 for the cases studied.
Further experiments in nearly homogeneous turbulent shear flow
Authors: Harris V. G. , Graham J. A. H. , Corrsin S.
Published: April 2006

The experiment of Champagne, Harris & Corrsin in generating and studying a nearly homogeneous turbulent shear flow has been extended to larger values of the dimensionless downstream time or strain by the use of a larger mean velocity gradient in the same wind tunnel. The system appears to reach an asymptotic state in which scales and turbulent energy grow monotonically. Two-point covariances and tensor structure of one-point ‘Reynolds stress’ and ‘pressure/strain-rate covariance’ agree with the earlier case. However, the linear intercomponent energy exchange hypothesis due to Rotta, very roughly confirmed by the earlier experiment, is contradicted by the present data.
Computation of the flow between two rotating coaxial disks
Authors: Holodniok M. , Kubicek M. , Hlavácek V.
Published: April 2006

A numerical investigation of the problem of rotating disks is made using the Newton–Raphson method. It is shown that the governing equations may exhibit one, three or five solutions. A physical interpretation of the calculated profiles will be presented. The results computed reveal that both Batchelor and Stewartson analysis yields for high Reynolds numbers results which are in agreement with our observations, i.e. the fluid may rotate as a rigid body or the main body of the fluid may be almost at rest, respectively. Occurrence of a two-cell situation at particular branches will be discussed.
Photogrammetry of spherical shocks reflected from real and ideal surfaces
Authors: Dewey J. M. , Mcmillin D. J. , Classen D. F.
Published: April 2006

A photogrammetrical technique has been used to study the interaction of two identical explosively produced spherical shock waves and to compare this interaction with the reflexion of one of the spherical shocks from the ground. It is postulated that there was no energy loss in the interaction of the two shock waves and that the interaction therefore simulated the reflexion of a spherical shock from an ideal non-energyabsorbing surface. The ‘ideal’ reflexions were compared with real reflexions from two types of ground surface: one smooth and the other rough. Experiments were carried out with the centres of the spherical shocks at two separations so that observations could be made of the interaction of shocks of different strength. Significant differences were shown to exist in both the strengths of the Mach shocks and in the triple-point trajectories over the different surfaces. The results are intended to aid in the evaluation of computer codes being developed to simulate spherical-shock reflexions from real surfaces.
Eddy diffusivity, eddy noise and subgrid-scale modelling
Authors: Rose Harvey A.
Published: April 2006

A subgrid model is presented for a passive scalar advected by a randomly prescribed frozen velocity field. In addition to an eddy diffusivity it has a term which describes the injection of noise from the subgrid scales, and a term which implicitly describes the coupling between the large eddies and the eddies just below the limit of resolution of the finite-difference grid. The construction of the model is based upon an iterative procedure which models away first the dissipation-range eddies and then the eddies of a slightly larger size, etc.
Viscous sheets advancing over dry beds
Authors: Buckmaster J.
Published: April 2006

The unsteady creeping motion of a thin sheet of viscous liquid as it advances over a gently sloping dry bed is examined. Attention is focused on the motion of the leading edge under various influences and four problems are discussed. In the first problem the fluid is travelling down an open channel formed by two straight parallel retaining walls placed perpendicular to an inclined plane. When the channel axis is parallel to the fall line there is a progressive-wave solution with a straight leading edge, but inclination of the axis generates distortions and these are calculated. In the second problem a sheet with a straight leading edge travelling over an inclined plane penetrates a region where the bed is uneven, and the subsequent deformation of the leading edge is followed. The third problem considers the flow down an open channel of circular cross-section (a partially filled pipe) and the time-dependent shape of the leading edge is calculated. The fourth problem is that of flow down an inclined plane with a single curved retaining wall. These problems are all analysed by assuming that a length characteristic of the geometry is large compared with the fluid depth divided by the bed slope, and all the solutions display extreme sensitivity to the data.
The formation of layers in a double-diffusive system with a sloping boundary
Authors: Linden P. F. , Weber J. E.
Published: April 2006

The flows induced by the presence of an insulating sloping boundary in a doublediffusive system are examined. In the diffusive case, when the component with the larger diffusivity is unstably distributed, it is known that under certain circumstances horizontal motions are induced near the slope, and that a series of horizontal layers forms. We investigate the formation and properties of the layers, in particular their vertical scale and its dependence on the stratification and the slope angle. The scale of the layers is found to be a strong function of Gρ, the ratio of the vertical density gradient of the unstably distributed component to that of the stably distributed component. At low values of Gρ, no layering was observed; at larger values of Gρ layers were formed, and their scale increased as Gρ → 1. A weak dependence of scale on slope angle was also observed with the scale diminishing as the angle of the slope to the horizontal increased.

A new form of layering has been observed when the basic stratification is in the finger sense. At high enough values of Gρ the basic stratification is unstable to finger motions and these exist throughout the fluid. When a slope is introduced, horizontal motions are set up near the slope which cause the fingers to break down and layers are produced. There is considerable horizontal motion in these layers as well as convective motions driven by the fingers in the interfaces between the layers. The formation of these layers and some of their properties are documented.
The unsteady expansion of a gas into a non-uniform near vacuum
Authors: Grundy R. E. , Mclaughlin R.
Published: April 2006

The paper generalizes an earlier problem of Grundy (1972) by considering the expansion of a (uniform) initially contained gas into a low-density non-uniform ambient atmosphere of density ρ0r−k, where k > 0 and r is a non-dimensional radial co-ordinate. Regarding the flow as a perturbation of the perfect-vacuum expansion, we set up a boundary-value problem with boundary conditions on the contact front separating the two gases and on the strong shock which propagates into the ambient atmosphere. A large time solution to the problem can be developed by constructing an outer expansion valid near the contact front and an inner expansion valid near the shock. The matching process encounters two kinds of difficulty both of which imply that the large time solution is indeterminate from an asymptotic analysis alone.

The asymptotic analysis does show however that the shock velocity tends to a constant only for restricted values of k. For the remaining values the shock has a k-dependent power-law behaviour. The paper examines the location of the transition and determines the asymptotic power-law dependence of the shock velocity.
Growth and decay of perturbations at an interface in a stagnation counterflow
Authors: Erickson Gary G. , Olfe D. B.
Published: April 2006

Integral-transform theory is used to solve the problem of sinusoidal initial perturbations in a planar stagnation counterflow, with extension to the axisymmetric case. The two incompressible fluids are assumed to be inviscid, so that across the initially plane interface the velocity shear is a velocity slip which grows linearly with the distance from the stagnation point. The solution for the interface displacement shows a competition between an amplification produced by the shear instability and a decay produced by the stretching effect of the accelerating unperturbed flow. At early times the interface perturbation grows exponentially with time, but eventually the stretching process reduces the interface displacement to a magnitude comparable to the initial perturbation.
Two-fluid spin-up in a centrifuge
Authors: Berman A. S. , Bradford J. , Lundgren T. S.
Published: April 2006

The behaviour of the interface between two immiscible fluids of different density and viscosity in a centrifuge is investigated both analytically and experimentally. The study includes the interfacial shape and behaviour during both steady and transient operation of the centrifuge. The interface shape is investigated for rigid-body rotation and during slow steady acceleration or deceleration of the centrifuge. The dependence of the interface shape on time is investigated during a rapid spin-up to a slightly different value of the angular velocity, which then remains constant. Some aspects of interface stability are also reported.
Numerical studies of some nonlinear hydrodynamic problems by discrete vortex element methods
Authors: Meng J. C. S. , Thomson J. A. L.
Published: April 2006

A class of nonlinear hydrodynamic problems is studied. Physical problems such as shear flow, flow with a sharp interface separating two fluids of different density and flow in a porous medium all belong to this class. Owing to the density difference across the interface, vorticity is generated along it by the interaction between the gravitational pressure gradient and the density gradient, and the motion consists of essentially two processes: the creation of a vortex sheet and the subsequent mutual induction of different portions of this sheet.

Two numerical methods are investigated. One is based upon the well-known Green's function method, which is a Lagrangian method using the Biot-Savart law, while the other is the vortex-in-cell (VIC) method, which is a Lagrangian-Eulerian method. Both methods treat the interface as sharp and represent it by a distribution of point vortices. The VIC method applies the FFT (fast Fourier transform) to solve the stream-function/vorticity equation on an Eulerian grid, and computational efficiency is further improved by using the reality properties of the physical variables.

Four specific problems are investigated numerically in this paper. They are: the Rayleigh-Taylor instability, the Saffman-Taylor instability, transport of aircraft trailing vortices in a wind shear, and the gravity current. All four problems are solved using the VIC method and the results agree well with results obtained by previous investigators. The first two problems, the Rayleigh-Taylor instability and the Saffman-Taylor instability, are also solved by the Green's function method. Comparisons of results obtained by the two methods show good agreement, but, owing to its computational economy, the VIC method is concluded to be the better method for treating the class of hydrodynamic problems considered here.
The physics of vortex-ring evolution in a stratified and shearing environment
Authors: Meng J. C. S.
Published: April 2006

A semi-analytical numerical study was performed to simulate the development of a vortex ring in a stratified and/or shearing environment. Practical applications of results of this study can be found in turbulence modelling and in studies of plumes and wakes. The objective is to follow exactly the evolution of a vortex ring so that the three-dimensional vortex-stretching mechanisms due to stratification and the shear effects, respectively, can be understood.

The basic formulation consists of the solution of the vorticity equation in a stratified medium. The approach adopted is unique in that discrete vortex elements are used and arbitrary nonlinear interactions are allowed (therefore three-dimensional effects) among various vorticity generators. One of the two fundamental assumptions in this approach is that the vorticity is allowed to be generated only along the density discontinuity. The second assumption is that, while the vorticity carried by the vortex ring is modelled by vortex elements tangential to the vortex loop (which was a vortex ring initially), the vorticity generated by stratification effects is modelled by long vortex lines parallel to the axis of the vortex ring. This limits the validity of the present calculation to high Froude number flow.

Numerical stability is guaranteed by the finite core radius for each discrete vortex element and uniform spacing between them; the former is determined by consideration of the momentum integral over the vortex-ring plane. The latter is determined by a cubic spline interpolation method which conserves the circulation and centroids of the vorticity. The velocity of each vortex element is determined by the discretized Biot-Savart law, and motion of the vortex loop is calculated by a predicator-corrector time integration method.

Calculations were carried out for both momentum-carrying and momentumless vortex rings. A particular two-dimensional case gives good agreement with Kármán's theory. The evolution of the vortex loop reveals a process in which only the vorticity normal to the stratification is conserved; the remaining vorticity is dissipated through a simulated viscous dissipation. Evolution of a vortex loop on a shear layer reveals a vortex-loop rotation rate equal to the velocity shear, and a twisting motion due to the Magnus force which can lead to the turbulence energy cascade phenomenon. Numerical results demonstrate effects of each individual vorticity source and observed phenomena can be explained.
A theoretical study of the effects of wall conductivity, non-uniform magnetic fields and variable-area ducts on liquid-metal flows at high Hartmann number
Authors: Holroyd Richard J. , Walker John S.
Published: April 2006

Flows of incompressible, electrically conducting liquids along ducts with electrically insulating or weakly conducting walls situated in a strong magnetic field are analysed. Except over a short length along the duct where the magnetic field strength and/or the duct cross-sectional area vary, the duct is assumed to be straight and the field to be uniform and aligned at right angles to the duct. Magnitudes of the field strength B0 and the mean velocity V are taken to be such that the Hartmann number M [Gt ] 1, the interaction parameter N (= M2/Re) [Gt ] 1 (Re being the Reynolds number of the flow) and the magnetic Reynolds number Rm [Lt ] 1.

For an O(1) change in the product VB0 along the duct across the non-uniform region, it is shown that:

(i) In the non-uniform region the streamlines and current flow lines follow surfaces containing the field lines satisfying $\int B^{-1}ds = {\rm constant}$, the integration being carried out along the field line within the duct; these surfaces are equipotentials and isobarics. This leads to

(ii) a tube of stagnant, but not current-free fluid at the centre of the duct parallel to the field lines around which the flow divides to bypass it. To accommodate this flow,

(iii) the usual uniform field/straight duct flow is disturbed over very large distances upstream and downstream of this region, the maximum length O(duct radius × M½) occurring in a non-conducting duct;

(iv) a large pressure drop is introduced into the pressure distribution regardless of the direction of the flow, the effect being most severe in a non-conducting duct, where the drop is O(duct radius × (uniform field/straight duct pressure gradient) × M½);

(v) in the part of the duct with the lower value of VB0 a region of reverse flow occurs near the centre of the duct and the stagnant fluid.
Rapid distortion of axisymmetric turbulence
Authors: Sreenivasan K. R. , Narasimha R.
Published: April 2006

A generalization of the isotropic theory of Batchelor & Proudman (1954) is developed to estimate the effect of sudden but arbitrary three-dimensional distortion on homogeneous, initially axisymmetric turbulence. The energy changes due to distortion are expressed in terms of the Fourier coefficients of an expansion in zonal harmonics of the two independent scalar functions that describe the axisymmetric spectral tensor. However, for two special but non-trivial forms of this tensor, which represent possibly the simplest kinds of non-isotropic turbulence and specify the angular distribution but not the wavenumber dependence, the energy ratios have been determined in closed form. The deviation of the ratio from its isotropic value is the product of a factor containing R, the initial value of the ratio of the longitudinal to the transverse energy component, and another factor depending only on the geometry of the distortion. It is found that, in axisymmetric and large two-dimensional contractions, the isotropic theory gives nearly the correct longitudinal energy, but (when R > 1) over-estimates the increase in the transverse energy; the product of the two intensities varies little unless the distortion is very large, thus accounting for the stress-freezing observed in rapidly accelerated shear flows.

Comparisons with available experimental data for the spectra and for the energy ratios show reasonable agreement. The different ansatzes predict results in broad qualitative agreement with a simple strategem suggested by Reynolds & Tucker (1975), but the quantitative differences are not always negligible.
The stability of a two-dimensional stagnation flow to three-dimensional disturbances
Authors: Wilson S. D. R. , Gladwell I.
Published: April 2006

Experiments have shown that the two-dimensional flow near a forward stagnation line may be unstable to three-dimensional disturbances. The growing disturbance takes the form of secondary vortices, i.e. vortices more or less parallel to the original streamlines. The instability is usually confined to the boundary layer and the spacing of the secondary vortices is of the order of the boundary-layer thickness. This situation is analysed theoretically for the case of infinitesimal disturbances of the type first studied by Görtler and Hämmerlin. These are disturbances periodic in the direction perpendicular to the plane of the flow, in the limit of infinite Reynolds number. It is shown that the flow is always stable to these disturbances.
The hydrodynamics of the spreading of one liquid on the surface of another
Authors: Dipietro N. D. , Huh C. , Cox R. G.
Published: April 2006

The mechanisms involved in the spreading of one liquid on the surface of another are considered for the case of a positive spreading coefficient. Taking into account the effects of gravity, capillary pressure and the spreading coefficient, the general equations determining the spreading are derived. These are then solved for the situation where the spreading liquid is introduced onto the surface of a uniformly flowing substratum at a position upstream of a barrier on the substratum surface. In this manner a steady-state situation is achieved for which the variation of spreading-liquid thickness with position is obtained as a function of the deposited volume of spreading liquid and the velocity of the substratum.
The effect of fluid motions on the absorption of molecules by suspended particles
Authors: Purcell Edward M.
Published: April 2006

The rate at which a particle in suspension can capture diffusing solute molecules can be increased by stirring the fluid. It is shown that the increase is closely related to the total power expended, per unit volume of fluid, by the stirring device. The increase in diffusion current to a particle is related to the local rate of deformation of the fluid Ω (which, in turn, determines the dissipation) by a function F(Ωa2/D), where a is the particle radius and D the diffusion constant for the molecule in question. The function F has been determined experimentally by investigating the corresponding problem in heat transfer. In a fluid of viscosity η, stirring which is vigorous enough to double the mean diffusion current to a particle must entail a power dissipation, per unit volume, not less than 500ηD2/a4. For particles a few microns in size, or smaller, in water, effective stirring is not feasible. The results can be used also to predict the effect of stirring on the coagulation of similar particles. To double, by stirring, the rate at which particles of radius b form dimers requires a stirring power proportional to b−6, and is not feasible in water if b is less than 10−5 cm.
Structure functions of temperature fluctuations in turbulent shear flows
Authors: Antonia R. A. , Atta C. W. Van
Published: April 2006

Structure functions of turbulent temperature and velocity fluctuations are measured both for the atmosphere, in the surface layer over land, and for the laboratory, in the inner region of a thermal boundary layer and on the axis of a heated jet. Even-order temperature structure functions, up to order eight, generally compare favourably with the analysis of Antonia & Van Atta over the inertial subrange. The Reynolds number dependence of these structure functions, as predicted by the analysis, is in qualitative agreement with the measured data. Odd-order temperature structure functions depart significantly from the isotropic value of zero, particularly at large time delays. This departure is reasonably well predicted, over the inertial subrange, by postulating a simple ramp model for the temperature fluctuations. Assumptions involved in this model are directly tested by measurements in the heated jet. The ramp structure does not seriously affect either the even-order temperature structure functions or the mixed velocity-temperature functions, which include even-order moments of the temperature difference.
The influence of buoyancy on turbulent transport
Authors: Lumley John L. , Zeman Otto , Siess J.
Published: April 2006

Turbulent transport of fluctuating turbulent energy, turbulent momentum flux, temperature variance, turbulent heat flux, etc. in the upper part of the atmospheric boundary layer is usually dominated by buoyant transport. This transport is responsible for the erosion of the overlying stably stratified region, resulting in progressive thickening of the mixed layer. It is easy to show that a classical gradient transport model for the transport will not work, because it transports energy in the wrong direction. On the other hand, application of the eddy-damped quasi-Gaussian approximation to the equations for the third moments results in a transport model which predicts realistic inversion rise rates and heat-flux profiles. This is also a gradient transport model, but like molecular transport in solutions, a flux of one quantity depends on gradients of all relevant quantities. Transport coefficients are modified by the heat flux, so that the vertical transport is severely reduced near the inversion base. A simple Lagrangian model of transport of an indelible scalar in a stratified flow indicates that the form of the modified transport coefficients results from a marked anisotropic change in the Lagrangian time scale in stratification.
Meandering and braiding of rivers
Authors: Fredsøe Jørgen
Published: April 2006

The origin of meandering and braiding of alluvial rivers is re-analysed in terms of stability theory. The flow is described by a two-dimensional model, and the transportation of sediment is separated into bed-load transport and transport of suspended sediment, by use of the improved knowledge of sediment transport mechanisms achieved in recent years. The paper explains why it is important to distinguish between the sediment transported as bed load and that in suspension.

The analysis is able to predict whether a river remains stable or tends to meander or braid.

The results of the stability analysis are compared with laboratory experiments and data from natural rivers, and the agreement is satisfactory.
The number of waves on unstable vortex rings
Authors: Saffman P. G.
Published: April 2006

An explanation is proposed for the dependence on Reynolds number and other parameters of the number of waves which appear on vortex rings formed by pushing fluid out of a tube. It is shown that the number of waves can be sensitive to the vorticity distribution in the core of the ring. The process of ring formation is discussed and it is concluded that peaked vorticity distributions, limited by viscosity, will occur. Quantitative estimates of the number of waves are made. Agreement with observation is satisfactory.
Similarity in the initial region of annular jets: three configurations
Authors: Ko N. W. M. , Chan W. T.
Published: April 2006

This paper describes part of a detailed study of the initial region of three annular jets. The configurations are the basic one, without any bullet in the centre, and those with a conical and an elliptical bullet. From the mean velocity and turbulence intensity measurements the initial region can be divided into the initial merging, the intermediate and the fully merged zones. Within these three zones similarity of both the mean velocity and the turbulence intensity profiles has been found. The similarity curves are compared with those for a single jet.
Artificial control of the laminar-turbulent transition of a two-dimensional wake by external sound
Authors: Sato Hiroshi , Saito Hironosuke
Published: April 2006

Artificial acceleration and deceleration of the transition process in a two-dimensional wake were attempted. The wake was produced behind a thin aerofoil placed parallel to uniform flow. The sound from a loudspeaker introduced into the wake acted as an artificial disturbance. Various kinds of sound were tested and the effect on the transition was judged by the energy spectrum. Sinusoidal sound of the frequency of the maximum growth rate in the linear region decelerates the transition, whereas sound of a different frequency accelerates it. Sound of two or four frequencies is more effective in accelerating the transition when the frequencies are properly chosen. White noise from the loudspeaker is not effective, but a two-peak noise specially designed for strong nonlinear interaction is the most effective in accelerating the transition process. These results can be explained by two empirical properties of the nonlinear interaction: the growth suppression induced by a large amplitude fluctuation and the stronger interaction between fluctuations of closer amplitudes.
The noise from the large-scale structure of a jet
Authors: Williams J. E. Ffowcs , Kempton A. J.
Published: April 2006

In this paper we assess the importance as a noise source of the well-ordered large-scale structure of a jet. We propose two simple models of the structure: the first emphasizes those features in common with waves that initially grow on an unstable shear layer but eventually saturate and decay, while the second regards the abrupt pairing of eddies as the most significant event in the jet's development. Our models demonstrate the possibility that forcing at one frequency could increase the broad-band noise of a jet, though, for jets with supersonic eddy convection velocities, the sound propagating in the direction of the Mach angle retains the spectrum of the excitation field. These features are consistent with the available experimental data, and strongly support the view that the large-scale structure of jet turbulence provides the dominant contribution to jet noise.
Measurements of velocity distributions in the laminar wake of a flat plate
Authors: Nishioka Michio , Miyagi Tosio
Published: April 2006

The two-dimensional wake of a thin flat plate parallel to the stream was maintained laminar and steady at Reynolds numbers up to 3000 in a low-turbulence wind tunnel. Velocity distributions in the wake were measured in detail for Reynolds numbers from 20 to 3000. One of the interesting results is the appearance of a velocity overshoot, namely that the velocity in the outer part of the shear layer exceeds that of the uniform flow in the vicinity of the trailing edge. Comparisons between the experimental results and Goldstein's theoretical predictions show good agreement in the far wake irrespective of the Reynolds number, but not in the near wake even at higher Reynolds numbers, in particular immediately behind the trailing edge.
The wave system attached to a finite slender body in a supersonic relaxing gas stream
Authors: Sinai Y. L. , Clarke J. F.
Published: April 2006

The results of a companion paper are extended to encompass the flow about smooth, but otherwise general body shapes. The wave behaviour depends on three important parameters, namely the body thickness ratio ε, the quantity δ, which is proportional to the difference between the frozen and equilibrium sound speeds, and the ratio λ of a relaxation time to a characteristic flow time. Both analytical and numerical solutions have been obtained; account is taken of nonlinearity for complete spectra of the three parameters, enabling an assessment to be made of the evolution of the wave forms for a host of situations. In particular, it is possible to predict the structures of the shock waves in various regions, and it transpires that under certain conditions vibrational relaxation can overwhelm other dissipative effects.
Instability of steady natural convection in a vertical fluid layer
Authors: Bergholz R. F.
Published: April 2006

The instability of steady natural convection of a stably stratified fluid between vertical surfaces maintained at different temperatures is analysed. The linear stability theory is employed to obtain the critical Grashof and Rayleigh numbers, for widely varying levels of the stable background stratification, for Prandtl numbers ranging from 0·73 to 1000 and for the limiting case of infinite Prandtl number. The energetics of the critical disturbance modes also are investigated. The numerical results show that, if the value of the Prandtl number is in the low to moderate range, there is a transition from stationary to travelling-wave instability if the stratification exceeds a certain magnitude. However, if the Prandtl number is large, the transition, with increasing stratification, is from travelling-wave to stationary instability. The theoretical predictions are in excellent agreement with the experimental observations of Elder (1965) and of Vest & Arpaci (1969), for stationary instability, and in fair to good agreement with the experimental results of Hart (1971), for travelling-wave instability.
Resonant interactions between topographic planetary waves in a continuously stratified fluid
Authors: Mysak Lawrence A.
Published: April 2006

The resonant interactions between topographic planetary waves in a continuously stratified fluid are investigated theoretically. The interacting waves form a resonant triad and travel along a channel with a uniformly sloping bottom. The basic state stratification in the channel is characterized by a constant buoyancy frequency. The existence of solutions to the quadratic resonance conditions is established graphically. Each wave by itself is a bottom-intensified oscillation of the type discovered by Rhines (1970) except for the addition of a small positive frequency correction. This correction must be included to satisfy higher-order terms in the bottom boundary condition. For strong stratification (r2[Gt ]L2, wherer= internal deformation radius andL= channel width), the waves are strongly bottom-trapped and this frequency correction is negligible. For weak stratification (r2[Lt ]L2) the waves are barotropic and the frequency correction isO(δ), where δ = fractional change in depth across the channel. In many oceanic contexts, δ lies in the range 0·1-0·4 and therefore this correction can produce a significant change in the phase speed. The amplitudes of the waves in the triad obey the classical gyroscopic equations usually encountered in quadratic resonance problems. In particular, the amplitudes evolve on the slow time scale\[ t=O(1/f_0\delta^2), \]which for our scaling assumptions is alsoO(1/f0Ro), whereRois the Rossby number.

The results are applied to the Norwegian continental slope region. It is shown that, in this vicinity, there may exist resonant triads consisting of two short, high-frequency waves (periods around 3-4 days) and one long, low-frequency wave (period around 9 days).
A one-dimensional piston problem of gasdynamics
Authors: Mclaughlin R.
Published: April 2006

This paper considers the case of a one-dimensional piston moving outwards with a speed proportional to rα and driving a strong shock into a non-uniform ambient gas whose density is initially proportional to r−k, k > 0. This problem is connected with that studied by Grundy & McLaughlin (1977), who effectively discussed the case α = 0. We discover further important uses of the Sedov similarity solutions and find kc, the upper limit to k for the shock path to be asymptotically similar to the piston path.
On the shape and breaking of finite amplitude internal gravity waves in a shear flow
Authors: Thorpe S. A.
Published: April 2006

This paper is concerned with two important aspects of nonlinear internal gravity waves in a stably stratified inviscid plane shear flow, their shape and their breaking, particularly in conditions which are frequently encountered in geophysical applications when the vertical gradients of the horizontal current and the density are concentrated in a fairly narrow depth interval (e.g. the thermocline in the ocean). The present theoretical and experimental study of the wave shape extends earlier work on waves in the absence of shear and shows that the shape may be significantly altered by shear, the second-harmonic terms which describe the wave profile changing sign when the shear is increased sufficiently in an appropriate sense.

In the second part of the paper we show that the slope of internal waves at which breaking occurs (the particle speeds exceeding the phase speed of the waves) may be considerably reduced by the presence of shear. Internal waves on a thermocline which encounter an increasing shear, perhaps because of wind action accelerating the upper mixing layer of the ocean, may be prone to such breaking.

This work may alternatively be regarded as a study of the stability of a parallel stratified shear flow in the presence of a particular finite disturbance which corresponds to internal gravity waves propagating horizontally in the plane of the flow.
Wall region of a relaxing three-dimensional incompressible turbulent boundary layer
Authors: Hebbar K. S. , Melnik W. L.
Published: April 2006

An experimental investigation was conducted at selected locations in the wall region of a three-dimensional turbulent boundary layer relaxing in a nominally zero external pressure gradient behind a transverse hump (in the form of a 30° swept, 5 ft chord, wing-type model) faired into the side wall of a low-speed wind tunnel. The boundary layer (approximately 3·5 in. thick near the first survey station, where the length Reynolds number was 5·5 × 106) had a maximum cross-flow velocity ratio of 0·145 and a maximum cross-flow angle of 21·9° close to the wall. The hot-wire data indicated that the apparent dimensionless velocity profiles in the viscous sublayer are universal and that the wall influence on the hot wire is negligible beyond y+= 5. The existence of wall similarity in the relaxing flow field was confirmed in the form of a log law based on the resultant mean velocity and resultant friction velocity (obtained from the measured skin friction).

The smallest collateral region extended from the point nearest to the wall (y+≈ 1) up to y+= 9·7, corresponding to a resultant mean velocity ratio (local to free-stream) of 0·187. The unusual feature of these profiles was the presence of a narrow region of slightly decreasing cross-flow angle (1° or less) that extended from the point of maximum cross-flow angle down to the outer limit of the collateral region. A sublayer analysis of the flow field using the measured local transverse pressure gradient slightly overestimated the decrease in cross-flow angle. It is concluded that, in the absence of these gradients, the skewing of the flow could have been much more pronounced practically down to the wall (limited only by the resolution of the sensor), implying a near-wallnon-collateralflow field consistent with the equations of motion in the neighbourhood of the wall.

The streamwise relaxation of the mean flow field based on the decay of the cross-flow angle was much faster in the inner layer than in the outer layer. Over the stream-wise distance covered, the mean flow in the inner layer and the wall shear-stress vector relaxed to a two-dimensional state in approximately 10 boundary-layer thicknesses whereas the relaxation of the turbulence was slower and was not complete over the same distance.
Measurements and prediction of fully developed turbulent flow in an equilateral triangular duct
Authors: Aly A. M. M. , Trupp A. C. , Gerrard A. D.
Published: April 2006

Fully developed air-flows through an equilateral triangular duct of 12·7 cm sides were investigated over a Reynolds number range of 53 000 to 107 000. Based on equivalent hydraulic diameter, friction factors were found to be about 6% lower than for pipe flow. Mean axial velocity distributions near the wall were describable by the inner law of the wall (when based on local wall shear stress) but the constants differ slightly from those for pipe flow. As expected, the secondary flow pattern was found to consist of six counter-rotating cells bounded by the corner bisectors. Maximum secondary velocities of about 1 ½% of the bulk velocity were observed. The effects of secondary currents were evident in the cross-sectional distributions of mean axial velocity, wall shear stress and Reynolds stresses, and very prominent in the turbulent kinetic energy distribution. For the flow prediction, the vorticity production terms were expressed by modelling the Reynolds stresses in the plane of the cross-section in terms of gradients in the mean axial velocity and a geometrically calculated turbulence length scale. The experimental and predicted characteristics of the flow are shown to be in good agreement.
Propagation of perturbations in a gas-liquid mixture
Authors: Kuznetsov V. V. , Nakoryakov V. E. , Pokusaev B. G. , Shreiber I. R.
Published: April 2006

The present investigation has been performed over a wide range of the dimensionless parameters characterizing the process of propagation of pressure perturbations in a gas-liquid mixture; these are the Reynolds number, and a dispersion parameter responsible for the relation between the values of dispersion and signal intensity. The values of the above parameters were changed mainly by varying the initial perturbation. The results obtained show a complete agreement between the Burgers-Korteweg-de Vries model and the real process of propagation of long-wave perturbations in a liquid with gas bubbles. In addition to signal propagation with the formation of monotonic and oscillatory shock waves, the propagation of signals in the form of solitary waves (solitons) and wave packets was observed experimentally. Data have been obtained on signal damping, energy dissipation and the influence of mixture viscosity on the signal evolution.
The multiple-scale cumulant expansion for isotropic turbulence
Authors: Tatsumi Tomomasa , Kida Shigeo , Mizushima Jiro
Published: April 2006

A method of multiple-scale expansion is applied to the theory of incompressible isotropic turbulence in order to close the infinite system of cumulant equations. The dynamical equation for the energy spectrum derived from this method is found to give positive-definite solutions at all Reynolds numbers. At large Reynolds numbers the spectrum takes the form of Kolmogorov's$-\frac{5}{3}$power spectrum in the inertial subrange, whose extent increases indefinitely with Reynolds number. The spectrum in the energy-containing range satisfies an inviscid similarity law, so that the rate of energy decay or of viscous dissipation is also independent of the viscosity. In the higher wavenumber region beyond the inertial subrange the spectrum takes a universal form which is independent of its structure at lower wavenumbers. The universal spectrum is composed of three different subspectra, which are, in order of increasing wavenumber, the$k^{-\frac{5}{3}}$spectrum, thek−1spectrum and the exp [−σk1·5] spectrum, σ being a constant. Various statistical quantities such as the energy, the skewness of the velocity derivative, the microscale and the microscale Reynolds number are calculated from the numerical data for the energy spectrum. Theoretical results are discussed in detail in comparison with experimental results.
On the interactions of slender ships in shallow water
Authors: Yeung Ronald W.
Published: April 2006

The unsteady hydrodynamic interaction of two bodies moving in a shallow fluid is examined by applying slender-body theory. The bodies are assumed to be in each other's far field and the free surface is assumed to be rigid. By matched asymptotics, the inner and outer problems are formulated and a pair of coupled integro-differential equations for determining the unknown cross-flows is derived. The degree of coupling is shown to be related to a bottom-clearance parameter. Expressions are given for the unsteady sinkage force, trimming moment, sway force, and yaw moment. Numerical calculations for two weakly coupled cases are presented. One corresponds to the interaction of a stationary body with a passing one, the other to the interaction of two bodies moving in a steady configuration. Theoretical results are compared with existing experimental data.
The behaviour of naturally oscillating three-dimensional flow around a cylinder
Authors: Tournier Claude , Py Bernard
Published: April 2006

Split-film electrochemical transducer theory is briefly outlined so as to show its ability to separate statistical properties of each component of the surface velocity gradient in regions as different as a boundary layer, a separated zone and a three-dimensional separation line. A lot of measurements of the flow field near a cylinder which are not yet available elsewhere are carried out everywhere on the cross-section of a yawed cylinder. A direct verification of the independence principle and Wild's thermal analogy in separated zones is executed. The periodic and random parts of each component of the surface velocity gradient are separated. Cross-spectral analysis between any pair of points shows that the periodic surface flow is coherent upon any cross-section and in a large region in the spanwise direction. The stationary wave system is investigated in space and time. The reconstitution, instant by instant, of the averaged integral wall streamlines leads to an understanding of the synchronization of the natural oscillations. The four main stagnation or separation lines quickly move from one extreme position to the other, and at certain times contrary vortices stretching in the direction of the generators can appear. In the rearward stagnation region random small-scale fluctuations are probably turbulent, but in the intermediate region high-level random fluctuations in the spanwise direction are much more coherent and probably contribute to keeping the flow in phase at large distances.
Visual observations of the flow past a sphere at Reynolds numbers between 104 and 106
Authors: Taneda S.
Published: April 2006

The wake configuration of a sphere has been determined by means of the surface oil-flow method, the smoke method and the tuft-grid method in a wind tunnel at Reynolds numbers ranging from 104 to 106. It was found that the wake performs a progressive wave motion at Reynolds numbers between 104 and 3·8 × 105, and that it forms a pair of stream wise line vortices at Reynolds numbers between 3·8 × 105 and 106.
The inertial damping and resonance of cellular convection in a rotating fluid annulus: steady linear theory
Authors: Daniels P. G.
Published: April 2006

The phenomenon of steady cellular convection in a rotating fluid in which the stratification is statically unstable is well known. If the temperature field also varies in the horizontal direction a thermal wind is generated which can diminish the amplitude of the cells, or if inertial effects are strong enough, confine them to a narrow vertical band. On the other hand, in an enclosed container resonance can occur which increases the amplitude of the cells beyond the scope of a linear theory.
Radial source flow between parallel disks
Authors: Raal J. D.
Published: April 2006

The vorticity transport equation is solved for radial incompressible flow between disks by a finite-difference method with discretization based on the method of Allen & Southwell. The solution permits detailed characterization of the flow for the Reynolds number range investigated, 1 ≤ Re ≤ 300. Above Re = 60 separation is observed with the bubble size increasing rapidly with Re. The streamwise and transverse pressure and velocity gradients are examined to interpret the observed phenomena.
Experiments on strong interactions between solitary waves
Authors: Weidman P. D. , Maxworthy T.
Published: April 2006

Experiments on the interaction between solitary shallow-water waves propagating in the same direction have been performed in a rectangular channel. Two methods were devised to compensate for the dissipation of the waves in order to compare results with Hirota's (1971) solution for the collision of solitons described by the Kortewegde Vries equation. Both qualitative and quantitative agreement with theory is obtained using the proposed corrections for wave damping.
The structure of the Stewartson layers in a gas centrifuge. Part 1. Insulated end plates
Authors: Matsuda Takuya , Hashimoto Kiyoshi
Published: April 2006

The structure of the Stewartson E¼-layer (E being the Ekman number) in a compressible gas contained in a rapidly rotating cylinder is investigated for the case in which the end plates of the cylinder are thermally insulated. It was found by Matsuda & Hashimoto (1976) that the E¼-layer could not have a relevant structure in the ordinary configuration in which the E¼-layer meets the end plates through its Ekman extension of thickness E½. In this paper the E¼ × E¼ square region, in addition to the Ekman extension, is considered. The heat generation due to the radial fluid motions in the Ekman extension causes the temperature fields in the E¼ × E¼ square region through which heat is conducted to the side wall of the cylinder. Numerical calculations were made to obtain the temperature fields, which are shown in several figures.