bluuebunny/crossref_metadata_2025 huggingface dataset:
On the mass transport induced by oscillatory flow in a turbulent boundary layer
Authors: Johns B.
Published: March 2006

Oscillatory flow in a turbulent boundary layer is modelled by using a coefficient of eddy viscosity whose value depends upon distance from a fixed boundary. A general oscillatory flow is prescribed beyond the layer, and the model is used to calculate the mass transport velocity induced by this within the layer. The result is investigated numerically for a representative distribution of eddy viscosity and the conclusions interpreted in terms of the mass transport induced by progressive and standing waves. For progressive waves, the limiting value of the mass transport velocity at the outer edge of the layer is the same as for laminar flow. For standing waves, the limiting value is reduced relative to its laminar value but, within the lowermost 25% of the layer, there is a drift which is reversed relative to the limiting value. This is considerably stronger than its counterpart in the laminar case and, in view of the greater thickness of the turbulent layer, it may make a dominant contribution to the net movement of loose bed material by a standing wave system.
The motion of large bubbles in horizontal channels
Authors: Gardner G. C. , Crow I. G.
Published: March 2006

An experimental investigation of a large long air bubble moving into stationary water in a horizontal channel of rectangular cross-section is presented and three well-defined flow régimes for the water discharged beneath the bubble are described. The influence of surface tension on the bubble velocity is explained using the hypothesis that the radius of curvature of the two-phase interface close to the upper wall does not vary greatly with channel depth and is close to the theoretical value for a channel of such depth that the bubble is just motionless.
Rheometrical flow systems Part 3. Flow between rotating eccentric cylinders
Authors: Abbott T. N. G. , Walters K.
Published: March 2006

We give further consideration to flow situations which are steady in the sense that ∂/∂t ≡ 0 but for which individual fluid elements are subjected to a small sinusoidal deformation. The particular situation studied involves the flow between eccentric circular cylinders which rotate about their axes with the same angular velocity Ω. The eccentricity is assumed to be small. It is shown that measurements of the force on the inner cylinder can be used to determine the complex dynamic viscosity of an elastico-viscous liquid.

The theory provides the necessary mathematical background for the operation of a new commercial rheometer. Consideration is given to the possibility of ‘on-line’ use of such an instrument for control purposes.
The error minimization technique with application to a transonic nozzle solution
Authors: Prozan Robert J. , Kooker Douglas E.
Published: March 2006

The error minimization technique is introduced as a method of obtaining the simultaneous solution to a set of partial differential equations. Because this numerical technique is at worst neutrally stable, it is believed to have fundamental advantages over existing techniques. The method is formulated in general for the steady fluid dynamic conservation equations and then applied to a specific case of irrotational isentropic flow of a perfect gas through a nozzle. Flow-field solutions were found in nozzle contours having a throat radius of curvature as low as 0·5. Comparison between experimental Mach number contours and the theoretical solution for a finite inlet nozzle with a conical exit is excellent.
The stability of pipe flow Part 1. Asymptotic analysis for small wave-numbers
Authors: Graebel W. P.
Published: March 2006

The instability of Poiseuille flow in a pipe is considered for small disturbances. An asymptotic analysis is used which is similar to that found successful in plane Poiseuille flow. The disturbance is taken to travel in a spiral fashion, and comparison of the radial velocity component with the transverse component in the plane case shows a high degree of similarity, particularly near the critical point where the disturbance and primary flow travel with the same speed. Instability is found for azimuthal wave-numbers of 2 or greater, although the corresponding minimum Reynolds numbers are too small to compare favourably with either experiments or the initial restrictions on the magnitude of the wave-number.
Statistical properties of turbulent density fluctuations
Authors: Wilson L. N. , Damkevala R. J.
Published: March 2006

The cross-correlation technique has been used to obtain statistical properties of scalar density fluctuations. Two schlieren instruments with their optical beams intersecting in the turbulent field each give a signal proportional to the density gradient in the flow direction but integrated along the beam path. Cross-correlation of the two signals gives an area integral of the density-gradient covariance. For locally isotropic conditions the area integration can exactly compensate for the two gradients giving a result proportional to the local mean-square density fluctuation at the beam intersection point.

Experiments performed in the shear layer of a subsonic jet show results which tend to verify the principles of crossed-schlieren measurement. Intensity levels are close to those predicted assuming density fluctuations are related isentropically to local, incompressible pressure fluctuations.
The break-up of axisymmetric liquid sheets
Authors: Huang J. C. P.
Published: March 2006

The break-up mechanism of axisymmetric liquid sheets formed by the impingement of two co-axial jets has been examined. Three break-up regimes in the Weber number range from 100 to 3 × 104 are reported. In the first break-up regime, droplets are formed through successive mergings of liquid beads along the nearly circular periphery of the sheet. The formation of beads is caused by Rayleigh instability. In the transition regime, Taylor's cardioid wave pattern prevails in the first half of this regime, while the sheet begins to flap in the second half.

In the second break-up regime, antisymmetric waves on the sheet grow radially. A semi-empirical equation has been deduced to predict the break-up radius of the sheet. The motion of an axisymmetric vibrating membrane with radially decreasing thickness has been studied to include Helmholtz instability as an analogue of the wave motion of the expanding circular sheet. A distorted progressive wave equation has been solved by the WKBJ method to indicate the effect of cylindrical geometry. The calculated wave speed agrees fairly well with experimental data at low Weber numbers.
Transmission of an acoustic pulse through a plane vortex sheet
Authors: Howe M. S.
Published: March 2006

This paper discusses the linear theory of the transmission of an acoustic pulse through a plane discontinuity of velocity. It is shown that elementary ideas of geometrical acoustics which have received much attention in the recent literature lead to the erroneous prediction of a zone of silence. It is in precisely this zone that unstable disturbances and broad-fronted pulses of enhanced intensity propagate, having been triggered-off by the arrival of the pulse at the vortex sheet. The apparent qualitative agreement between geometrical acoustics and experimental data regarding sound radiation from the interior of supersonic jets is shown to be purely fortuitous, and it is argued that a complete analysis of such problems must depend on a deeper and possibly non-linear treatment.
Fluid dynamics of the resonance tube
Authors: Brocher E. , Maresca C. , Bournay M.-H.
Published: March 2006

Using a simplified wave-diagram and the gas-speed/sound-speed diagram, it is shown how the oscillations start and grow within a resonance tube. It is found that the oscillation amplitude tends to a limiting value which is obtained when the jet is fully swallowed by the tube during the phase of compression of the cycle. Experiments are carried out for jet Mach numbers from 0·1 up to 2. To achieve an adequate evacuation of the tube in the expansion phase, a thin cylindrical body must be used, which is laid along the axis of the jet to produce a wake and a correlative local deficiency of the kinetic energy of the jet. Measured amplitudes of pressure fluctuations are in good agreement with theoretical values.
Similarity solution for a spherical radiation-driven shock wave
Authors: Wilson C. R. , Turcotte D. L.
Published: March 2006

A similarity solution has been obtained for a radiation-driven shock wave. Radiation propagating radially inwards is completely absorbed in the shock layer of a spherical, expanding shock wave. For a strong shock wave and a constant power input a similarity solution is obtained. It is found that the radial position of the shock wave rs ∼ t⅗. The shock wave propagates as an overdriven detonation. The jump conditions and complete flow field are obtained.
The drag of a body moving transversely in a confined stratified fluid
Authors: Foster M. R. , Saffman P. G.
Published: March 2006

The slow motion of a body through a stratified fluid bounded laterally by insulating walls is studied for both large and small Peclet number. The Taylor column and its associated boundary and shear layers are very different from the analogous problem in a rotating fluid. In particular, the large Peclet number problem is non-linear and exhibits mixing of statically unstable fluid layers, and hence the drag is order one; whereas the small Peclet number flow is everywhere stable, and the drag is of the order of the Peclet number.
Channel flow induced by a travelling thermal wave
Authors: Chow Chuen-Yen
Published: March 2006

Experiments conducted elsewhere show that a mean fluid motion can be induced in a channel by a travelling thermal wave. An analysis is carried out, linearized under the assumption that the induced motion is slower than the speed of the heat source. The expression for the mean motion is obtained for any Prandtl number and circular frequency of the thermal wave, to complete the results presented by Davey (1967) for low and high frequency ranges.

In the problem of the flow between two parallel plates, it is found that with a temperature profile symmetric about the centre of the channel, the induced flow does not exert a net shear force on either plate, while with a non-symmetric one, the plates are subjected to equal and opposite forces.

For the problem that the upper surface of the fluid is free and thermally insulated, an approximated result can be deduced from that of the previous problem by a simple transformation. It should agree with the result of Davey, obtained through a more elaborate procedure, except in the low frequency range when the surface deformation becomes important.

In agreement with the experiments, our analysis indicates that the induced mean motion is always in a direction opposite to that of the thermal wave, and its magnitude increases rapidly with decreasing Prandtl number. According to the theory, some of the previous experiments were not conducted under the optimum situations, and improved experimental conditions are suggested.
Bottomless harbours
Authors: Garrett C. J. R.
Published: March 2006

Does the harbour of an artificial island need a bottom? The excitation of waves inside a partially immersed open circular cylinder is considered. An incident plane wave is expanded in Bessel functions and for each mode the problem is formulated in terms of the radial displacement on the cylindrical interface below the cylinder. The solution is obtainable either from an infinite set of simultaneous equations or from an integral equation. It is shown that the phase of the solution is independent of depth and resonances are found at wave-numbers close to those of free oscillations in a cylinder extending to the bottom. If the resonances of the cylinder are made sharper (by increasing the depth of immersion) the peak response of the harbour increases, but the response to a continuous spectrum remains approximately constant. Numerical results are obtained by minimizing the least squares error of a finite numberNof simultaneous equations. Convergence is slow, but the error is roughly proportional to 1/Nand this is exploited. The solution obtained from a variational formulation using the incoming wave as a trial function is found to give a very good approximation for small wave-numbers, but is increasingly inaccurate for large wave-numbers. Away from resonance the amplitude of the harbour oscillation is less than 10% of the amplitude of the incoming wave provided the depth of the cylinder is greater than about ¼ wavelength, and it is argued that in practice at the resonant wave-number oscillations excited through the bottom of the harbour will leak out through the entrance before they can reach large amplitudes. In an appendix the excitation of harbour oscillations through the harbour entrance is discussed, and some results of Miles & Munk (1961) on an alleged harbour paradox are re-interpreted.
Contrails and aircraft downwash
Authors: Scorer R. S. , Davenport L. J.
Published: March 2006

Aircraft downwash consists initially of a vortex pair descending with its accompanying fluid through the atmosphere. Condensation trails are formed in exhaust emitted into the accompanying fluid and the shapes of them and their evolution depend on the positions of the engines in relation to the wing tip vortices.

The atmosphere is stably stratified and so the descending accompanying fluid acquires upward buoyancy. Consequently vorticity is generated at the outside of the accompanying fluid and the flow pattern in the vortex pair is altered so as to produce detrainment of its exterior part. So long as any air which is a mixture of accompanying fluid and exterior air is detrained, the vortices remain stable, but the width of the pair decreases and its downward velocity increases with time as a result of the buoyancy. Eventually the upper stagnation point in the motion relative to the vortices begins to move upwards relative to the vortices so that some mixed fluid is entrained into the circulation and the vortices immediately become unstable, mixing occurs, the pressure in the core rises, and any vortex core trails that may exist appear to burst.

The motion produces downward-thrust blobs in trails from centrally placed engines, which correspond to the holes sometimes seen in cloud when distrails are formed.
Periodic boundary layer near a two-dimensional stagnation point
Authors: Ishigaki Hiroshi
Published: March 2006

The time-mean characteristics of the laminar boundary layer near a two-dimensional stagnation point, when the velocity of the oncoming flow relative to the body oscillates are investigated analytically. First, when the amplitude of the oscillating velocity is small compared with the oncoming flow velocity, a series expansion is made and the obtained equations are solved numerically. The equations are also solved approximately in the extreme cases when the frequency is low and high. The obtained approximate solutions are compared with the numerical solutions in terms of skin friction. Next, when the frequency is high, the finite-velocity-amplitude case is treated. Time-mean velocity profiles and skin friction are obtained and compared with the small-amplitude case.
Large amplitude waves in stratified media: acoustic pulses
Authors: Varley E. , Cumberbatch E.
Published: March 2006

A general theory is presented which describes disturbances generated by large amplitude, high frequency pulses in stratified media. The theory is used to discuss large amplitude, but shockless, acoustic pulses propagating under the influence of a constant gravity force into an atmosphere which need not be in thermal equilibrium before their arrival.

The modulating influences of pressure and temperature stratification on the amplitudes of such pulses as they move towards or away from earth are described in detail.

The paper generalizes techniques already established by Whitham (1956) so that they are applicable to disturbances of any amplitude.
A note on the vorticity expulsion hypothesis
Authors: Strittmatter P. A. , Illingworth G. , Freeman K. C.
Published: March 2006

The astrophysical importance of the hypothesis that vorticity is expelled from regions of strong turbulence is briefly reviewed. An experiment from which Gough & Lynden-Bell claimed to provide positive evidence of vorticity expulsion has been repeated. The results are reproduced here and are shown to be due to thermally driven circulation currents. No unambiguous laboratory evidence for (or against) the vorticity expulsion hypothesis therefore exists at present.
On the stability of plane flow of a conducting fluid in the presence of a coplanar magnetic field
Authors: Sozou C.
Published: March 2006

The equations governing the propagation of small perturbations to plane flow of a viscous incompressible conducting fluid are re-examined with special reference to the case when the constant unperturbed magnetic field and flow velocity are parallel. We use the relationship between two parameters in one equation and, without computations, show the following: If for a non-zero value of the Alfvén number the flow is unstable when the Reynolds and magnetic Reynolds numbers take particular finite values, then, for that value of the Alfvén number, the flow cannot be completely stabilized for all finite Reynolds numbers, when the magnetic Reynolds number is finite. Since for a finite Alfvén number one expects that unstable flow cannot be stabilized for all finite Reynolds numbers, unless the magnetic Reynolds number exceeds some value, we deduce the following: An unstable parallel flow of a finitely conducting fluid cannot be completely stabilized for all finite Reynolds numbers by a constant magnetic field, which is coplanar with the flow.
The radiated fields of multipole point sources near a solid spherical surface
Authors: Davies Huw G.
Published: March 2006

The acoustic field radiated by a multipole point source positioned near to the surface of a solid sphere is calculated at both low and high frequencies. It is shown that the scattered field at low frequencies is always dipole, but at high frequencies is of the same type as the incident field. The application of the results to the acoustic field radiated by turbulence near a sphere is briefly discussed.
Pressure drop due to the motion of neutrally buoyant particles in duct flows
Authors: Brenner Howard
Published: March 2006

The additional pressure drop arising from the presence of a neutrally-buoyant, eccentrically positioned, spherical particle in a Poiseuille flow is calculated toO(a/Ro)5(a= sphere radius;Ro= tube radius). Similar calculations (of a lesser order of accuracy) are given for non-circular conduits and for ellipsoidal particles. Due to changes in particle orientation resulting from rotation, the instantaneous pressure drop for an ellipsoid of revolution varies periodically with time. This pressure diminution is averaged over one period to obtain the time-average pressure drop.
Sound generation by hydrodynamic sources near a cavitated line vortex
Authors: Williams J. E. Ffowcs , O'shea S.
Published: March 2006

The paper examines the scattering properties of a cavitated line vortex when excited by line and point sources of sound. It is found that the vortex resonances discovered by Kelvin for incompressible flow are essentially unmodified by fluid compressibility, and that many of the resonant modes radiate energy to infinity. Those resonant modes dominate the vortex response, their amplitude growing algebraically with time in a driven instability of the model flow.

The off resonance response is dependent on the value of a normalized frequency parameter (ω/Ω)2|ln ka|. Ω denotes the angular velocity of the steady vortex flow, k the acoustic wave-number, and a the cavity radius. Even off resonance the cavity is an extremely efficient wave scatterer, the scattering efficiency increasing with source order. For example, the scattered energy of a point quadrupole is shown to exceed that of the direct field by a factor of 108 for the typical underwater flow Mach number of 10−2.
Turbulent flow drag reduction and degradation with dilute polymer solutions
Authors: Paterson R. W. , Abernathy F. H.
Published: March 2006

Experimental studies of drag reduction and polymer degradation in turbulent pipe flow with dilute water solutions of unfractionated polyethylene oxide are described. Drag reduction results indicate that the magnitude of the reduction cannot be correlated on the basis of weight average molecular weight, rather the phenomenon depends strongly on the concentration of the highest molecular weight species present in the molecular weight distribution. Polymer degradation in turbulent flow is found to be severe for high molecular weight polymers causing appreciable changes in drag reduction and molecular weight with the duration of flow. Data indicates that drag reduction exists in the limit of infinite dilution suggesting that the phenomenon is due to the interaction of individual polymer molecules with the surrounding solvent and that the extent of reduction is relatively independent of pipe diameter when a comparison is carried out at equal solvent wall shear stresses. Consideration of the high viscosity obtained with solutions in an irrotational laminar flow field suggests this is due to polymer molecule deformation and that this phenomenon is central to the mechanism of turbulent flow drag reduction.
Universal stability of hydromagnetic flows
Authors: Carmi S. , Lalas D. P.
Published: March 2006

The non-linear stability of hydromagnetic flows is investigated by applying energy methods. A universal stability estimate, namely a stability limit for motions subject to arbitrary non-linear disturbances, is obtained for bounded or periodic domains. Our analysis is restricted to fluids possessing constant density and electrical conductivity and we do not take into account temperature or Hall effects. This result establishes the existence of an open region of certain stability near the origin of the $(\tilde{R}_e, \tilde{R}_m)$ Cartesian plane for every fixed Pm (where $(\tilde{R}_e, \tilde{R}_m)$ and Pm are the Reynolds number, magnetic Reynolds number and magnetic Prandtl number, respectively). The universal stability limit can then be improved by suitably defining a maximum problem using variational techniques, and obtaining the relevant Euler–Lagrange equations. The tentative solution to this problem gives a stability limit which enlarges the universal stability region. Our results are then compared with linear and experimental ones, with special emphasis given to the role played by the magnetic field.
The decay of a plane shock wave
Authors: Ardavan-Rhad H.
Published: March 2006

An analytic solution of the non-isentropic equations of gas-dynamics, for the one-dimensional motion of a non-viscous and non-conductive medium, is derived in this paper for the first time. This is a particular solution which contains only one arbitrary function. On the basis of this solution, the interaction of a centred simple wave with a shock of moderate strength is analyzed; and it is shown that, for a weak shock, this analysis is compatible with Friedrichs's theory. Furthermore, in the light of this analysis, it is explained why the empirical methods employed by the shock-expansion theory, including Whitham's rule for determining the shock path, work.
The flat plate boundary layer. Part 1. Numerical integration of the Orr–-Sommerfeld equation
Authors: Jordinson R.
Published: March 2006

Numerical space-amplified solutions of the Orr-Sommerfeld equation for the case of a boundary layer on a flat plate have been calculated for a wide range of values of frequency and Reynolds number. The mean flow is assumed to be parallel and given by the appropriate component of the Blasius solution. The results are presented in a form suitable for comparison with experiment and are also compared with calculations of earlier authors.
The flat plate boundary layer. Part 3. Comparison of theory with experiment
Authors: Ross J. A. , Barnes F. H. , Burns J. G. , Ross M. A. S.
Published: March 2006

A study of Tollmien–Schlichting waves in the Blasius boundary layer has been carried out under good flow conditions. The maximum r.m.s. amplitude of u, the downstream component of perturbation velocity, was limited to about 0·06% of U0, the free-stream velocity. Measurements of the wave-number and of the distribution of u/U0 normal to the plate agree closely with the theoretical results obtained in parts 1 and 2 of this paper. The experimental critical Reynolds number, Rc, is 400; the theoretical Rc derived from the imaginary part of the eigenvalue is 500 (part 2), but additional amplification carried by the eigenvector removes most of this discrepancy.
The growth of three-dimensional disturbances in inviscid flows
Authors: Gaster M.
Published: March 2006

It is shown by linear inviscid theory that the most highly amplified instability mode in an incompressible plane parallel flow is a two-dimensional one for either temporally or spatially growing waves.
An elastic sublayer model for drag reduction by dilute solutions of linear macromolecules
Authors: Virk P. S.
Published: March 2006

Further evidence of a universal maximum drag reduction asymptote is presented. In the elastic sublayer model, inferred therefrom, the mean velocity profile during drag reduction is approximated by three zones: the usual viscous sublayer, an elastic sublayer where the mixing-length constant is derived from the maximum drag reduction asymptote, and an outermost region with Newtonian mixinglength constant. Upon integration the model yields a friction factor relation, parametric in elastic sublayer thickness, which properly reproduces the known features of turbulent dilute polymer solution flow. The dependence of elastic sublayer thickness upon flow and polymeric parameters is inferred from experimental data revealing two hitherto unknown relationships: namely that on Prandtl co-ordinates, 1/f½vs. log Re f½ the difference in slope between a polymer solution and solvent is proportional to the square root of molar concentration and to the three-halves power of backbone chain links in the macromolecule. The proportionality constant in the preceding relationship is approximately the same for several different polymer species of carbon-carbon or similar skeletal structure in various thin solvents; there is an indication that this constant further depends upon the product of solvent viscosity times the cube of the effective bond length per chain link of the polymer species. Some recent results regarding the onset of drag reduction are also summarized.
Cholesteric energies
Authors: Jenkins James T.
Published: March 2006

Repeated observations of a uniformly twisted director field in cholesteric liquid crystals are used to motivate an expression for a free energy which is obtained as an expansion about this state. Terms quadratic in the director perturbation and the gradients of this perturbation are retained. Utilizing invariance arguments, it is possible to obtain significant simplification of the coefficients which appear in the expansion. A properly invariant form of the free energy is produced which agrees with the expansion for small excursions about a twisted state, and which assigns arbitrary values to the non-vanishing coefficients.

The consequences of requiring that a free energy achieve a minimum at a twisted state are explored. A commonly used form of the free energy for cholesteric liquid crystals is seen to be rather severely restricted by this requirement. An alternative to this form is proposed which is a special case of the free energy previously produced. The particular form suggested attains a unique absolute minimum at a characteristic uniform twist.
Boundary-layer separation on a sphere in a rotating flow
Authors: Miles John W.
Published: March 2006

The velocity just outside the boundary layer and upstream of the separation ring on a sphere moving along the axis of a slightly viscous, rotating fluid is calculated through a least-squares approximation on the hypothesis of no upstream influence. A reverse flow is found in the neighbourhood of the forward stagnation point fork≡ 2Ωa/U>k= 2·20 (Ω = angular velocity of fluid,U= translational velocity of sphere,a= radius of sphere) and is accompanied by a forwardseparation bubble, such as that observed by Maxworthy (1970) fork[gsim ] 1. Rotation also induces a downstream shift of the peak velocity; the estimated shift of the separation ring in the absence of forward separation increases withkto a maximum of 24°, in qualitative agreement with Maxworthy's observations.

The least-squares formulation is compared with that given by Stewartson (1958) for unseparated flow (Stewartson did not consider separation). Both formulations require truncation of an infinite set of simultaneous equations, but Stewartson's formulation yields a non-positive-definite matrix that may exhibit spurious singularities. The least-squares formulation yields a positive-definite matrix, albeit at the expense of slower convergence for fixedk, and is especially well suited for automatic computation.

Anad hocincorporation of a cylindrical wave of strength [Uscr ], such that the maximum upstream axial velocity is [Uscr ]U, is considered in an appendix. It is found thatkdecreases monotonically from 2·2 to 0 as [Uscr ] increases from 0 to 1.
Wind-generated waves in thin liquid films with soluble contaminant
Authors: Smith F. I. P. , Craik Alex D. D.
Published: March 2006

Craik (1968) has previously examined the stability of horizontal liquid films when an air stream flows over the liquid surface and when the surface is contaminated by an insoluble surface-active agent. The present theoretical work extends this investigation to examine the role of soluble surface-active agents for cases where the liquid Reynolds number is small. This role is found to be a rather complex one which, under suitable conditions, may be either stabilizing or destabilizing.

Related experimental work is described which yields results in qualitative agreement with the theoretical analysis.
On stationary and travelling vortex breakdowns
Authors: Sarpkaya Turgut
Published: March 2006

This paper describes some experiments in swirling flows in a diverging cylindrical tube in which various types of vortex breakdowns were observed.

In one set of experiments, the position of the breakdown, axial component of the velocity of the vortex core, swirl angle distribution ahead of the breakdown, and the pressure distribution along the tube were determined for various flow rates and for various values of circulation imparted to the fluid (water). Basically, three types of vortex breakdown were observed, viz. mild (double helix) breakdown, spiral breakdown (followed by turbulent mixing), and axisymmetric breakdown (followed by a thicker vortex core, then a spiral breakdown, and finally by turbulent mixing). The type and the location of the stationary breakdowns were found to be dependent, for the particular vortex tube used, upon the Reynolds and circulation numbers of the flow. In a spiral breakdown, the vortex core filament maintained the same sense of rotation as the upstream fluid elements. In an axisymmetric breakdown, the bubble included an inclined vortex-ring whose axis gyrated about the axis of the tube.

In a second set of experiments, the response of the abrupt structural change along the axis of flow to gradual and abrupt changes in the upstream and downstream flow conditions was examined. The axisymmetric breakdown responded in a manner analogous to the hydraulic jump in open-channel flow before if reached a new stationary position along the axis of the tube.

The observations reported and the evidence presented herein revealed that the axisymmetric breakdown is a finite transition between two sequent states of flow as proposed by Benjamin (1962, 1965, 1967) on theoretical grounds.
Laminar momentum jets in a stratified fluid
Authors: List E. J.
Published: March 2006

Solutions are presented for creeping flows induced by two-and three-dimensional horizontal and vertical momentum jets in a linearly stratified unbounded diffusive viscous fluid. These linear problems are solved by replacing the momentum jet by a body force singularity represented by delta functions and solving the partial differential equations of motion by use of multi-dimensional Fourier transforms. The integral representations for the physical variables are evaluated by a combination of residue theory and numerical integration.

The solutions for vertical jets show the jet to be trapped within a layer of finite thickness and systems of rotors to be induced. The horizontal two-dimensional jet solution shows return flows above and below the jet and a pair of rotors. The three-dimensional horizontal jet has no return flow at finite distance and the diffusive contribution is found to be almost negligible in most situations, the primary character of the horizontal flows being given by the non-diffusive solution. Stokes's paradox is found to be non-existent in a density-stratified fluid.
Lateral diffusion of large particles in turbulent pipe flow
Authors: Sharp B. B. , O'Neill I. C.
Published: March 2006

A closed flow circuit, comprising a smooth horizontal plastic pipe transporting a dilute suspension of plastic particles in water, was modified to produce a satisfactory environment for the detection of mean particle location across a fixed plane normal to the mean turbulent flow direction. It was established that mean concentration in the vicinity of the vertical diameter was a function of the vertical co-ordinate only, and this result enabled the particle diffusivity to be evaluated for a core region of the cross-section. For a particle relative density in the range 1.035 to 1.126 and a variety of flows, a suitable expression for the dimensionless particle diffusivity is A (1 - BW/u) SN, where u is the friction velocity, W the fall velocity for a particle in still water, S the relative density of the suspended material, and A, B and N are constants.
Asymptotic solution for plume at very large and small Prandtl numbers
Authors: Kuiken H. K. , Rotem Zeëv
Published: March 2006

The investigation of laminar free convective plumes in an otherwise stationary environment has formed the basis of numerous investigations, initiated by Zeldovich (1937). For the non-rotating environment alone the authors have been able to locate twenty-nine papers: many of these repeat work previously undertaken. There are, however, two cases of some technological significance which have so far not been considered: (i) the plume in an otherwise quiescent environment for a fluid of very large Prandtl number, of importance in the heating of reservoirs of viscous fluid such as fuel oil; and (ii) the case of vanishingly small Prandtl number, of application to liquid metal-cooled nuclear reactors. Both of these cases have some theoretical interest, as will be shown. Their analysis leads to singular asymptotic perturbations and hence to matched-expansions techniques.
The formation of shock waves in a dense gas using a molecular-dynamics type technique
Authors: Macpherson A. K.
Published: March 2006

The formation of shock waves in. dense argon is studied using a numerical technique related to the molecular-dynamics approach. The kinetic and total pressures, density, temperature and mass velocity are calculated when a simulated tungsten piston is driven into the stationary gas. It is found that the pressure generated is similar to that found using binary collision assumptions, however the temperature is lower and the density much higher than under more rarefied conditions. Results are also given for the same experiments when the generating piston is composed of dense argon atoms. It is shown that the results are almost independent of the type of piston material and that the shock structure is a function of the gas interparticle force law only. The reflexion of a spherically imploding shock wave in dense argon is also examined and it is found that the shock wave reflects before reaching the centre due to high tangential stresses. Some data is also given, upon the velocity distribution and wall pressure fluctuations.
The motion of long slender bodies in a viscous fluid. Part 2. Shear flow
Authors: Cox R. G.
Published: March 2006

A long slender axisymmetric body is considered placed at rest in a general linear flow in such a manner that the undisturbed fluid velocity is identically zero on the body axis. Formulae for the total force and torque on the body are found as an expansion in terms of a small parameter κ defined as the radius-to-length ratio of the body. These general results are used to determine the resistance to axial rotation of the body and also the equivalent axis ratio of the body for motion in a shear flow.
An exact solution of linearized flow of an emitting, absorbing and scattering grey gas
Authors: Cheng Ping , Leonard A.
Published: March 2006

The governing equations for the problem of linearized flow through a normal shock wave in an emitting, absorbing, and scattering grey gas are reduced to two linear coupled integro-differential equations. By separation of variables, these equations are further reduced to an integral equation similar to that which arises in neutron-transport theory. It is shown that this integral equation admits both regular (associated with discrete eigenfunctions) and singular (associated with continuum eigenfunctions) solutions to form a complete set. The exact closed-form solution is obtained by superposition of these eigen-functions. If the gas downstream of a strong shock is absorption–emission dominated, the discrete mode of the solution disappears downstream. The effects of isotropic scattering are discussed. Quantitative comparison between the numerical results based on the exact solution and on the differential approximation are presented.
The effect of a depth discontinuity on Kelvin wave diffraction
Authors: Pinsent H. G.
Published: March 2006

The linearized problem of Kelvin wave diffraction at the sharp edge of a thin semi-infinite barrier on a rotating earth is considered in the case when a discontinuity in depth stems from the edge in a direction parallel to the barrier. The solution in closed form is obtained using the Wiener-Hopf technique.

It is shown that the direct effect of the depth discontinuity is always to divert additional energy away from the barrier, in the form of outgoing cylindrical waves if the period is small, and provided conditions are suitable as double Kelvin waves if the period is sufficiently long. Results suggest that Kelvin waves which are the most persistent in following an irregular coastline bounding a sea of abruptly varying depth are of intermediate period.
Boundary-value problems in the kinetic theory of gases. Part 2. Thermal creep
Authors: Williams M. M. R.
Published: March 2006

The effect of a temperature gradient in a gas inclined at an angle to a boundary wall has been investigated. For an infinite half-space of gas it is found that, in addition to the conventional temperature slip problem, the component of the temperature gradient parallel to the wall induces a net mass flow known as thermal creep. We show that the temperature slip and thermal creep effects can be decoupled and treated quite separately.

Expressions are obtained for the creep velocity and heat flux, both far from and at the boundary; it is noted that thermal creep tends to reduce the effective thermal conductivity of the medium.
Wave propagation in random media
Authors: Howe M. S.
Published: March 2006

This paper discusses a general theory of wave propagation through a random medium whose random inhomogeneities are confined to small deviations from the mean. The theory is initially worked out in detail for the propagation of transverse waves along an infinite stretched string whose density is a random function of position. The manner in which the mean wave profile is modified by scattering from the density inhomogeneities is discussed in great detail, with particular emphasis on physical interpretation. The general theory of wave propagation in arbitrary dispersive or non-dispersive media is then discussed, and it is shown how the theory may be extended to wave propagation problems involving scattering from rough boundaries.
On wave scattering by random inhomogeneities, with application to the theory of weak bores
Authors: Howe M. S.
Published: March 2006

This paper considers the propagation and scattering of waves in dispersive and non-dispersive media containing random inhomogeneities. A detailed discussion of the propagation of the coherent component of the wave field is presented, and a rather general method for obtaining the absorption coefficient and scattering cross-section per unit volume of medium is described. A major objective is to derive macroscopic equations for the propagation of the coherent field in the sense that the damping due to scattering appears in the wave equation as pseudo-viscosity. The paper is concluded by a detailed application of the theory to the problem of the propagation of surface gravity waves over a stretch of shallow water with a ‘rough’ bed. By including finite amplitude effects a balance is achieved between the dispersion of the pseudo-viscous term and the non-linear convective terms, which enables the steady profile of a weak bore to be calculated.
A numerical study of the Bénard cell
Authors: Cabelli André , de Vahl Davis G.
Published: March 2006

When a layer of liquid is heated from below at a rate which exceeds a certain critical value, a two- or three-dimensional motion is generated. This motion arises from the action of buoyancy and surface tension forces, the latter being due to variations in the temperature of the liquid surface.

The two-dimensional form of the flow has been studied by a numerical method. It consists of a series of rolls, rotating alternately clockwise and anticlockwise, which are shown to be symmetrical about the dividing streamlines. As well as a detailed description of the motion and temperature of the liquid, and of the effects on these characteristics of variations in the Rayleigh, Marangoni, Prandtl and Biot numbers, a study has been made of the conditions under which the motion first starts, the wavelength of the rolls and the rate of heat transfer across the liquid layer.
Some aspects of the initial-value problem for the inviscid motion of a contained, rotating, weakly-stratified fluid
Authors: Allen J. S.
Published: March 2006

The initial-value problem for the linear, inviscid motion of a contained, rotating stratified fluid is considered in the limit of weak stratification, that is, for small values of the stratification parameter S = N2/Ω2, where N is the Brunt–Väisälä frequency and Ω is the rotational frequency. The limiting flow is of interest because, although the initial-value problem has been studied, both for the case of a homogeneous, rotating fluid and for the case of a stratified, rotating fluid, the exact relationship of the two flows, in the limit of vanishing stratification, is not straightforward. For example, the method of determining, from the initial conditions, the steady geostrophic component of the flow of a rotating, stratified fluid does not in general give a motion that reduces, in the limit S → 0, to the steady component of the flow of a homogeneous fluid. By including a consideration of slow unsteady motions that vary on a time scale dependent on the stratification parameter, the relationship of the limiting flow to the flow of a homogeneous fluid is established.
Two-phase concave-type corner flows
Authors: Healy J. Val.
Published: March 2006

The flow of a two-phase system past an arbitrary corner has been studied by Healy (1970a), using the method of small perturbations, and some results were presented for convex-type flows. This paper, which is an extension of the abovementioned one to concave-type flows, also compares the particle streamlines found from the perturbation with those obtained by numerically integrating the unperturbed equations. The agreement is found to be quite good for ξ0.2 and excellent when ξ = 0·1 or less, where ξ = ατ is the particle parameter, α is proportional to the speed of the fluid and τ is the particle relaxation time. The nature of concave corner flows abruptly changes when the angle β through which the flow is deflected is 90°. For β < 90°, all particles collide directly except those approaching on streamlines near the stagnation line. When β = 90° the critical value of ξ is ξc = 0·25 and, for 180° > β > 90°, only particles approaching on streamlines near the stagnation line all collide. No particle-free zones exist in concave-type flows and the particle density increases monotonically in the downstream direction along all particle streamlines. The approximate effects of viscosity are also discussed.
An experimental investigation of pulsating turbulent water flow in a tube
Authors: Gerrard J. H.
Published: March 2006

Experiments were made on a pulsating water flow at a mean flow Reynolds number of 3770 in a cylindrical tube of diameter 3·81 cm. Pulsations were produced by a piston oscillating in simple harmonic motion with a period of 12 s. Turbulence was made visible by means of a sheet of dye produced by electrolysis from a fine wire stretched across a diameter. The sheet of dye is contorted by the turbulent eddies, and ciné-photography was used to find the velocity of convection which was shown to be the flow speed except in certain circumstances which are discussed. By subtracting the mean flow velocity profile the profile of the component of the motion oscillating at the imposed frequency was determined.

The Reynolds number of these experiments lies in the turbulent transition range, so that large effects of laminarization are observed. In the turbulent phase, the velocity profile was found to possess a central plateau as does the laminar oscillating profile. The level and radial extent of this were little different from the laminar ones. Near to the wall, the turbulent oscillating profile is well represented by the mean velocity power law relationship, u/U ∝ (y/a)1/n. In the laminarized phase, the turbulent intensity is considerably reduced at this Reynolds number. The velocity profile for the whole flow (mean plus oscillating) relaxes towards the laminar profile. Laminarization contributes appreciably to the oscillating component.

Extrapolation of the results to higher Reynolds numbers and different frequencies of oscillation is suggested.
Shock waves and non-stationary flow in a duct of varying cross-section
Authors: Asano Naruyoshi
Published: March 2006

Sound waves of finite but small amplitude propagating into a quasi-steady, supersonic flow in a non-uniform duct are analyzed by means of a perturbation method. General properties of the flow and of the wave propagation are studied using a one-dimensional approximation. A shock propagation law in the unsteady flow is obtained. As an example, the formation and development of shock waves are discussed for a duct with a conical convergence. Comparisons of the theory with an experiment are also made; fairly good agreement is found.
Radiation and scattering of water waves by rigid bodies
Authors: Black J. L. , Mei C. C. , Bray M. C. G.
Published: March 2006

Schwinger's variational formulation is applied to the radiation of surface waves due to small oscillation of bodies. By means of Haskind's theorem the wave forces on a stationary body due to a plane incident wave are found using only far-field properties. Results for horizontal rectangular and vertical circular cylinders are presented.
An investigation of the forces on flat plates normal to a turbulent flow
Authors: Bearman P. W.
Published: March 2006

Measurements on square and circular plates in turbulent flow show the mean base pressure to be considerably lower than that measured in smooth flow. Power spectral density measurements of the fluctuating component of the drag on square plates in both smooth and turbulent flow are presented. The measurements in turbulent flow show the importance of the ratio of turbulence scale to plate size. There is shown to be a strong correlation between the fluctuating drag force and the velocity fluctuations in the approaching flow. The distortion of the turbulence structure approaching a plate is also discussed.