bluuebunny/crossref_metadata_2025 huggingface dataset:
Experiments on the flow and acoustic properties of a moderate-Reynolds-number supersonic jet
Authors: Troutt T. R. , Mclaughlin D. K.
Published: April 2006

An experimental investigation of the flow and acoustic properties of a moderate-Reynolds-number (Re = 70000), Mach number M = 2·1, axisymmetric jet has been performed. These measurements extended the experimental studies conducted previously in this laboratory to a higher-Reynolds-number regime where the flow and acoustic processes are considerably more complex. In fact, mean-flow and acoustic properties of this jet were determined to be closely comparable to published properties of high-Reynolds-number jets.

The major results of the flow-field measurements demonstrate that the jet shear annulus is unstable over a broad frequency range. The initial growth rates and wavelengths of these instabilities as measured by a hot wire were found to be in reasonable agreement with linear stability theory predictions. Also, in agreement with subsonic-jet results, the potential core of the jet was found to be most responsive to excitation at frequencies near a Strouhal number of S = 0·3. The overall development of organized disturbances around S = 0·2 seems to agree in general with calculations performed using the instability theory originally developed by Morris and Tam.

The acoustic near field was characterized in terms of sound-pressure level and directivity for both natural and excited (pure-tone) jets. In addition, propagation direction and azimuthal character of dominant spectral components were also measured. It was determined that the large-scale flow disturbances radiate noise in a directional pattern centred about 30° from the jet axis. The noise from these disturbances appears from simple ray tracing to be generated primarily near the region of the jet where the coherent fluctuations saturate in amplitude and begin to decay. It was also determined that the large-scale components of the near-field sound are made up predominately of axisymmetric (n = 0) and helical (n = ±1) modes. The dominant noise-generation mechanism appears to be a combination of Mach-wave generation and a process associated with the saturation and disintegration of the large-scale instability. Finally, the further development of a noise-generation model of the instability type appears to hold considerable promise.
Transient wave propagation in bubbly liquids
Authors: Drumheller D. S. , Kipp M. E. , Bedford A.
Published: April 2006

A theoretical and numerical investigation of the propagation of one-dimensional waves in a bubbly liquid is presented. A variational formulation of the problem is used that yields both the linear-momentum equation and the equation that describes the oscillations of the bubbles. The compressibility of the liquid is taken into account in the formulation. The thermal dissipation is treated by solving the energy-balance equations simultaneously with the mechanical equations. Solutions are obtained by a finite-difference procedure and are compared to the experimental data of Kuznetsov et al. and Noordzij & van Wijngaarden. In some cases quite good agreement is obtained, but in others substantial errors are found. It is suggested that the observed discrepancies may be due to the breakup of the bubbles in the case of very large amplitude disturbances; the fact that the formulation does not include relative motion between the liquid and the bubbles; and possible non-planarity effects in the experiments.
Sedimentation in a dilute polydisperse system of interacting spheres. Part 1. General theory
Authors: Batchelor G. K.
Published: April 2006

Small rigid spherical partials are settling under gravity through Newtonian fluid, and the volume fraction of the particles (ϕ) is small although sufficiently large for the effects of interactions between pairs of particles to be significant. Two neighbouring particles interact both hydrodynamically (with low-Reynolds-number flow about each particle) and through the exertion of a mutual force of molecular or electrical origin which is mainly repulsive; and they also diffuse relatively to each other by Brownian motion. The dispersion contains several species of particle which differ in radius and density.

The purpose of the paper is to derive formulae for the mean velocity of the particles of each species correct to order ϕ, that is, with allowance for the effect of pair interactions. The method devised for the calculation of the mean velocity in a monodisperse system (Batchelor 1972) is first generalized to give the mean additional velocity of a particle of species i due to the presence of a particle of species j in terms of the pair mobility functions and the probability distribution pii(r) for the relative position of an i and a j particle. The second step is to determine pij(r) from a differential equation of Fokker-Planck type representing the effects of relative motion of the two particles due to gravity, the interparticle force, and Brownian diffusion. The solution of this equation is investigated for a range of special conditions, including large values of the Péclet number (negligible effect of Brownian motion); small values of the Ptclet number; and extreme values of the ratio of the radii of the two spheres. There are found to be three different limits for pij(r) corresponding to different ways of approaching the state of equal sphere radii, equal sphere densities, and zero Brownian relative diffusivity.

Consideration of the effect of relative diffusion on the pair-distribution function shows the existence of an effective interactive force between the two particles and consequently a contribution to the mean velocity of the particles of each species. The direct contributions to the mean velocity of particles of one species due to Brownian diffusion and to the interparticle force are non-zero whenever the pair-distribution function is non-isotropic, that is, at all except large values of the Péclet number.

The forms taken by the expression for the mean velocity of the particles of one species in the various cases listed above are examined. Numerical values will be presented in Part 2.
Subharmonics and vortex merging in mixing layers
Authors: Ho Chih-Ming , Huang Lein-Saing
Published: April 2006

In the present study, it is shown that the spreading rate of a mixing layer can be greatly manipulated at very low forcing level if the mixing layer is perturbed near a subharmonic of the most-amplified frequency. The subharmonic forcing technique is able to make several vortices merge simultaneously and hence increases the spreading rate dramatically. A new mechanism, ‘collective interaction’, was found which can bypass the sequential stages of vortex merging and make a large number of vortices (ten or more) coalesce.

A deeper physical insight into the evolution of the coherent structures is revealed through the investigation of a forced mixing layer. The stability and the forcing function play important roles in determining the initial formation of the vortices. The subharmonic starts to amplify at the location where the phase speed of the subharmonic matches that of the fundamental. The position where vortices are seen to align vertically coincides with the position where the measured subharmonic reaches its peak. This location is defined as the merging location, and it can be determined from the feedback equation (Ho & Nosseir 1981).

The spreading rate and the velocity profiles of the forced mixing layer are distinctly different from the unforced case. The data show that the initial condition has a longlasting effect on the development of the mixing layer.
Numerical studies of surface-tension effects in nonlinear Kelvin–Helmholtz and Rayleigh–Taylor instability
Authors: Pullin D. I.
Published: April 2006

We consider the behaviour of an interface between two immiscible inviscid incompressible fluids of different density moving under the action of gravity, inertial and interfacial tension forces. A vortex-sheet model of the exact nonlinear two-dimensional motion of this interface is formulated which includes expressions for an appropriate set of integral invariants. A numerical method for solving the vortex-sheet initial-value equations is developed, and is used to study the nonlinear growth of finite-amplitude normal modes for both Kelvin-Helmholtz and Rayleigh-Taylor instability. In the absence of an interfacial or surface-tension term in the integral-differential equation that describes the evolution of the circulation distribution on the vortex sheet, it is found that chaotic motion of, or the appearance of curvature singularities in, the discretized interface profiles prevent the simulations from proceeding to the late-time highly nonlinear phase of the motion. This unphysical behaviour is interpreted as a numerical manifestation of possible ill-posedness in the initial-value equations equivalent to the infinite growth rate of infinitesimal-wavelength disturbances in the linearized stability theory. The inclusion of an interfacial tension term in the circulation equation (which stabilizes linearized short-wavelength perturbations) was found to smooth profile irregularities but only for finite times. While coherent interfacial motion could then be followed well into the nonlinear regime for both the Kelvin-Helmholtz and Rayleigh-Taylor modes, locally irregular behaviour eventually reappeared and resisted subsequent attempts at numerical smoothing or suppression. Although several numerical and/or physical mechanisms are discussed that might produce irregular behaviour of the discretized interface in the presence of an interfacial-tension term, the basic cause of this instability remains unknown. The final description of the nonlinear interface motion thus awaits further research.
The effects of significant viscosity variation on convective heat transport in water-saturated porous media
Authors: Gary J. , Kassoy D. R. , Tadjeran H. , Zebib A.
Published: April 2006

Weakly nonlinear theory and finite-difference calculations are used to describe steadystate and oscillatory convective heat transport in water-saturated porous media. Two-dimensional rolls in a rectangular region are considered when the imposed temperature difference between the horizontal boundaries is as large as 200 K, corresponding to a viscosity ratio of about 6·5. The lowest-order weakly nonlinear results indicate that the variation of the Nusselt number with the ratio of the actual Rayleigh number to the corresponding critical value R/Rc, is independent of the temperature difference for the range considered. Results for the Nusselt number obtained from finite-difference solutions contain a weak dependence on temperature difference which increases with the magnitude of R/Rc. When R/Rc = 8 the constantviscosity convection pattern is steady, while those with temperature differences of 100 and 200 K are found to oscillate.
The slow translation of a sphere in a rotating viscous fluid
Authors: Dennis S. C. R. , Ingham D. B. , Singh S. N.
Published: April 2006

The motion of a sphere along the axis of rotation of an incompressible viscous fluid that is rotating as a solid mass is investigated by means of numerical methods for small values of the Reynolds and Taylor numbers. The Navier–Stokes equations governing the steady axisymmetric flow can be written as three coupled, nonlinear, elliptic partial differential equations for the stream function, vorticity and rotational velocity component. Two numerical methods are employed to solve these equations. The first is the method of series truncation in which the dependent variables are expressed as series of orthogonal Gegenbauer functions and the equations of motion are then reduced to three coupled sets of ordinary differential equations, which are integrated numerically subject to their boundary conditions. In the second method, specialized finite–difference techniques of solution are applied to the two-dimensional partial differential equations. These techniques employ finite-difference equations with coefficients that depend upon the exponential function; a particularly suitable form of approximation for use in calculating numerical solutions is obtained by expanding the exponential coefficients in powers of their exponents.

Calculated results obtained by the two methods are in good agreement with each other. The calculations have been carried out according to theoretical assumptions that simulate the experiments of Maxworthy (1965) in which the sphere experiences no resultant torque exerted by the surrounding fluid and is free to rotate with constant angular velocity. Numerical estimates of this angular velocity and of the drag exerted by the fluid on the sphere are found to agree well with the experimental results for Reynolds and Taylor numbers in the range from zero to unity. The results for small values of the Reynolds number are also consistent with theoretical work of Childress (1963, 1964) which is valid as the Reynolds number tends to zero.
Motion of a tank-treading ellipsoidal particle in a shear flow
Authors: Keller Stuart R. , Skalak Richard
Published: April 2006

A theoretical model is developed for the motion of a human red blood cell in a shear field. The model consists of a tank-treading ellipsoidal membrane encapsulating an incompressible Newtonian liquid immersed in a plane shear flow of another incom- pressible Newtonian liquid. Equilibrium and energy considerations lead to a solution for the motion of the particle that depends on the ellipsoidal-axis ratios and the ratio of the inner- to outer-liquid viscosities. The effect of variation in these parameters is explored and it is shown that, depending on their values, one of two types of overall motion is exhibited: a steady stationary-orientation motion or an unsteady flipping motion. A qualitative agreement of the predicted behaviour of the model with experi- mental observations on red blood cells is found.
Waves on glaciers
Authors: Fowler A. C.
Published: April 2006

This paper is an attempt at a mathematical synopsis of the theory of wave motions on glaciers. These comprise surface waves (analogous to water waves) and seasonal waves (more like compression waves). Surface waves have been often treated and are well understood, but seasonal waves, while observed, do not seem to have attracted any theoretical explanation. Additionally, the spectacular phenomenon of glacier surges, while apparently a dynamic phenomenon, has not been satisfactorily explained.

The present thesis is that the two wave motions (and probably also surging, though a discussion of this is not developed here) can both be derived from a rational theory based on conservation laws of mass and momentum, provided that the basal kinematic boundary condition involving boundary slip is taken to have a certain reasonable form. It is the opinion of this author that the form of this ‘sliding law’ is the crux of the difference between seasonal and surface waves, and that a further understanding of these motions must be based on a more satisfactory analysis of basal sliding.

Since ice is here treated in the context of a slow, shallow, non-Newtonian fluid flow, the theory that emerges is that of non-Newtonian viscous shallow-water theory; rather than balance inertia terms with gravity in the momentum equation, we balance the shear-stress gradient. The resulting set of equationsis, in essence, a first-order nonlinear hyperbolic (kinematic) wave equation, and susceptible to various kinds of analysis. We show how both surface and seasonal waves are naturally described by such a model when the basal boundary condition is appropriately specified. Shocks can naturally occur, and we identify the (small) diffusive parameters that are present, and give the shock structure: in so doing, we gain a useful understanding of the effects of surface slope and longitudinal stress in these waves.
LDV measurements of an air–-solid two-phase flow in a horizontal pipe
Authors: Tsuji Yutaka , Morikawa Yoshinobu
Published: April 2006

Measurements of air and solid velocities were made in an air-solid two-phase flow in a horizontal pipe by the use of a laser-Doppler velocimeter (LDV). The pipe was 30 mm inner diameter, and two kinds of plastic particles, 0.2 and 3.4 mm in diameter, were conveyed in addition to fine particles (ammonium chloride) for air-flow detection. The air velocities averaged over the pipe cross section ranged from 6 to 20m/s and the solid-to-air mass-flow ratio was up to 6. Simultaneous measurements of both air and 0.2 mm particle velocities were found possible by setting threshold values against the pedestal and Doppler components of the photomultiplier signal.

As the loading ratio increased and the air velocity decreased, mean-velocity distributions of both phases increased asymmetrical tendency. I n the presence of 0.2mm particles, a flattening of the velocity profile was remarkable. The effects of the solid particles on air-flow turbulence varied greatly with particle size. That is, 3.4 mm particles increased the turbulence markedly, while 0-2 mm ones reduced it. The probability-density function of the air flow deviated from the normal distribution (Gaussian) in the presence of particles. Finally, the frequency spectra of air-flow turbulence were obtained in the presence of 0.2 mm particles by using a fast Fourier transform (FFT). As a result, it was found that t,he higher-frequency components increased with increasing loading ratio.
The forced mixing layer between parallel streams
Authors: Oster D. , Wygnanski I.
Published: April 2006

The effect of periodic two-dimensional excitation on the development of a turbulent mixing region was studied experimentally. Controlled oscillations of variable ampli- tude and frequency were applied at the initiation of mixing between two parallel air streams. The frequency of forcing was at least an order of magnitude lower than the initial instability frequency of the flow in order to test its effect far downstream. The effect of the velocity difference between the streams was also investigated in this experiment. A typical Reynolds number based on the velocity difference and the momentum thickness of the shear layer was l04.

It was determined that the spreading rate of the mixing layer is sensitive to periodic surging even if the latter is so small that it does not contribute to the initial energy of the fluctuations. Oscillations at very small amplitudes tend to increase the spreading rate of the flow by enhancing the amalgamation of neighbouring eddies, but at higher amplitudes the flow resonates with the imposed oscillation. The resonance region can extend over a significant fraction of the test section depending on the Strouhal number and a dimensionless velocity-difference parameter. The flow in the resonance region consists of a single array of large, quasi-two-dimensional vortex lumps, which do not interact with one another. The exponential shape of the mean-velocity distribution is not affected in this region, but the spreading rate of the flow with increasing distance downstream is inhibited. The Reynolds stress in this region changes sign, indicating that energy is extracted from the turbulence to the mean motion; the intensity of the spanwise fluctuations is also reduced, suggesting that the flow tends to become more two-dimensional.

Amalgamation of large coherent eddies is resumed beyond the resonance region, but the flow is not universally similar. There are many indications suggesting that the large eddies in the turbulent mixing layer at fairly large Re are governed by an inviscid instability.
Dispersion of tracers in the deep ocean
Authors: Smith Ronald
Published: April 2006

Exact solutions are used to contrast the behaviour of vertical dye streaks and of point discharge in the deep ocean. After a few inertial periods the growth of the contaminant cloud in both cases can be modelled by a diffusion equation with slowly varying coefficients. However, the apparent long-term diffusivity for the dye streak can be as much as three times as large as the horizontal diffusivity for the point discharge, depending upon the precise time of release. This anomalously large rate of spreading for the dye streak can persist for several weeks until sufficient time has elapsed for vertical diffusion over the vertical lengthscale of the dominant inertial- frequency waves.
The effects of surface roughness on the flow past circular cylinders at high Reynolds numbers
Authors: Nakamura Y. , Tomonari Y.
Published: April 2006

Measurements of’ the mean-pressure distribution and the Strouhal number on a smooth circular cylinder, circular cylinders with distributed roughness, and circular cylinders with narrow roughness strips were made over a Reynolds-number range 4.0 × l04 to 1.7 × l06 in a uniform flow. A successful high-Reynolds-number (trans- critical) simulation for a smooth circular cylinder is obtained using a smooth circular cylinder with roughness strips. High-Reynolds-number simulation can only be obtained by roughness strips and not by distributed roughness. A similarity parameter correlating the pressure distributions on circular cylinders with distributed roughness in the supercritical range is presented. The same parameter can also be applicable to the drag coefficients of spheres with distributed roughness.
Measurements and predictions of fully developed turbulent flow in a simulated rod bundle
Authors: Seale W. J.
Published: April 2006

Fully developed air flow has been investigated over a Reynolds-number range of 82800-346700 in a duct that simulates two interconnected subchannels of a rod bundle with a pitchldiameter ratio of 1.20. Based on equivalent hydraulic diameter, friction factors were found to be 2% lower than for pipe flow. Detailed measurements were made at a Reynolds number of 200000 of axial velocities, secondary velocities, and the Reynolds stresses. The distribution of axial velocity near the walls (normalized with the local friction velocity) could be expressed by an inner law of the wall for y+ up to 1500. Distributions of the normal Reynolds stresses and the mean turbulence kinetic energy were similar to those observed in a number of pipe and two-dimensional channel flows and could be correlated using the axial-velocity fluct,uations normalized with the local friction velocity. Maximum secondary velocities were about 1.5 % of the bulk axial velocity. The ‘k-ε’ turbulence model and an algebraic vorticity source for generating secondary velocities enabled the computation of axial velocities, secondary velocities, and mean turbulence kinetic energies that are in satisfactory agreement with those measured.
On a fourth-order envelope equation for deep-water waves
Authors: Janssen Peter A. E. M.
Published: April 2006

The ordinary nonlinear Schrödinger equation for deep-water waves (found by a perturbation analysis to O(ε3) in the wave steepness ε) compares unfavourably with the exact calculations of Longuet-Higgins (1978) for ε > 0·10. Dysthe (1979) showed that a significant improvement is found by taking the perturbation analysis one step further to O(ε4). One of the dominant new effects is the wave-induced mean flow. We elaborate the Dysthe approach by investigating the effect of the wave-induced flow on the long-time behaviour of the Benjamin–Feir instability. The occurrence of a wave-induced flow may give rise to a Doppler shift in the frequency of the carrier wave and therefore could explain the observed down-shift in experiment (Lake et al. 1977). However, we present arguments why this is not a proper explanation. Finally, we apply the Dysthe equations to a homogeneous random field of gravity waves and obtain the nonlinear energy-transfer function recently found by Dungey & Hui (1979).
On the method of moments for solute dispersion
Authors: Barton N. G.
Published: April 2006

A cloud of solute injected into a pipe or channel is known to spread out by a dispersion process based on cross-sectional diffusion across a velocity shear. The original description of the process is due to Taylor (1953, 1954), and an important subsequent contribution was by Aris (1956), who framed and partially solved equations for the integral moments of the cloud of contaminant. The present work resolves some technical difficulties that occur when Aris’ solution method (separation of variables) is pursued in depth. In particular, it is shown that Aris’ technique has to be modified to give the moments at short and moderate times after the injection of solute into the flow. The paper is concerned with dispersion in those parallel flows for which an associated eigenvalue problem has a discrete spectrum of eigenvalues; fortunately, this case appears to be the rule rather than the exception. Expressions are obtained for the second and third moment about the mean, and the theory is applied to three cases of interest.
The settling of a porous body through a density interface
Authors: Thornham S. A. , Wilson S. D. R.
Published: April 2006

In a large-scale process at I.C.I. Mond Division a flocculated suspension of fine solid particles is allowed to settle through an aqueous solution towards the horizontal interface with an underlying denser solution. When the solids have settled into the lower layer they are pumped away and dumped while the clarified upper layer can be safely disposed of or recycled. The passage of the floes through the interface is the rate-determining step in the process, and the analysis of this part of it is the subject of the paper. It is hoped that the analysis may have a much wider application in that the settling process could be used as the basis of a direct laboratory method of measuring properties of floes. At present both the porosity and permeability of flocs are almost impossible to measure directly, but, using the present analysis, the settling of a single floc through two successive density interfaces would provide (in principle) values for both.
The breaking and non-breaking wave resistance of a two-dimensional hydrofoil
Authors: Duncan James H.
Published: April 2006

Measurements of the surface-height profile and the vertical distributions of velocity and total head were made behind a two-dimensional fully submerged hydrofoil moving horizontally at constant speed and angle of attack. These measurements were used to resolve the drag on the foil into two parts: one associated with the turbulent breaking region that is sometimes present on the forward face of the first wave, and the other associated with the remaining non-breaking wavetrain. It was found that at ‘incipient breaking’ the first wave existed in either a breaking or a non-breaking state depending on the starting procedures. It was possible to induce steady breaking when the wave slope was 17° or higher. The wake survey measurements showed that the drag associated with breaking reached more than three times the maximum drag that could theoretically be obtained with non-breaking waves. The drag associated with breaking was found to be proportional to the downslope component of the weight of the breaking region.
Magnetic-flux transport by a convecting layer – topological, geometrical and compressible phenomena
Authors: Arter Wayne
Published: April 2006

Numerical calculations by Drobyshevski & Yuferev (1974) of the redistribution of magnetic flux by a Bénard layer with cells of square planform have been extended to higher values of electrical conductivity and to other velocity patterns, using a computer code developed for another purpose. Reconnection does not proceed as they supposed, but leads to overall field enhancement, and although the energy is greater at the bottom, there is as much unsigned flux in the upper half as in the lower half of the layer. However, compressible velocity patterns can concentrate flux at their bases.
Resistance and stability of a line of particles moving near a wall
Authors: Goren Simon L.
Published: April 2006

Corrections to Stokes’ law are determined to first order in a/b and a/h for a sphere of radius a in a one-dimensional array of identical spheres having centre-to-centre-spacing b and translating a distance h from a no-slip wall. When h/b is small the drag is greater than that given by Stokes’ law; as h/b increases, the drag generally decreases and becomes less than that given by Stokes’ law. Stability of the array is examined. Motion along the line of centres is found to be stable, but the other two motions are unstable. The wall is a stabilizing influence when motion is toward the wall and a destabilizing influence when motion is away from the wall. For motion parallel to the wall, the presence of the wall shifts the region of maximum instability to smaller wavelengths. Crowley's results, which neglect any influence of the wall, are approached for h/b greater than about 5.
The turbulent recirculating flow field in a coreless induction furnace, a comparison of theoretical predictions with measurements
Authors: El-Kaddah N. , Szekely J.
Published: April 2006

A mathematical representation has been developed for the electromagnetic force field and the fluid-flow field in a coreless induction furnace. The fluid flow field was represented by writing the axisymmetric turbulent Navier–Stokes equations, containing the electromagnetic body-force term. The electromagnetic body force field was calculated by using a technique of mutual inductances. The k-ε model was employed for evaluating the turbulent viscosity, and the resultant differential equations were solved numerically.

The theoretically predicted velocity fields were in reasonably good agreement with the experimental measurements reported by Hunt & Moore; furthermore, the agreement regarding the turbulence intensities was essentially quantitative. These results indicate the k-ε model does provide a good engineering representation of the turbulent recirculating flows occurring in induction furnaces. At this stage it is not clear whether the discrepancies between measurements and the predictions, which were not very great in any case, are attributable either to the model or to the measurement techniques employed.
How rapidly is a passive scalar mixed within closed streamlines?
Authors: Rhines P. B. , Young W. R.
Published: April 2006

The homogenization of a passive ‘tracer’ in a flow with closed mean streamlines occurs in two stages: first, a rapid phase dominated by shear-augmented diffusion over a time ≈P1/3(L/U), where the Péclet number P=LU/κ (L,U and κ are lengthscale, velocity scale and diffusivity), in which initial values of the tracer are replaced by their (generalized) average about a streamline; second, a slow phase requiring the full diffusion time ≈ L2/κ. The diffusion problem for the second phase, where tracer isopleths are held to streamlines by shear diffusion, involves a generalized diffusivity which is proportional to κ, but exceeds it if the streamlines are not circular. Expressions are also given for flow fields that are oscillatory rather than steady.
An experimental investigation of laminar axisymmetric submerged jets
Authors: Rankin G. W. , Sridhar K. , Arulraja M. , Kumar K. R.
Published: April 2006

Detailed measurements of the velocity profiles in a laminar axisymmetric submerged jet of water were taken using a laser-Doppler anemometer. A non-intrusive measurement technique is particularly advantageous in this application owing to the unstable nature of the laminar jet and the destabilizing effect which objects submerged in the jet have. Flow visualization was employed to ensure that all of the measuring points were located within the laminar region of the jet.

The variation of centreline velocity, jet half-radius and velocity-profile shape are investigated for various Reynolds numbers and axial distances. Emphasis is placed on the jet-development region; however, data from the fully developed region are also presented. Particular attention is given to determine the proper non-dimensional groups which are required to collapse the data. The predictions of a simple boundary-layer analysis are used as a guide in this regard and found to give an accurate representation of the flow field.

Velocity-profile data were taken at sufficiently small radial increments to allow a determination of the jet kinematic momentum using the basic integral definition. Although approximately constant, a slight variation with axial distance is indicated. The momentum initially decreases, and then increases gradually to a value greater than that at the tube exit. An attempt to explain the trend of the variation is made using certain hypotheses regarding the velocity and pressure conditions at the tube exit.
The growth of a grid-generated turbulent mixed layer in a two-fluid system
Authors: Fernando Harindra J. S. , Long Robert R.
Published: April 2006

This paper describes a laboratory experiment designed to compare measurements with published theoretical ideas of the mixed-layer growth of a two-layer system in which the turbulence is induced by an oscillating grid. Experimental results show excellent agreement with an earlier theory by one of us (Long), in which the mixed-layer depth D* measured from a virtual origin is given by $D_{*}\sim V_0^{-\frac{7}{11}}K^{\frac{9}{11}}t^{\frac{2}{11}}$, where K is action, t is time and V0 is a characteristic velocity of the problem. The experiments also verify Long's theoretical entrainment relation E = α2Ri−7/4, where E is the entrainment coefficient and $Ri = D^3_{*}\Delta b/K^2$, and Δb is the buoyancy difference between the two layers. The interfacial-layer thickness was observed to be proportional to the depth of the mixed layer, as also predicted by Long. After a certain depth, the entrainment law tends to deviate from Long's theory. The deviation may be due to wall effects.
Zero-crossings in turbulent signals
Authors: Sreenivasan K. R. , Prabhu A. , Narasimha R.
Published: April 2006

A primary motivation for this work arises from the contradictory results obtained in some recent measurements of the zero-crossing frequency of turbulent fluctuations in shear flows. A systematic study of the various factors involved in zero-crossing measurements shows that the dynamic range of the signal, the discriminator characteristics, filter frequency and noise contamination have a strong bearing on the results obtained. These effects are analysed, and explicit corrections for noise contamination have been worked out. New measurements of the zero-crossing frequency N0 have been made for the longitudinal velocity fluctuation in boundary layers and a wake, for wall shear stress in a channel, and for temperature derivatives in a heated boundary layer. All these measurements show that a zero-crossing microscale, defined as Λ = (2πN0)−1, is always nearly equal to the well-known Taylor microscale λ (in time). These measurements, as well as a brief analysis, show that even strong departures from Gaussianity do not necessarily yield values appreciably different from unity for the ratio Λ/λ. Further, the variation of N0/N0 max across the boundary layer is found to correlate with the familiar wall and outer coordinates; the outer scaling for N0 max is totally inappropriate, and the inner scaling shows only a weak Reynolds-number dependence. It is also found that the distribution of the interval between successive zero-crossings can be approximated by a combination of a lognormal and an exponential, or (if the shortest intervals are ignored) even of two exponentials, one of which characterizes crossings whose duration is of the order of the wall-variable timescale ν/U2*, while the other characterizes crossings whose duration is of the order of the large-eddy timescale δ/U∞. The significance of these results is discussed, and it is particularly argued that the pulse frequency of Rao, Narasimha & Badri Narayanan (1971) is appreciably less than the zero-crossing rate.
The generation of cross-waves in a long deep channel by parametric resonance
Authors: Jones A. F.
Published: April 2006

The evolution equations are obtained which govern the growth of cross-waves generated in a long deep channel by a wavemaker with small amplitude when the waves are modified by finite-amplitude effects. The linearized equations are compared with previous theoretical and experimental work. Some numerical solutions are obtained for illustration.
A laboratory study of stratified accelerating shear flow over a rough boundary
Authors: Thorpe S. A.
Published: April 2006

Experiments are made in which a stratified shear flow, accelerating from rest and containing a level where the direction of flow reverses, is generated over a rough floor. The roughness elements consist of parallel square bars set at regular intervals normal to the direction of flow. Radiating internal gravity waves are generated in the early stages of flow, whilst flow separation behind the bars produces turbulent mixing regions which eventually amalgamate and entirely cover the floor. This turbulent layer spreads vertically less rapidly than the internal waves. Observed features of the waves are compared with those predicted by a model in which the floor is assumed to be sinusoidal, and fair agreement is found for the amplitude, phase and vertical wavenumber of the waves, even when the latter becomes large.

The rate of spread of the turbulent layer depends on the separation of the bars. Some interaction between the turbulence and the internal waves occurs near the edge of the turbulent layer. Wave-breaking is prevalent and the vertical scale of the waves is affected by turbulent eddies. The radiating internal waves are suppressed by replacing the bars by an array of square cubes, but there is continued evidence of features resembling internal waves near the boundary of the turbulent region. Structures are observed which bear some similarities to those found at the foot of the near-surface mixing layer in a lake.
Influence of non-uniform temperature distribution on the steady motion of ice sheets
Authors: Morland L. W. , Smith G. D.
Published: April 2006

The plane steady flow of a grounded ice sheet is analysed under the assumption that the ice behaves as a nonlinearly viscous fluid with a strongly temperature-dependent rate factor. It is supposed that the accumulation/ablation distribution on the (unknown) free surface is prescribed, and that there is a given basal sliding condition connecting the tangential velocity, tangential traction and normal pressure. The basal boundary is defined as the smooth contour which describes the mean topography viewed on the ice-sheet lengthscale, and is assumed to have small slope. The perturbation analysis which reduces the isothermal or constant rate factor equations to an ordinary differential equation for the leading-order profile is now extended with similar success to the non-isothermal problem when the temperature distribution is prescribed. That is, the thermomechanically coupled energy balance is not solved, but families of temperature distributions qualitatively compatible with observed patterns are adopted to exhibit the effects of significant creep-rate variation with temperature.
Mass transport around a horizontal cylinder beneath waves
Authors: Chaplin John R.
Published: April 2006

Around a horizontal cylinder submerged beneath waves with its axis parallel to the wave crests there exists, owing to streaming flow in the boundary layer, circulation with the same sense of rotation as that of the orbital motion in the waves. Experimental results, for conditions in which the effects of separation are not important, confirm theoretical predictions of the mass-transport velocity at the outer edge of the oscillatory boundary layer. Pressure measurements on the cylinder reveal a nonlinear component which is interpreted as a consequence of circulation induced by steady streaming.
Oscillations of a rotating liquid drop
Authors: Busse F. H.
Published: April 2006

The effect of rotation on the frequencies of oscillations of a liquid drop is investigated. It is assumed that the drop is imbedded in a fluid of the same or different density and that a constant surface tension acts on the interface. Rotation influences the oscillations through the Coriolis force and through the centrifugal distortion of the drop. For non-axisymmetric oscillations only the Coriolis force is important in first approximation and causes the expected splitting of the frequency for the two modes differing in their sign of circular polarization with respect to the axis of rotation. In the case of axisymmetric oscillations the centrifugal distortion and the Coriolis force combine to increase the frequency whenever the density ρi of the drop exceeds the density of ρ° of the surrounding fluid. For ρi < ρ° a decrease of the frequency of oscillation is possible for some modes of higher degree.
On modifications of the Zakharov equation for surface gravity waves
Authors: Stiassnie Michael , Shemer Lev
Published: April 2006

The Zakharov integral equation for surface gravity waves is modified to include higher-order (quintet) interactions, for water of constant (finite or infinite) depth. This new equation is used to study some aspects of class I (4-wave) and class II (5-wave) instabilities of a Stokes wave.
Prandtl–Batchelor flow past a flat plate with a forward-facing flap
Authors: Saffman P. G. , Tanveer S.
Published: April 2006

Two-dimensional steady inviscid flow past an inclined flat plate with a forward-facing flap attached to the rear edge is considered for the case when a vortex sheet separates from the leading edge of the flat plate and reattaches at the leading edge of the flap, with uniform vorticity distributed between the vortex sheet and the body. Solutions are found for a particular geometry and a range of values of the vorticity. The method used to calculate the flow is an extension of a free-streamline method widely used in cases where the velocity is a constant on the separating streamline.
Axisymmetric thermal-creep flow of a slightly rarefied gas induced around two unequal spheres
Authors: Onishi Yoshimoto
Published: April 2006

A thermal-creep flow of a slightly rarefied gas induced axisymmetrically around two unequal spheres is studied on the basis of kinetic theory. The spheres, whose thermal conductivities are assumed to be identical with that of the gas, for simplicity, are placed in an infinite expanse of the gas at rest with a uniform temperature gradient at a far distance. Owing to the poor thermal conductivities of the spheres, a tangential temperature gradient is established on the surfaces, and this causes a thermal-creep flow in its direction. Consequently, the spheres experience forces in the opposite direction.

The flow considered here is a low-Reynolds-number flow in the ordinary fluid-dynamic sense (except for the Knudsen layer), and the solution is obtained in terms of bispherical coordinates, with respect to which the system of equations of Stokes type is well developed. The velocity field around the spheres and the forces acting on them are given explicitly. The results show the interesting feature that the smaller sphere experiences the minimum force at a value of the separation distance that depends on the radius ratio. This is in contrast with the case of the axisymmetric motion of two spheres treated by Stimson & Jeffery (1926) in ordinary fluid dynamics at low Reynolds number.

The ultimate velocities that the spheres would have under the action of the present thermal force when they are freely suspended are also obtained by utilizing the results for the forces of axisymmetric translational problems of two spheres at low Reynolds number. For a given temperature gradient in the gas, both spheres acquire larger velocities than those they would have if they were alone, and the smaller sphere tends to move faster than the larger one in the direction opposite to the temperature gradient.

Also presented, for completeness, are the results for the sphere–plane case and for the case of eccentric spheres, the solutions for which are derived as special cases of the preceding problem of two unequal spheres.
Study of the effects of wall conductance on natural convection in differently oriented square cavities
Authors: Kim D. M. , Viskanta R.
Published: April 2006

This paper reports experimental and numerical results on the effects of wall conductance on natural convection in a two-dimensional rectangular cavity. Three different configurations in which the external wall is heated from the side, top and bottom and cooled from the side, bottom and top respectively have been investigated. Experiments have been performed in a square enclosure with solid walls made from Lexan and forming a square air-filled cavity. A Mach–Zehnder interferometer was used to determine the temperature distributions in the fluid. Solutions for stationary two-dimensional equations of energy and motion governing heat conduction in the solid and natural convection flow and heat transfer of a Boussinesq fluid contained in the cavity have been obtained numerically. The coupled flow distributions, including the appearance of multicellular flow, temperature profiles and heat-transfer predictions compare favourably with experimental results. Heat conduction in the connecting (unheated) walls is shown to simultaneously stabilize and destabilize the fluid in the cavity.
On the formation of ripples on an erodible bed
Authors: Sumer B. Mutlu , Bakioglu Mehmet
Published: April 2006

A linear stability analysis is presented of both hydraulically smooth and transitional flows over an erodible bed. The present theory is developed to account for the formation of ripples. It is essentially an extension of the theory of Richards (1980) to include the effect of viscosity upon the bed wave stability. The theory takes into consideration that the formation of ripples does not depend on flow depths, and that only the bed-load transport is involved in the formation of ripples. The effect of gravity is included in the analysis through the local inclination of the wavy bed surface. The results show that the bed is unstable (i.e. ripples exist) when the grain Reynolds number is less than a certain value. The limiting values of the grain Reynolds number for ripple existence obtained through present analysis are found to be in good agreement with observations.
Local isotropy and the decay of turbulence in a stratified fluid
Authors: Gargett A. E. , Osborn T. R. , Nasmyth P. W.
Published: April 2006

The validity of the assumption of local isotropy is investigated using measurements of three orthogonal components of the turbulent velocity fields associated with initially high-Reynolds-number geophysical turbulence. The turbulent fields, generated by various large-scale internal motions caused by tidal flows over an estuarine sill, decay under the influence of stable mean density gradients. With measurements from sensors mounted on a submersible, we examine the evolution of spectral shapes and of ratios of cross-stream to streamwise components, as well as the degree of high-wavenumber universality, for the observational range of the parameterI≡ks/kb=lb/ls. This ratio is a measure of separation between the Kolmogoroff wavenumberks≡ (ε/ν3)¼≡ 2π/lstypical of scales by which turbulent kinetic energy has been dissipated (at rate ε), and the buoyancy wavenumberkb≡ (N3/ε)½≡ 2π/lbtypical of scales at which the ambient stratification parameterN≡ (−gρz/ρ0)½becomes important. For values of I larger than ∼ 3000, inertial subranges are observed in all spectra, and the spectral ratio ϕ22/ϕ11of cross-stream to streamwise spectral densities reaches the isotropic value of 4/3 for about a decade in wavenumber. As ks/kbdecreases, inertial subranges vanish, but spectra of the cross-stream and streamwise components continue to satisfy isotropic relationships at dissipation wavenumbers. We provide a criterion for when ε may safely be estimated from a single measured component of the dissipation tensor, and also explore questions of appropriate low-wavenumber normalization for buoyancy-modified turbulence.