bluuebunny/crossref_metadata_2025 huggingface dataset:
Fully developed asymmetric flow in a plane channel
Authors: Hanjalić K. , Launder B. E.
Published: March 2006

The paper presents the results of a detailed experimental examination of fully developed asymmetric flow between parallel planes. The asymmetry was introduced by roughening one of the planes while the other was left smooth; the ratio of the shear stresses at the two surfaces was typically about 4:1.

The main emphasis of the research has been on establishing the turbulence structure, particularly in the central region of the channel where the two dissimilar wall flows (generated by the smooth and rough surfaces) interact. Measurements have included profiles of all non-zero double and triple velocity correlations; spectra of the same correlations at several positions in the channel; skewness and flatness factors; and lateral two-point space correlations of the streamwise velocity fluctuation.

The region of greatest interaction is characterized by strong diffusional transport of turbulent shear stress and kinetic energy from the rough towards the smooth wall region, giving rise,inter alia, to an appreciable separation between the planes of zero shear stress and maximum mean velocity. The profiles of length scales of the larger-scale motion are, in contrast to the turbulent velocity field, nearly symmetric. Moreover, it appears that at high Reynolds numbers the small-scale motion may in many respects be treated as isotropic.
Laminar dispersion in curved tubes and channels
Authors: Nunge R. J. , Lin T.-S. , Gill W. N.
Published: March 2006

Dispersion in curved tubes and channels is treated analytically, using the velocity distribution of Topakoglu (1967) for tubes and that of Goldstein (1965) for curved channels. The result for curved tubes is compared with that obtained previously by Erdogan & Chatwin (1967) and it is found that the presentdispersion coefficient contains the Erdogan & Chatwin result as a limiting case.

The most striking difference between the results is that Erdogan & Chatwin predict that the dispersion coefficient is always decreased by curvature if the Schmidt number exceeds 0.124, which is the ease for essentially all systems of practical interest. In contrast, the present result, equation (76), predicts that the dispersion coefficient may be increased substantially by curvature in low Reynolds number flows, particularly in liquid systems which would be of interest in biological systems.

Two competing mechanisms of dispersion are present in curved systems. Curvature increases the variation in residence time across the flow in comparison with straight systems and this in turn increases the dispersion coefficient. The secondary flow which occurs in curved tubes creates a transverse mixing which decreases the dispersion coefficient. The results demonstrate that the relative importance of these two effects changes with the Reynolds number, since the dispersion coefficient first increases and then decreases as the Reynolds number increases. Since secondary flows are not present in curved channels the dispersion coefficient is increased over that in straight channels for all cases.
Hydrodynamic stability of surfactant solutions heated from below
Authors: Palmer Harvey J. , Berg John C.
Published: March 2006

The interfacial hydrodynamics of pools of dilute binary solutions heated from below is examined using linear stability analysis. Results show that the stabilizing effect of the solute can vary greatly with its interfacial properties, its concentration, and the rate and mechanism of its transfer between the bulk phase and the surface.
An experiment on the adiabatic compressible turbulent boundary layer in adverse and favourable pressure gradients
Authors: Lewis J. E. , Gran R. L. , Kubota T.
Published: March 2006

A wind-tunnel model was developed to study the two-dimensional turbulent boundary layer in adverse and favourable pressure gradients with out the effects of streamwise surface curvature. Experiments were performed at Mach 4 with an adiabatic wall, and mean flow measurements within the boundary layer were obtained. The data, when viewed in the velocity transformation suggested by Van Driest, show good general agreement with the composite boundary-layer profile developed for the low-speed turbulent boundary layer. Moreover, the pressure gradient parameter suggested by Alber & Coats was found to correlate the data with low-speed results.
Hydrodynamic stability in plane Poiseuille flow with finite amplitude disturbances
Authors: George W. D. , Hellums J. D.
Published: March 2006

A general method for studying two-dimensional problems in hydrodynamic stability is presented and applied to the classical problem of predicting instability in plane Poiseuille flow. The disturbance stream function is expanded in a Fourier series in the axial space dimension which, on substitution into the Navier-Stokes equation, leads to a system of parabolic partial differential equations in the coefficient functions. An efficient, stable and accurate numerical method is presented for solving these equations. It is demonstrated that the numerical process is capable of accurate reproduction of known results from the linear theory of hydrodynamic stability.

Disturbances that are stable according to linear theory are shown to become unstable with the addition of finite amplitude effects. This seems to be the first work of quantitative value for disturbances of moderate and larger amplitudes. A relationship between critical amplitude and Reynolds number is reported, the form of which indicates the existence of an absolute critical Reynolds number below which an arbitrary disturbance cannot be made unstable, no matter how large its initial amplitude. The critical curve shows significantly less effect of amplitude than do those obtained by earlier workers.
The acoustics of turbulence near sound-absorbent liners
Authors: Williams John E. Ffowcs
Published: March 2006

Acoustic liners are often perforated screens backed by sound-absorbent material. Turbulence can interact with these screens to generate additional sound. The dynamics of the generation process is examined in this paper, where the liner is modelled as an infinite rigid plane boundary with a homogeneous array of circular orifices or rigid pistons. The acoustic properties of these boundaries are derived in the long wavelength limit. Small-scale turbulence is scattered by individual apertures into sound. Acoustically transparent surfaces support dipole scattering centres while more ‘opaque’ surfaces have monopoles at the apertures which convert turbulence into sound more effectively. It is shown that the process can be described once the response of an individual aperture in an infinite baffle is known. At low Mach numbers the screen can increase the sound radiated by adjacent turbulence by a factor equal to the inverse fourth power of the Mach number. Mean-flow effects are ignored but they are thought to increase the effects deduced in this preliminary study.
Wave-induced wind fluctuation over the sea
Authors: Kondo Junsei , Fujinawa Yukio , Naito Gen'ichi
Published: March 2006

Simultaneous measurements of the sea surface displacement and the longitudinal component of the wind velocity at several levels are reported. They were obtained at the Marine Tower under various conditions, with the air and the waves moving either in the same or in opposite directions. The spectral analysis was made. The cross-correlation coefficient between the sea surface displacement and the wind velocity is large at the layer adjacent to the surface and decreases with increasing mean wind velocity and height. Below a certain level which is several times or several tens of times higher than the height of the critical level where the wind velocity component in the direction of wave propagation equals the wave velocity, the phase lag of the Fourier component of the wind velocity compared with the surface elevation component is about 160 to 190°. Above this layer the wave-induced wind component is very weak and the phase reversal takes place at the height where the mean wind velocity equals 1·2 to 1·5C, C being the phase velocity of wave. When the wind blows in the opposite direction from that of the wave propagation, the wind fluctuation is in phase with respect to the wave motion and the amplitude of wave-induced wind component is relatively large. Some discrepancies are shown between the observations and the predictions from the theory of inviscid fluids.
Measurement of local entrainment rate in the initial region of axisymmetric turbulent air jets
Authors: Hill B. J.
Published: March 2006

The local entrainment rate in the initial region of axisymmetric turbulent air jets has been measured by a novel method, which is an adaptation of the ‘porous-wall’ technique used by Ricou & Spalding (1961). The local entrainment rate, which is independent of the nozzle Reynolds number for values greater than 6 × 104, is strongly dependent upon the axial distance. At an axial distance of one nozzle diameter the local entrainment rate is only about one-third of that in the fully developed jet; the entrainment rate increases with increasing axial distance to reach the fully developed value at an axial distance of about thirteen nozzle diameters.
On Long's hypothesis of no upstream influence in uniformly stratified or rotating flow
Authors: McIntyre Michael E.
Published: March 2006

The weakly nonlinear, two-dimensional problem for the disturbance due to a slender obstacle in a uniformly stratified, Boussinesq fluid moving past the obstacle with constant basic horizontal velocityU, is considered up to second order in the amplitude ε of the disturbance. Analogous rotating problems are also treated. Particular attention is given to calculating explicitly the columnar-disturbance strengths upstream and downstream of the obstacle, both in the stratified and in the rotating problems, with a view to discussing the truth or otherwise of Long's hypothesis (LH).

Whether or not columnar disturbances are found far upstream, violating LH, depends,interalia, on whether or not the flow is externally bounded by rigid horizontal planes (or by a tube or annulus, in the rotating problem), and on whether the problem is made determinate by means of an ‘inviscid transient’ formulation, or by means of a ‘viscous’ one.

The inviscid, transient, bounded problem, for time-development of lee waves from a state of no initial disturbance, always exhibits columnar disturbances oforder ε2somewhere in the fluid. They are generated, not near the obstacle, but in the ‘tails’ or transient terminal zones of the lee-wave trains. The columnar-disturbance strengths are largely independent of how the flow is set up from an initially undisturbed state. I n all but one instance the effect is non-zero far up-stream. The exception is the singly-subcritical stratified (or narrow-gap rotating) case, in which the excitation has modal structure sin(2z), the fluid region being 0 [les ]z[les ] π in this case the only columnar disturbance that can penetrate up-stream has structure sinzand so is not excited.

A completely different result holds for ‘viscous’ formulations for unseparated, bounded régimes (with steady lee waves spatially attenuated by effects of small molecular diffusion). The strengths of all columnar disturbances, upstream and downstream, vanish in the limit of small diffusivity.

In the inviscid, transient, unbounded problem, the upstream influence is, likewise, evanescent, beingO(ε2t−2) as timet→ ∞.

The basic expansion in powers of ε will be invalid for times ∝ ε−1or greater, because of resonant-interactive instability of the lee waves.
Propagation of a blast wave in uniform or non-uniform media: a uniformly valid analytic solution
Authors: Sachdev P. L.
Published: March 2006

The shock propagation theory of Brinkley & Kirkwood (1947) is extended to provide a uniformly valid analytic solution of point-explosion problems both when the undisturbed medium is uniform and when it is stratified. This is achieved mainly by selecting the parameter expressing a similarity restraint in this theory such that initially it gives precisely the Taylor–Sedov solution, while asymptotically, in the weak regime, still retaining the well-known Landau–Whitham–Sedov form of the solution for shock overpressure. The shock overpressure, as calculated by the present method for spherical and cylindrical blast waves in the entire regime from the point of explosion to where they have become very weak, shows excellent agreement with that from the exact numerical solutions of Lutzky & Lehto (1968) and Plooster (1970). The solution for a spherical shock propagating in an exponential atmosphere stratified by a constant acceleration due to gravity also shows a good agreement with the exact numerical solution of Lutzky & Lehto.
Nonlinear Kelvin and continental-shelf waves
Authors: Smith Ronald
Published: March 2006

Equations are derived for the variation along a straight coastline of Kelvin and continental-shelf waves. It is assumed that the effects of nonlinearity and dispersion are of the same order in a small parameter ε defined by the equation ε2 = f2=L2/gH, in which f is the Coriolis parameter, L the shelf width and H the water depth beyond the shelf. Kelvin waves are found to satisfy the Korteweg–de Vries equation, while continental-shelf waves satisfy a closely related equation. An approximate rule is derived for the variation along a real coastline of the maximum wave height for fully developed nonlinear Kelvin waves.
An experimental study of turbulent separating and reattaching flows at a high Mach number
Authors: Batham J. P.
Published: March 2006

Separating and reattaching flows in a two-dimensional compression corner were investigated experimentally at a Mach number of 7·0 and Reynolds numbers (based on the distance from the leading edge to the corner) of 4·75 × 106, 9·51 × 106and 1·55 × 107. Heat-transfer measurements and Pitot traverses in the upstream boundary layer showed that the boundary layer had become fully turbulent at the start of the interactions. Increases in the Reynolds number gave increases in the length of separated shear layers and decreases in the corner angle required for incipient, separation. The reattachment pressure coefficients gave good agreement with the criterion of Batham (1969).
Unsteady transonic flows in two-dimensional channels
Authors: Adamson T. C.
Published: March 2006

A two-dimensional, unsteady, transonic, irrotational, inviscid flow of a perfect gas with constant specific heats is considered. The analysis involves perturbations from a uniform sonic isentropic flow. The governing perturbation potential equations are derived for various orders of the ratio of the characteristic time associated with a temporal flow disturbance to the time taken by a sonic disturbance to traverse the transonicregime. The case where this ratio is large compared to one is studied in detail. A similarity solution involving an arbitrary function of time is found and it is shown that this solution corresponds to unsteady chimel flows with either stationary or time-varying wall shapes. Numerical computations are presented showing the temporal changes in flow structure as a disturbance dies out exponentially for the following typical nozzle flows: simple accelerating (Meyer) flow and flow with supersonic pockets (Taylor and limiting Taylor flow).
The collection efficiencies of small droplets falling through a sheared air flow
Authors: Jonas P. R. , Goldsmith P.
Published: March 2006

Experiments in which collection efficiencies have been measured for small droplets falling through a sheared air flow are described. The results indicate that these collection efficiencies are much greater than for the same droplets falling in still air when the collecting droplets are less than about 25μm in radius, but that for larger droplets there is very little effect. Calculations of the collision efficiencies of rigid spheres moving in a sheared air flow are presented but these fail to account for the experimental results. These discrepancies are discussed.
A model for the micro-structure in ciliated organisms
Authors: Blake John
Published: March 2006

Improved models for the movement of fluid by cilia are presented. A theory which models the cilia of an organism by an array of flexible long slender bodies distributed over and attached at one end to a plane surface is developed. The slender bodies are constrained to move in similar patterns to the cilia of the microorganismsOpalina, ParameciumandPleurobrachia.

The velocity field is represented by a distribution of force singularities (Stokes flow) along the centre-line of each slender body. Contributions to the velocity field from all the cilia distributed over the plane are summed, to give a streaming effect which in turn implies propulsion of the organism. From this we have been able to model the mean velocity field through the cilia sublayer for the three organisms. We find that, in a frame of reference situated in the organism, the velocity near the surface of the organism is very small – up to one half the length of the cilium – but it increases rapidly to near the velocity of propulsion from then on. This is because of the beating pattern of the cilia; they beat in a near rigid-body rotation during the effective (‘power’) stroke, but during the recovery stroke move close to the wall. Backflow (‘reflux’) is found to occur in the organisms exhibiting antiplectic metachronism (i.e.ParameciumandPleurobrachia). The occurrence of gradient reversal, but not backflow, has recently been confirmed experimentally (Sleigh & Aiello 1971).

Other important physical values that are obtained from this analysis are the force, bending moment about the base of a cilium and the rate of working. It is found, for antiplectic metachronism, that the force exerted by a cilium in the direction of propulsion is large and positive during the effective stroke whereas it is small and negative during the recovery stroke. However, the duration of the recovery stroke is longer than the effective stroke so the force exerted over one cycle of a ciliary beat is very small. The bending moment follows a similar pattern to the component of force in the direction of propulsion, being larger in the effective stroke for antiplectic metachronism. In symplectic metachronism (i.e.Opalina) the force and bending moment are largest in magnitude when the bending wave is propagated along the cilium. The rate of working indicates that more energy is consumed in the effective stroke forParameciumandPleurobrachiathan in the recovery stroke, whereas inOpalinait is found to be large during the propagation of the bending wave.
The intermittent small-scale structure of turbulence: data-processing hazards
Authors: Tennekes H. , Wyngaard J. C.
Published: March 2006

Velocity derivatives in turbulence at large Reynolds numbers exhibit probability densities with a large kurtosis. If the value of the kurtosis is about 40, as in many measurements of atmospheric turbulence, careful attention to the processing of such signals is required in order to obtain an acceptable level of accuracy. Signal-to-noise and integration-time limitations make measurements of moments higher than the fourth nearly impossible for signals of this kind.
Transmission of water waves through small apertures
Authors: Guiney D. C. , Noye B. J. , Tuck E. O.
Published: March 2006

The water-wave transmission coefficient for a small slit in a thick vertical barrier is obtained theoretically and verified both experimentally and by comparison with an exact theory for the case of zero thickness. Similar shallow-water results are presented.
Forced resonant second-order interaction between damped internal waves
Authors: Mcewan A. D. , Mander D. W. , Smith R. K.
Published: March 2006

A theoretical and experimental study is made of the second-order resonant interaction between triads of linearly damped waves, one common member of which is continuously forced. In the case of a single triad, if the forced wave exceeds a critical amplitude defined by properties of the triad members, energy proceeds irreversibly to the other two waves. A stable limit state is reached where all power in excess of that required to sustain a critical amplitude in the forced wave is transferred to the other waves, which also reach steady terminal amplitudes.

It is shown that when two or more triads are simultaneously at resonance the only stable limit state is one wherein the forced wave has fallen to the lowest critical amplitude, and the only other two waves remaining are those of the triad possessing this critical amplitude. Regardless of their initial amplitudes, all other waves not externally forced ultimately disappear.

The theory is applied to the interaction of standing internal gravity waves in a linearly stratified liquid. The experiments described here quantitatively confirm the major predictions.
Axisymmetric slow viscous flow past an arbitrary convex body of revolution
Authors: Gluckman Michael J. , Weinbaum Sheldon , Pfeffer Robert
Published: March 2006

Considerable advances have been made in the past few years in treating a variety of problems in slender-body Stokes flow (Taylor 1969; Batchelor 1970; Cox 1970, 1971; Tillett 1970). However, the problem of treating the creeping motion past bluff objects, whose boundaries do not conform to a constant co-ordinate surface of one of the special orthogonal co-ordinate systems for which the Stokes slow-flow equation is simply separable, is still largely unsolved. In the slender-body Stokes flow studies mentioned above, the viscous-flow boundary-value problem is formulated approximately as an integral equation for an unknown distribution of Stokeslets over a line enclosed by the body. The theory is valid for only very extended shapes, since the error in drag decays inversely as the logarithm of the aspect ratio of the object. By contrast, the present authors show that the boundary-value problem for the axisymmetric flow past an arbitrary convex body of revolution can be formulated exactly as an integral equation for an unknown distribution of ring-like singularities over the surface of the body. The kernel in this integral equation is closely related to the fundamental separable solutions of the Stokes slow-flow equation when written in an oblate spheroidal co-ordinate system of vanishing aspect ratio. The two lowest-order appropriate spheroidal singularities are found to provide a complete description for all surface elements, except those perpendicular to the axis. Higher-order singularities of all orders are required to describe axially perpendicular surfaces, such as the ends of a cylinder or the blunt base of an object. The newly derived integral equation is solved numerically to provide the first theoretical solutions for low aspect ratio cylinders and cones. The theoretically predicted drag results are in excellent agreement with experimentally measured values.
Some exact statistics of two-dimensional viscous flow with random forcing
Authors: Thompson Philip Duncan
Published: March 2006

By regarding the amplitudes of a set of orthogonal modes as the co-ordinates in an infinite-dimensional phase space, the probability distribution for an ensemble of randomly forced two-dimensional viscous flows is determined as the solution of the continuity equation for the phase flow. For a special, but infinite, class of types of random forcing, the exact equilibrium probability distribution can be found analytically from the Navier-Stokes equations. In these cases, the probability distribution is the product of exponential functions of the integral invariants of unforced inviscid flow.
Flow in a deep turbulent boundary layer over a surface distorted by water waves
Authors: Townsend A. A.
Published: March 2006

Linearized equations for the mean flow and for the turbulent stresses over sinusoidal, travelling surface waves are derived using assumptions similar to those used by Bradshaw, Ferriss & Atwell (1967) to compute boundary-layer development. With the assumptions, the effects on the local turbulent stresses of advectal, vertical transport, generation and dissipation of turbulent energy can be assessed, and solutions of the equations are expected to resemble closely real flows with the same conditions. The calculated distributions of surface pressure indicate rates of wave growth (expressed as fractional energy gain during a radian advance of phase) of about 15(ρa/ρw) (τo/c2), where τo is the surface stress, co the phase velocity and ρa and ρw the densities of air and water, unless the wind velocity at height λ/2π is less than the phase velocity. The rates are considerably less than those measured by Snyder & Cox (1966), by Barnett & Wilkerson (1967) and by Dobson (1971), and arguments are presented to show that the linear approximation fails for wave slopes of order 0.1.
Capsular flow in pipelines
Authors: Vardy A. E. , Bloor M. I. G. , Fox J. A.
Published: March 2006

The problem considered is that of the steady motion of a series of neutrally buoyant, flat-faced, rigid, cylindrical capsules along the axis of a pipeline under the influence of a hydraulic pressure gradient. The Navier-Stokes equations are non-dimensionalized and expressed in central-difference form. Numerical solutions are found by the method of relaxation for Reynolds numbers up to 20 000 and a close agreement is obtained with readings from a laboratory apparatus for Reynolds numbers up to 2200.

The flow is examined in detail and the existence of toroidal vortices between successive capsules is demonstrated. Their shape is shown to be increasingly influenced by inertial forces as the Reynolds number increases, but the overall pressure gradient is not greatly dependent on the Reynolds number.
The energy balance in modulated plane Poiseuille flow
Authors: Herbert D. M.
Published: March 2006

Plane Poiseuille flow in which the pressure gradient has a small amplitude time-periodic component in addition to a constant component is considered. The velocity field close to the boundaries, arising from a small amplitude high frequency disturbance to the flow, is calculated to second order in the modulation amplitude. The energy-transfer integral for the disturbance is then calculated to the same order. It is found that, if the thickness of the disturbance shear wave relative to that of the modulation shear wave is greater than ½, the modulation inhibits energy transfer into the disturbance and so stabilizes the flow.
Asymptotic analysis of premixed burning with large activation energy
Authors: Fendell Francis E.
Published: March 2006

The structure and propagation rates of premixed flames are determined by singular perturbation in the limit where the activation temperature is large relative to other flow temperatures for several basic flows. Specifically, the simple kinetics of an exothermic first-order monomolecular decomposition under Arrhenius kinetics is studied for one-dimensional laminar flame propagation, spherically symmetric quasi-steady monopropellant droplet burning, and other simple geometries. Results elucidate Lewis-number effects, losses owing to fuel gasification processes, and conditions under which the thin-flame approximation is a limit of finite-rate Arrhenius kinetics.
Laser anemometry: a report on EUROMECH 36
Authors: Durst F. , Melling A. , Whitelaw J. H.
Published: March 2006

The 36th European Mechanics Colloquium (EUROMECH 36) which was held at Imperial College from 17 to 19 April 1972 was the first to be devoted to laser anemometry. It brought together European researchers whose primary interests included physics, electronics and fluid mechanics with the following purposes.
Boundary-layer development at a two-dimensional rear stagnation point
Authors: Robins A. J. , Howarth J. A.
Published: March 2006

This paper examines the nature of the development of two-dimensional laminar flow of an incompressible fluid at the rear stagnation point on a cylinder which is started impulsively from rest. Proudman & Johnson (1962) first examined this type of flow, andobtainedasimilarity solution of the inviscid form of the equations of motion. This solution describes the nature of the flow at large distances from the surface, for large times after the start of the motion. Here, the flow at the rear stagnation point is examined in greater detail. The solution found by Proudman & Johnson constitutes the leading term in an asymptotic expansion, valid for large times. Further terms in this expansion are now calculated, and the method of matched asymptotic expansions is used to obtain an inner solution describing the flow near the surface. A numerical integration of the full initial-value problem gives good agreement with the analytical solution.
Nonlinear source-sink flow in a rotating pie-shaped basin
Authors: And George Veronis , Yang C. C.
Published: March 2006

Source-sink flows in a rotating pie-shaped basin provide a laboratory analogue of wind-driven ocean circulation (Stommel, Arons & Faller 1958). Experiments and theory are presented here for flows which are mildly nonlinear. Theory and experiment show satisfactory agreement for the intense flow in the western boundary-layer region which contains the strongest nonlinear effects. The strengths of the sources and sinks were increased in the experiments in an attempt to induce an instability in the western boundary layer. However, the western boundary layer was always stable, even for relatively large Rossby numbers. Photographs from experiments with a basin of semicircular cross-section show the difference between eastern and western boundary layers in a striking manner.
Heat transfer in a periodic boundary layer near a two-dimensional stagnation point
Authors: Ishigaki Hiroshi
Published: March 2006

Following the previous velocity-field study (Ishigaki 1970), this paper studies how the temperature field in the laminar boundary layer near a two-dimensional stagnation point responds to the main-stream oscillation. The time-mean temperature field is of particular interest and is studied in detail. The velocity field is treated as known and is taken from the previous paper. In § 3 the solutions over the whole frequency range are obtained under the assumption of small amplitude oscillation and the results are compared with the existing approximate solutions for low and high frequency in terms of heat transfer. Time-mean heat transfer decreases at low frequency, but slightly increases at high frequency. Two factors that cause time-mean modification of the temperature field are examined quantitatively. In § 4 the finite amplitude case is treated under the assumption of high-frequency oscillation and a few examples of the time-mean temperature profile are shown.
Viscous effects in a vertically propagating internal wave
Authors: Gordon D. , Stevenson T. N.
Published: March 2006

A circular cylinder is positioned horizontally in an incompressible stably stratified fluid which has a constant Brunt-Väisälä frequency. A vertical two-dimensional internal wave is produced when the cylinder is oscillated at this natural frequency. A small amplitude viscous similarity solution which explains the main features of the internal wave is presented.
The excess noise field of subsonic jets
Authors: Crighton D. G.
Published: March 2006

The sound field generated by the interaction of spatial instabilities on the shear layer shed from a duct with the nozzle lip is studied. It is shown that the intensity varies with direction θ from the exhaust and with the subsonic exhaust speedUaccording toI∼U6(1 − cosθ)2andI∼U6sin2θ for the axisymmetric and first azimuthal (sinuous) modes respectively. The first of these results is interpreted in terms of monopole and dipole sources at the exit plane, representing the acoustic effect of fluctuating mass flow and axial thrust across the exit plane, and the second in terms of a transverse dipole at the exit plane, corresponding to fluctuations in cross-stream thrust. A correlated thrust fluctuation of 1% is shown to overwhelm the jet mixing noise in the forward arc, θ > 90° while the acoustic efficiency of the interaction process is never less than 10−6M3even under the cleanest possible exit conditions. Forward flight of the duct a t Mach numberMαis shown to increase the forward-arc intensity by the factor (1 + Mαcos θ)−4. It is suggested that much of the discrepancy between the noise fields of real engines and the predictions of Lighthill's theory of jet mixing noise – the so-called ‘excess noise’ problem – can be explained in terms of this interaction mechanism.
Experiments on the nonlinear stages of free-shear-layer transition
Authors: Miksad Richard W.
Published: March 2006

An experimental study is made of the instability and transition of a laminar free shear layer by sound excitation. Primary emphasis is placed on the nonlinear stages of transition. Transition from laminar instability to turbulent breakdown covers approximately five wavelengths of downstream distance. The instability has six distinct regions of behaviour : a region of exponential growth described by linear theory; a nonlinear region where critical-layer effects are important, and harmonics and subharmonics are generated; a region of finite amplitude equilibration of the fundamental mode; a region of finite amplitude triggered sub-harmonic instabilities; a region of three-dimensional longitudinal vortex formation; and a final region of weak secondary instabilities and turbulent breakdown.
A general method for solving steady-state internal gravity wave problems
Authors: Hurley D. G.
Published: March 2006

The paper describes a simple but general method for solving 'steady-state’ problems involving internal gravity waves in a stably stratified liquid. Under the assumption that the motion is two-dimensional and that the Brunt-Väisälä frequency is constant, the method is used to re-derive in a very simple way the solutions to problems where the boundary of the liquid is either a wedge or a circular cylinder. The method is then used to investigate the effect that a model of the continental shelf has on an incident train of internal gravity waves. The method involves analytic continuation in the frequency of the disturbance, and may well prove to be effective for other types of wave problem.
On the rippling of small waves: a harmonic nonlinear nearly resonant interaction
Authors: Mcgoldrick L. F.
Published: March 2006

We show that the rippling often observed on small progressive gravity waves can be explained in terms of a nearly resonant harmonic nonlinear interaction. The resonance condition is that the phase speeds of the two waves must be nearly identical. The in viscid analysis is generalized to any order in a small parameter proportional to the wave steepness. Wave tank measurements provide experimental evidence for most of the predicted results. The phenomenon of resonant rippling is further shown to be not just peculiar to capillary-gravity waves, but in fact possible for any weakly nonlinear dispersive wave system whose dispersion relation has discrete pairs of solutions nearly satisfying the resonance conditions.
On generalized-vortex boundary layers
Authors: Belcher R. J. , Burggraf O. R. , Stewartson K.
Published: March 2006

We define a generalized vortex to have azimuthal velocity proportional to a power of radiusr−n. The properties of the steady laminar boundary layer generated by such a vortex over a fixed coaxial disk of radiusaare examined. Though the boundary-layer thickness is zero a t the edge of the disk, reversals of the radial component of velocity u must occur, so that an extra boundary condition is needed at any interior boundary radiusrEto make the structure unique. Numerical integrations of the unsteady governing equations were carried out forn= − 1, 0, ½ and 1. Whenn= 0 and − 1 solutions of the self-similar equations are known for an infinite disk. Assuming terminal similarity to fix the boundary conditions atr=rEwhenur> 0, a consistent solution was found which agrees with those of the self-similar equations whenrEis small. However, ifn= ½ and 1, no similarity solutions are known, although the terminal structure forn= 1 was deduced earlier by the present authors. From the numerical integration forn= ½, we are able to deduce the limit structure forr→ 0 by using a combination of analytic and numerical techniques with the proviso of a consistent self-similar form asrE→ 0. The structure is then analogous to a ladder consisting of an infinite number of regions where viscosity may be neglected, each separated by much thinner viscous transitional regions playing the role of the rungs. This structure appears to be characteristic of all generalized vortices for which 0.1217 <n< 1.
Simple waves on shear flows: similarity solutions
Authors: Freeman N. C.
Published: March 2006

A class of similarity solutions is derived for the equations of simple waves on inviscid shear flows discovered by Blythe, Kazakia & Varley (1972). Such solutions all have propagation speeds proportional to the square root of the depth and contain the uniform flow solution as a special case.
Waves in a gas in solid-body rotation
Authors: Morton J. B. , Shaughnessy E. J.
Published: March 2006

The axial and transverse wave motions of an inviscid perfect gas in isothermal solid-body rotation in a cylinder are investigated. Solutions of the resulting eigenvalue problem are shown to correspond to two types of waves. The acoustic waves are the rotational counterparts of the well-known Rayleigh solutions for a gas at rest in a cylinder. The rotational waves, whose amplitudes and frequencies go to zero in the non-rotating limit, exhibit phase speeds both larger and smaller than the speed of sound. The effect of rotation on the frequency and structure of these waves is discussed.
Test-field model for inhomogeneous turbulence
Authors: Kraichnan Robert H.
Published: March 2006

The test-field model for isotropic turbulence is restated in a form which is independent of the choice of orthogonal basis functions for representing the velocity field. The model is then extended to non-stationary inhomogeneous turbulence with a mean shearing velocity, contained by boundaries of arbitrary shape. A modification of the model is introduced which makes negligible changes in the numerical predictions but which greatly simplifies computations when the co-variance matrix and related statistical matrices are non-diagonal. The altered model may be regarded as a kind of generalization of Orszag's eddy-damped Markovian model, with the damping factors determined systematically, in representation-independent form, from dynamical equations. The final equations of the test-field model are presented in a sufficiently explicit form to serve as a starting point for numerical work. To facilitate comparison, the corresponding direct-interaction equations for inhomogeneous turbulence with mean shear are presented also, in a uniform notation. The test-field model is much faster to compute than the direct-interaction approximation because, in the former, only single-time statistical functions need be computed. This advantage is at the cost of a less rich and less faithful representation of the dynamics.
Statistical hydromechanics of disperse systems. Part 3. Pseudo-turbulent structure of homogeneous suspensions
Authors: Buyevich Yu. A.
Published: March 2006

The theory of concentrated two-phase mixtures developed in the previous parts of this paper is applied to analysis of the structure of the local random motion (pseudo-turbulence) occurring in flows of suspensions of small solid spheres. Suspensions under study are assumed to be locally homogeneous in the sense that large-scale agglomerates of many particles or voids filled with the pure liquid do not arise in their flows and particles can be approximately regarded as statistically independent units.

Coefficients of the particle diffusion caused by pseudo-turbulence are calculated without restrictions imposed on the value of the Reynolds number Re characterizing the fluid flow around one particle. Other pseudo-turbulent quantities (the r.m.s. pseudo-turbulent velocities of both phases, their effective pseudo-turbulent viscosities in a shear flow, etc.) are considered for small Re. In particular, a natural explanation is given to the known effect of the reduced hydraulic resistance of a fluidized bed as compared with that of a stationary particulate bed of the same porosity.

Additionally, some properties of the mean motion of a suspension influenced by pseudo-turbulence are discussed brifly. By way of example, two problems are considered: stability of the upward flow of a homogeneous suspension with respect to small perturbations depending upon the vertical co-ordinate and time, and the spatial distribution of particles suspended by the upward flow of a fluid under gravity.
The Stokes-flow drag on prolate and oblate spheroids during axial translatory accelerations
Authors: Lai Robert Y. S. , Mockros Lyle F.
Published: March 2006

Stokes's linearized equations of motion are used to calculate the flow field generated by a spheroid executing axial translatory oscillations in an infinite, otherwise still, incompressible, viscous fluid. The flow field, expressed in terms of spheroidal wave functions of order one, is used to develop general expressions for the drag on oscillating prolate and oblate spheroids. Formulae for the approximate drag, useful in making calculations, are obtained for small values of an oscillation parameter. These formulae reduce to the Stokes result in the limit when the spheroid becomes a sphere and the steady-state drag for a spheroid as the frequency of oscillation becomes zero. The fluid forces on spheroids of various shapes are compared graphically. The approximate formulae for the drag are integrated over all frequencies to obtain formulae for the drag on spheroids executing general axial translatory accelerations. The fluid resistance on the spheroid is expressed as the sum of an added mass effect, a steady-state drag and an effect due to the history of the motion. A table of added mass, viscous and history coefficients is given.
The reattachment and relaxation of a turbulent shear layer
Authors: Bradshaw P. , Wong F. Y. F.
Published: March 2006

Existing experiments on the low-speed flow downstream of steps and fences, and some new measurements downstream of a backward-facing step, are used to demonstrate the complicated nature of the flow in the reattachment region and its effect on the slow non-monotonic return of the shear layer to the ordinary boundary-layer state. A key feature of the flow is found to be the splitting of the shear layer at reattachment, where part of the flow is deflected upstream into the recirculating flow region to supply the entrainment; the part of the flow that continues downstream suffers a pronounced decrease in eddy length scale, evidently because the larger eddies are torn in two. This phenomenon will occur in all cases where a shear layer reattaches after a prolonged region of separation, either at low speed or in supersonic flow. For simplicity, the discussion in the present paper is confined to low-speed flows.
Flow patterns in models of small airway units of the lung
Authors: Davidson M. R. , Fitz-Gerald J. M.
Published: March 2006

Quasi-steady creeping flow in models of small airway units of the lung is investigated. A respiratory unit of the lung is modelled by a sphere, an oblate and a prolate ellipsoid of revolution, and a circular cylinder of finite length. The solution of the Stokes equations for each of these geometries is indicated for general axi-symmetric boundary conditions. For particular cases consistent with the models, streamlines are plotted and some velocity profiles are shown. It is suggested that bulk 00w in the ha1 generations of the lung is significant for gas transport even though diffusion is the predominant mechanism there.
On the interaction of surface and internal waves
Authors: Gargettt A. E. , Hughes B. A.
Published: March 2006

The steady-state interaction between surface waves and long internal waves is investigated theoretically using the radiation stress concepts derived by Longuet-Higgins & Stewart (1964) (or Phillips 1966). It is shown that, over internal wave crests, those surface waves for which cg0cosϕ0 > ci experience a change in direction of propagation towards the line of propagation of the internal waves and their amplitudes are increased. Here cg0 is the surface-wave group speed at U = 0, ϕ0 is the angle between the propagation direction of the surface waves at U = 0 and the propagation direction of the internal waves, and ci is the phase speed of the internal waves. If cg0cos ϕ0 < ci the direction of the surface waves is turned away and their amplitudes are decreased. Over troughs the opposite effects occur.

At positions where the local velocity of surface-wave energy transmission measured relative to the internal wave phase velocity is zero, i.e. cg + U − ci = 0, there is a singularity in the energy of the surface waves with resulting infinite amplitudes. It is shown that at these critical positions two wavenumbers which were real and distinct on one side coalesce and become complex on the other. The critical positions are thus shown to be barriers to the propagation of those wave-numbers. It is also shown that there is a critical position representing the coalescence of three wavenumbers. Surface-wave crest configurations are shown for three numerical examples. The frequency and direction of propagation of surface waves that exhibit critical positions somewhere in an internal wave field are shown as a function of the maximum horizontal surface current. This is compared with measurements of wind waves that have been reported elsewhere.
On the Weis-Fogh mechanism of lift generation
Authors: Lighthill M. J.
Published: March 2006

Weis-Fogh (1973) proposed a new mechanism of lift generation of fundamental interest. Surprisingly, it could work even in inviscid two-dimensional motions starting from rest, when Kelvin's theorem states that the total circulation round a body must vanish, but does not exclude the possibility that if the body breaks into two pieces then there may be equal and opposite circulations round them, each suitable for generating the lift required in the pieces’ subsequent motions! The ‘fling’ of two insect wings of chord c (figure 1) turning with angular velocity Ω generates irrotational motions associated with the sucking of air into the opening gap which are calculated in § 2 as involving circulations −0·69Ωc2 and + 0.69Ωc2 around the wings when their trailing edges, which are stagnation points of those irrotational motions, break apart (position (f)). Viscous modifications to this irrotational flow pattern by shedding of vorticity at the boundary generate (§ 3) a leading-edge separation bubble, and tend to increase slightly the total bound vorticity. Its role in a three-dimensional picture of the Weis-Fogh mechanism of lift generation, involving formation of trailing vortices at the wing tips, and including the case of a hovering insect like Encarsia formosa moving those tips in circular paths, is investigated in § 4. The paper ends with the comment that the far flow field of such very small hovering insects should take the form of the exact solution (Landau 1944; Squire 1951) of the Navier-Stokes equations for the effect of a concentrated force (the weight mg of the animal) acting on a fluid of kinematic viscosity v and density p, whenever the ratio mg/pv2 is small enough for that jet-type induced motion to be stable.
Experiment on convex curvature effects in turbulent boundary layers
Authors: So Ronald M. C. , Mellor George L.
Published: March 2006

Turbulent boundary layers along a convex surface of varying curvature were investigated in a specially designed boundary-layer tunnel. A fairly complete set of turbulence measurements was obtained.

The effect of curvature is striking. For example, along a convex wall the Reynolds stress is decreased near the wall and vanishes about midway between the wall and the edge of a boundary layer where there exists a velocity profile gradient created upstream of the curved wall.