bluuebunny/crossref_metadata_2025 huggingface dataset:
The effects of capillarity on free-streamline separation
Authors: Ackerberg R. C.
Published: March 2006

The effect of a small surface-tension coefficient on the classical theory of free-streamline separation from a sharp trailing edge is studied. The classical solution fails in a small region surrounding the edge, where it predicts singular behaviour, and an inner solution, satisfying linear boundary conditions, is required to obtain a uniformly valid first approximation. The solution valid near the edge removes the curvature and pressure-gradient singularities of the classical solution and predicts a standing capillary wave along the free streamline.
On the development of noise-producing large-scale wavelike eddies in a plane turbulent jet
Authors: Merkine Lee-Or , Liu J. T. C.
Published: March 2006

In this paper we study the development of large-scale wavelike eddies in a two-dimensional turbulent jet, extending earlier work on the mixing region (Liu 1974). The basic mean flow develops from one of mixing-region type with an initially specified boundary-layer thickness into a fully developed jet. This study brings out the role of the varicose and sinuous modes as they develop in a growing mean flow. In general, it is found that, for a given frequency parameter, the varicose mode has a shorter streamwise lifetime than the sinuous mode. For lower frequencies, the latter persists past the end of the potential core only to become subject to dissipation by the enhanced fine-scale turbulent activity in that region.
Laser-Doppler anemometer measurements in drag-reducing channel flows
Authors: Reischman M. M. , Tiederman W. G.
Published: March 2006

The objective of this study was to make velocity measurements in drag-reducing flows which would be sufficient in scope and accuracy to test proposed models of drag-reducing flows and to yield new information about the mechanisms of drag reduction. Consequently, measurements of the mean and turbulence intensity of the streamwise velocity component were made in fully developed, turbulent, drag-reducing flow in a two-dimensional channel with a laser-Doppler anemometer. The anemometer was operated in the individual-realization mode and corrections were made to eliminate statistical biasing of the data. Two polyacrylamides and a polyethylene oxide were used to produce seven flows which had drag reductions ranging from 24 to 41 %. Measurements were also made in water to establish the standard characteristics of the flow channel.

The data show that the drag-reducing mean velocity profile can be divided into three zones: a viscous sublayer, a buffer or interactive region and a logarithmic region. There is no evidence that the viscous sublayers of the drag-reducing channel flows are thicker than those in the solvent flows. In addition the normalized streamwise fluctuations are essentially the same in both the solvent and drag-reducing sublayers. The changes caused by the polymer addition occur in the buffer region. The drag-reducing buffer region is thicker and the velocity profile in the outer flow region adjusts in order to accommodate this buffer-region thickening. The measurements of the streamwise velocity fluctuations also show that the polymer additives redistribute the primary turbulent activity over a broadened buffer region. The normalized magnitude of these fluctuations is, however, considerably lower in these two-dimensional drag-reducing channel flows than in those previously reported by Rudd (1972), Logan (1972) and Kumor & Sylvester (1973). Moreover, the mean velocity profiles in the buffer region do not confirm the hypothesis of Virk, Mickley & Smith (1970) that the data will follow their proposed ‘ultimate profile’ when the drag reduction is less than that given by the maximum asymptote. The mean velocity measurements also show that the proposed methods for predicting the upward shift in the outer portion of the mean velocity profile are inconsistent and lack universality. However, these results do confirm the previous suggestions of Virk (1971), Tomita (1970) and Lumley (1973) that the buffer region is the area of importance and change in drag-reducing flows.
Wind-generated gravity-capillary waves: laboratory measurements of temporal growth rates using microwave backscatter
Authors: Larson T. R. , Wright J. W.
Published: March 2006

The growth rates of wind-induced water waves at fixed fetch were measured in a laboratory wave tank using microwave backscatter. The technique strongly filters out all wavenumber component pairs except for a narrow window at the resonant Bragg scattering conditions. For these waves the spectral amplitude was measured as a function of the time after a fixed wind was abruptly started. The radars were aligned to respond to waves travelling in the downwind direction at wavelengths of 0·7-7 cm. Wind speeds ranged from 0·5 to 15 m/s. Fetches of 1·0, 3·0 and 8·4 m were used. In every case, the spectral amplitude initially grew at a single exponential rate β over several orders of magnitude, and then abruptly ceased growing. No dependence of the growth rate on fetch was observed. For all wavelengths and wind speeds the data can be fitted by
\[
\beta (k,u_{*},{\rm fetch})=f(k)\,u^n_{*},
\]
with n = 1·484 ± 0·027. Here u* is the friction velocity obtained from vertical profiles of mean horizontal velocity. For each wind speed, f(k) had a relative maximum near k = kn ≃ 3·6 cm−1. Rough estimates of β/2ω, where ω is the water wave frequency, and of the wind stress supported by short waves indicate that the observed growth rates are qualitatively very large. These waves are tightly coupled to the wind, and play a significant role in the transfer of momentum from wind to water.
Intensity, scale and convection of turbulent density fluctuations
Authors: Davis M. R.
Published: March 2006

This paper extends the quantitative schlieren technique to the separate determination of the local scales and intensity of turbulent density fluctuations. Measurements in an unheated supersonic jet are also extended to positions substantially further away from the jet than those reported hitherto, and show that high levels close to the nozzle reduce to levels comparable to subsonic velocity fluctuations beyond 18 diameters from the nozzle exit. Trends for the integral scales are similar to those based on subsonic jet velocity fluctuations. Separated-beam measurements show reflexion of disturbances on the jet centre-line just beyond the potential core. Spectra show a more peaked form close to the jet, and exhibit a rapid decrease in level with wavenumber.
Inviscid interpenetration of two streams with unequal total pressures
Authors: Goldstein M. E. , Braun Willis H.
Published: March 2006

A theory is developed for analysing the inviscid interpenetration of two streams. It is assumed that the difference in total pressure between the streams is not large. Several examples of the general results are presented.
The development of magnetohydrodynamic flow due to an electric current discharge
Authors: Sozou C. , Pickering W. M.
Published: March 2006

The development of the magnetohydrodynamic flow field due to the discharge of an electric current J0 from a point on a plate bounding a semi-infinite viscous incompressible conducting fluid is considered. The flow field is the response of the fluid to the Lorentz force set up by the electric current and the associated magnetic field. The problem is formulated in terms of the dimensionless variable (vt)½/r and solved numerically. Here ν is the coefficient of kinematic viscosity, t the time from the application of the electric current and r the distance from the discharge. It is shown that the streamlines of the developing flow field in a cross-section through the axis of the discharge are closed loops about a stagnation point. As the flow field develops, the stagnation point moves to infinity along a ray emanating from the discharge with a speed proportional to t−½. The steady state, within a distance r from the discharge, is practically established when t = r2/ν.
An experimental investigation of low Reynolds number secondary streaming effects associated with an oscillating viscous flow in a curved pipe
Authors: Bertelsen Arnold F.
Published: March 2006

This paper deals with nonlinear streaming effects in an oscillating fluid in a curved pipe. The secondary steady velocity field in the cross-sectional plane of the pipe is studied in detail. Our experimental results are compared with the theory of Lyne (1970; that part of his theory which is valid for Reynolds numbers Rs [Lt ] 1) and the theory of Zalosh & Nelson (1973). On the basis of these comparisons we conclude that the theories are in practice valid for higher Reynolds numbers Rs than was formally expected.
Supercritical Reynolds number simulation for two-dimensional flow over circular cylinders
Authors: Szechenyi Edmond
Published: March 2006

In wind-tunnel tests on bluff bodies the Reynolds number is often limited to values that are very much smaller than those of the flows being simulated. In such cases the experiments may have no practical significance whatsoever since both the fluctuating and the steady aerodynamic phenomena can vary considerably with Reynolds number.

This difficulty was encountered in an investigation of supercritical incompressible flow over cylinders, and an attempt at artificially increasing the Reynolds number by means of surface roughness was made. In order to evaluate this simulation technique, the influence of various grades of surface roughness on the aerodynamic forces acting on cylinders of different diameters was studied over a wide range of Reynolds numbers in two very different wind tunnels. The results allow very positive conclusions to be drawn.
The low frequency sound from multipole sources in axisymmetric shear flows, with applications to jet noise
Authors: Goldstein M. E.
Published: March 2006

We have obtained a closed-form solution for the sound radiation from multipole sources imbedded in an infinite cylindrical jet with an arbitrary velocity profile. It is valid in the limit where the wavelength is large compared with the jet radius. Simple formulae for the acoustic pressure field due to convected point sources are also obtained. The results show (in a simple way) how the mean flow affects the radiation pattern from the sources. For convected lateral quadrupoles it causes the exponentnof the Doppler factor (1 -Mcosθ)−nmultiplying the far-field pressure signal to be increased from the value of 3 used by Lighthill to 5.
The generation of sound by density inhomogeneities in low Mach number nozzle flows
Authors: Williams J. E. Ffowcs , Howe M. S.
Published: March 2006

This paper discusses the sound generated when an inhomogeneity in density is convected in a low Mach number steady flow through a contraction in a duct of infinite extent, and also when the inhomogeneity exhausts through a nozzle into free space. The analyses of Candel (1972) and Marble (1973) for the case of duct flow were based on a frequency decomposition of the incident inhomogeneity and cannot adequately deal with sharp-fronted inhomogeneities and entropy spots. However, the practical difficulties of this earlier work can be avoided at low flow Mach numbers by conducting the analysis in terms of an approximate expression for the acoustic Green's function in the manner described by Howe (1975). This method also permits a considerable extension of the range of the earlier investigations to the determination of the sound generated when the inhomogeneity is swept out of a nozzle orifice into free space. It is shown that the acoustic pressure perturbations developed in a duct at a contraction are in general proportional to the fractional difference between the density of the inhomogeneity and that of the mean flow times a typical mean flow pressure level, and are due principally to the fluctuation in thrust accompanying the passage of the inhomogeneity through the region of variable pressure gradient. The pressure waves generated at a nozzle orifice and radiated into free space are O(M0) smaller, where M0 is a mean flow Mach number based on the speed of sound in the jet.
Incompressible potential flow past ‘not-so-slender’ bodies of revolution at an angle of attack
Authors: Prasad P. Sivakrishna , Subramanian N. R.
Published: March 2006

Using the method of matched asymptotic expansions, an expansion of the velocity potential for steady incompressible flow has been obtained to order ε4for slender bodies of revolution at an angle of attack by representing the potential due to the body as a superposition of potentials of sources and doublets distributed along a segment of the axis inside the body excluding an interval near each end of the body. Also, expansions of the coefficients of longitudinal virtual mass and lateral virtual mass have been found. The pressure distributions over an ellipsoid of revolution of thickness ratio ε = 0·3 at zero angle of attack and at an angle of attack of 3° obtained by the present method are compared with results obtained from the exact theory and that of Van Dyke. The virtual-mass coefficients are also compared with those obtained from the exact theory and are found to be in good agreement up to ε = 0·3.
Water waves and conjugate streams
Authors: Keady G. , Norbury J.
Published: March 2006

Steady plane periodic waves on the surface of an ideal liquid above a horizontal bottom are considered. The flow is irrotational. LetQdenote the volume flow rate,Rthe total head andSthe flow force for the wave train. Bounds on wave properties are obtained in terms of the properties of (i) the conjugate streams with the sameQandR, and (ii) the conjugate streams with the sameQandS.
Internal waves around a body moving in a compressible density-stratified fluid
Authors: Peat K. S. , Stevenson T. N.
Published: March 2006

A body is started from rest and moves on an arbitrary path in an inviscid isothermal compressible atmosphere. The phase configuration of the internal waves and the gravity-modified acoustic waves which are generated by the body is studied using small amplitude wave theory. When the body moves at supersonic speeds and the background density gradient approaches zero, it is shown how the wave solutions approach the pure acoustic wave solutions of Lilleyet al.(1953).
Pressure- and buoyancy-driven thermal convection in a rectangular enclosure
Authors: Spradley L. W. , Churchill S. W.
Published: March 2006

Results are presented for unsteady laminar thermal convection in compressible fluids at various reduced levels of gravity in a rectangular enclosure which is heated on one side and cooled on the opposite side. The results were obtained by solving numerically the equations of conservation for a viscous, compressible, heat-conducting, ideal gas in the presence of a gravitational body force. The formulation differs from the Boussinesq simplification in that the effects of variable density are completely retained. A conservative, explicit, time-dependent, finite-difference technique was used and good agreement was found for the limited cases where direct comparison with previous investigations was possible. The solutions show that the thermally induced motion is acoustic in nature at low levels of gravity and that the unsteady-state rate of heat transfer is thereby greatly enhanced relative to pure conduction. The nonlinear variable density profile skews the streamlines towards the cooler walls but is shown to have little effect on the steady-state isotherms.
Pressure-wave propagation through a separated gas-liquid layer in a duct
Authors: Morioka Shigeki , Matsui Goichi
Published: March 2006

Pressure-wave propagation through a separated gas-liquid layer at rest in a duct of constant rectangular cross-section and infinite length is considered. Such a system is dispersive, possessing an infinite number of modes which depend on the ratios of the densities, thicknesses and sound speeds of the two phases. The transitional variation of an infinitesimal disturbance initially having a step profile is investigated analytically and numerically. In addition, it is shown that a weak but finite disturbance is described asymptotically by the solution of the Korteweg-de Vries equation.
Lifting-line theory for an unsteady wing as a singular perturbation problem
Authors: James E. C.
Published: March 2006

A linearized theory, which treats unsteady motions of a wing of large aspect ratio at variable forward speed in an inviscid incompressible fluid, is developed, using the method of matched asymptotic expansions. The wing geometry and motions are specified; and the time-dependent lift and moment are obtained. Long-time asymptotic behaviour of an initial-value harmonic motion is presented, as are the short-time solutions of a wing starting from rest, with constant acceleration and with impulsive acceleration to constant speed. Some attention is given to flapping flight. Results are presented in quadrature form for a general class of unsteady wing motions.
Transition in a two-dimensional plane wall jet
Authors: Bajura R. A. , Catalano M. R.
Published: March 2006

Transition in a two-dimensional plane wall jet was examined for the range of exit Reynolds numbers between 100 and 600. The wall jet was produced by the flow of water, which issued either from a smoothly-contoured nozzle or from the end of a long parallel channel. Observations were recorded both visually and with a hot-film anemometer. Both natural and forced transition cases were studied. Natural transition generally occurred in the following stages: (i) formation of discrete vortices in the outer shear layer; (ii) coalescence of adjacent vortices in the outer shear layer, coupled with the rolling up of the inner shear layer; (iii) eruption of the wall jet off the surface of the flat plate into the ambient fluid; (iv) dispersion of the organized flow pattern by three-dimensional turbulent motions; and (v) re-laminarization of the upstream flow, until another vortex pairing occurred. The initial stages of transition are two-dimensional in nature; and are dominated by the mechanism of vortex pairing, which is commonly observed in free shear layers. The inner-region shear layer exerts a stabilizing influence on the velocity profile at low Reynolds numbers. Forced transition was essentially similar to natural transition, except for the elimination of the downstream intermittency and the establishment of a fixed downstream location for transition.
The distortion of a jet by tabs
Authors: Bradbury L. J. S. , Khadem A. H.
Published: March 2006

In an attempt to explain the discrepancies that have been observed in the spread of nominally axisymmetric jets, an experimental investigation has been carried out in which the effects of a number of factors which it was thought might be important to jet development have been studied. These factors included the nozzle boundary-layer thickness, turbulence level and convergence. However, over the limited range of the tests, it was found that none of these factors had a very strong influence on the jet development. By contrast, the insertion of small rectangular tabs into the jet flow on the nozzle perimeter was found to have a very profound effect on the jet development. In particular, it was found that just two tabs produced gross distortions in the jet development resulting in the jet almost splitting in two with high velocity regions on either side of the diameter joining the tabs. Some explanations for this effect based on further tests with wedges are put forward.

In addition to the measurements of the mean flow field, a few spectrum and correlation measurements are reported for jets both from a clean nozzle and also from a nozzle with two tabs. In the former tests, evidence additional to the results of other experimenters was found for the existence of flow structures which have some coherence around the entire circumference of the jet. It has been suggested that these ‘vortex rings’ or ‘puffs’ may be of some importance in producing jet noise and it seems that the effect of inserting tabs is to prevent the occurrence of these structures.
A transport-equation description of nonlinear ocean surface wave interactions
Authors: Watson Kenneth M. , West Bruce J.
Published: March 2006

The evolution of the power spectrum of surface gravity waves is described by means of an energy transport equation. A slowly varying, prescribed ocean current and wind source are assumed to account for spatial inhomogeneities in the surface wave spectrum. These inhomogeneities lead to a new nonlinear wave-wave interaction mechanism.
A numerical study of the descent of a vortex pair in a stably stratified atmosphere
Authors: Hill F. M.
Published: March 2006

Numerical methods are used to investigate the motion of a horizontal vortex pair through a stably stratified atmosphere. The vortices carry with them a mass of fluid whose density differs from that of the air through which it descends, and the surface of this accompanying fluid becomes a vortex sheet, which is modelled by a set of discrete line vortices.

It is shown that, at first, the vortex pair slows down with the shape of the envelope of the accompanying fluid remaining constant. Later, vorticity concentrates at the rear, initiating detrainment and causing a downward acceleration of the vortex pair. Throughout the motion, the vortices approach each other.
Boundary-layer theory for blast waves
Authors: Kim K. B. , Berger S. A. , Kamel M. M. , Korobeinikov V. P. , Oppenheim A. K.
Published: March 2006

The necessity for developing a boundary-layer theory in the case of blast waves stems from the fact that inviscid flow solutions often yield physically unrealistic results. For example, in the classical problem of the so-called non-zero counterpressure explosion, one obtains infinite temperature and zero density in the centre at all times even after the shock front deteriorates into a sound wave. In reality, this does not occur, as a consequence, primarily, of heat transfer that modifies the structure of the flow field around the centre without drastically affecting the outer region. It is profitable, therefore, to consider the blast wave as a flow field consisting of two regions: the outer, which retains the properties of the inviscid solution, and the inner, which is governed by flow equations including terms expressing the effects of heat transfer and, concomitantly, viscosity. The latter region thus plays the role of a boundary layer. Reported here is an analytical method developed for the study of such layers, based on the matched asymptotic expansion technique combined with patched solutions.
On blast waves in exponential atmospheres
Authors: Bach G. G. , Kuhl A. L. , Oppenheim A. K.
Published: March 2006

The paper presents a comprehensive analysis of gas motion created by a strong explosion in an atmosphere whose density is an exponential function of altitude. For the near field (i.e. short times after initiation), an exact analytical solution of the equations of motion is obtained by means of a perturbation technique. For the far field (i.e. long times after initiation), a similarity solution associated with a logarithmic front trajectory is derived. The two are shown to be well matched with each other. Finally, a fully-algebraic approximate solution is given that qualitatively reproduces all the salient features of the exact and asymptotic solutions, while quantitatively it is in fair agreement with their results.
Optical compensation measurements on the unsteady exit condition at a nozzle discharge edge
Authors: Bechert D. , Pfizenmaier E.
Published: March 2006

The exit condition at the trailing edge of a nozzle for slightly unsteady flow has been investigated experimentally. This problem plays a crucial role in sound transmission through nozzles with flow. The measuring technique used is new and is based on the synchronization of a laser beam to the wave motion of a small smoke filament in the boundary layer leaving the nozzle. The resolution of the jet flow deflexion measurements is of the order of 1–3μm. The authors found the jet deflexion envelope to have a nearly parabolic shape near the nozzle edge. The size of this ‘parabolic’ region decreases with decreasing Strouhal number. This statement applies to the motion of the exterior border of the boundary layer at the dividing streamline between flow originating from the interior of the nozzle and flow coming from outside. It was found that the unsteady flow problem near the edge remains linear for fluctuating velocities of small magnitude.
The effects of wake splitter plates on bluff-body flow in the range 104 < R < 5 × 104. Part 2
Authors: Apelt C. J. , West G. S.
Published: March 2006

The work reported in part 1 has been extended to cover flows past circular cylinders with wake splitter plates having 2 [les ] L/D [les ] 7 and to include flows past normal flat plates with splitter plates having L/D [les ] 3·7. Pressure distributions and wake Strouhal numbers were measured and visualization studies carried out. The results obtained indicate that no further changes would be produced by lengthening the splitter plates beyond the limits tested.

The combined results of parts 1 and 2 provide coherent descriptions of the effects of wake splitter plates for all values of L/D of significance for the two profiles, which are representative of two distinct classes of bluff bodies, viz., those with cross-sections of curvilinear shape for which the flow separation points are not determined uniquely by the geometry and those for which the separation points are fixed.
Overstable hydromagnetic convection in a rotating fluid layer
Authors: Eltayeb I. A.
Published: March 2006

The effect of the simultaneous action of a uniform magnetic field and a uniform angular velocity on the linear stability of the Bénard layer to time-dependent convective motions is examined in the Boussinesq approximation. Four models, characterized by the relative directions of the magnetic field, angular velocity and gravitational force, are discussed under a variety of boundary conditions. Apart from a few cases, the treatment applies when the Taylor number T and the Chandrasekhar number Q (the square of the Hartmann number) are large. (These parameters are dimensionless measures of angular velocity and magnetic field, respectively.)

It is shown that the motions at the onset of instability can be of three types. If the Coriolis forces dominate the Lorentz forces, the results for the rotating non-magnetic case are retained to leading order. If the Coriolis and Lorentz forces are comparable, the minimum temperature gradient required for instability is greatly reduced. Also, in this case, the motions that ensue at marginal stability are necessarily three-dimensional and the Taylor-Proudman theorem and its analogue in hydromagnetics are no longer valid. When the Lorentz forces dominate the Coriolis forces, the results obtained are similar to those for the magnetic non-rotating case at leading order.

The most unstable mode is identified for all relations T = KQα, where K and α are positive constants, taking into account both time-dependent and time-independent motions

Various types of boundary layers developing on different boundaries are also examined.
Seepage flow in unconfined aquifers
Authors: Shercliff J. A.
Published: March 2006

The paper concerns one- and two-dimensional models of steady seepage flow in unconfined aquifers and the relationship between them. The first part gives a new proof of Charnyi's result that one- and two-dimensional theory yield the same value for the flow rate in a horizontal aquifer or porous bed between vertical ends and shows the extent to which it can be generalized to non-uniform or anisotropic media. The second part solves the highly two-dimensional problem of flow from a line source (line of springs) in an otherwise impermeable, sloping stratum and compares the result with the predictions of a one-dimensional Dupuit–Pavlovsky approach. Confirmatory experiments using the Hele Shaw analogue of seepage flow are also reported.
Finite amplitude axisymmetric thermoconvective flows in a bounded cylindrical layer of fluid
Authors: Charlson G. S. , Sani R. L.
Published: March 2006

Finite amplitude axisymmetric thermoconvective flows in a bounded cylindrical layer of fluid heated from beneath were calculated using Galerkin's method. Both systems with insulated and with conducting lateral boundaries were investigated for radius-to-depth ratios of 1, 2·25, 2·55 and 2·66. Flows bounded by a conducting lateral boundary were found to be unstable for Rayleigh numbers greater than 1·1 times the critical value. The cell size was found to be an increasing function of the Rayleigh number.
‘Crackle’: an annoying component of jet noise
Authors: Williams J. E. Ffowcs , Simson J. , Virchis V. J.
Published: March 2006

The paper describes an investigation of a subjectively distinguishable element of high speed jet noise known as ‘crackle’. ‘Crackle’ cannot be characterized by the normal spectral description of noise. It is shown to be due to intense spasmodic short-duration compressive elements of the wave form. These elements have low energy spread over a wide frequency range. The crackling of a large jet engine is caused by groups of sharp compressions in association with gradual expansions. The groups occur at random and persist for some 10−1s, each group containing about 10 compressions, typically of strength 5 × 10−3 atmos at a distance of 50 m. The skewness of the amplitude probability distribution of the recorded sound quantifies crackle, though the recording process probably changes the skewness level. Skewness values in excess of unity have been measured; noises with skewness less than 0·3 seem to be crackle free. Crackle is uninfluenced by the jet scale, but varies strongly with jet velocity and angular position. The jet temperature does not affect crackle, neither does combustion. Supersonic jets crackle strongly whether or not they are ideally expanded through convergent-divergent nozzles. Crackle is formed (we think) because of local shock formation due to nonlinear wave steepening at the source and not from long-term nonlinear propagation. Such long-term effects are important in flight, where they are additive. Some jet noise suppressors inhibit crackle.
Interaction of waves with two-dimensional obstacles: a relation between the radiation and scattering problems
Authors: Newman J. N.
Published: March 2006

A relation connecting the reflexion and transmission coefficients for scattering of water waves by a fixed body with the far-field radiated waves due to forced motions of the same body is derived. Two alternative derivations are given, including a simple argument based on the analysis of an appropriate linear superposition of the two problems, and a more formal application of Green's theorem to the two potentials. For bodies with horizontal symmetry, the transmission and reflexion coefficients are related to the phase angles of the far-field radiated waves associated with symmetric and antisymmetric forced motions of the body. Some general conclusions follow for arbitrary symmetric bodies, and these are verified in specific cases by comparison with existing solutions. The applicability of these relations to other types of wave problem is noted.
The flow near the bow of a steadily turning ship
Authors: Hirata Miguel Hiroo
Published: March 2006

The flow near the bow of a steadily turning ship is analysed using a modified slender-body theory. The rate of change of flow quantities in the longitudinal (x) direction is assumed to be greater than that implied by ‘conventional’ slender-body theory. As a consequence some features of high Froude number flow are apparent which cannot be predicted by the ‘conventional’ theory. The modified slender-body theory proposed requires the solution of a two-dimensional Laplace equation (in y and z) but its free-surface condition still involves an x derivative. A Fourier-transform method is used to solve this problem. A simple bow configuration of constant draft is analysed and numerical results for the free-surface elevation are presented.
A study of the freezing of sea water
Authors: Farhadieh R. , Tankin R. S.
Published: March 2006

A Mach-Zehnder interferometer was used to study the interaction between convection currents in the sea water and the ice-water interface during freezing. The temperature at the ice-water interface during the early stages of freezing was approximately 0 °C, not the equilibrium freezing temperature. Salt plumes were observed to appear first at specific sites on the ice-water interface. This is contrary to earlier results reported by Farhadieh & Tankin (1972). The salinity profiles in the salt plumes were measured using interferograms in conjunction with Abel inversion. The maximum salinity, along the centre-line of the salt plume, is an indication of the salinity of the brine trapped within the ice.
The creeping motion of liquid drops through a circular tube of comparable diameter
Authors: Ho B. P. , Leal L. G.
Published: March 2006

The creeping motion through a circular tube of neutrally buoyant Newtonian drops which have an undeformed radius comparable to that of the tube was studied experimentally. Both a Newtonian and a viscoelastic suspending fluid were used in order to determine the influence of viscoelasticity. The extra pressure drop owing to the presence of the suspended drops, the shape and velocity of the drops, and the streamlines of the flow are reported for various viscosity ratios, total flow rates and drop sizes.
The onset of transient convective instability
Authors: Nield D. A.
Published: March 2006

The stability of a horizontal fluid layer when the thermal (or concentration) gradient is not uniform is examined by means of linear stability analysis. Both buoyancy and surface-tension effects are considered, and the analogous problem for a porous medium is also treated. Attention is focused on the situation where the critical Rayleigh number (or Marangoni number) is less than that for a linear thermal gradient, and the convection is not (in general) maintained. The case of constant-flux boundary conditions is examined because then a simple application of the Galerkin method gives useful results and general basic temperature profiles are readily treated. Numerical results are obtained for special cases, and some general conclusions about the destabilizing effects, with respect to disturbances of infinitely long wavelength, of various basic temperature profiles are presented. If the basic temperature gradient (considered positive, for a fluid which expands on heating, if the temperature decreases upwards) is nowhere negative, then the profile which leads to the smallest critical Rayleigh (or Marangoni) number is one in which the temperature changes stepwise (at the level at which the velocity, if motion were to occur, would be vertical) but is otherwise uniform. If, as well as being non-negative, the temperature gradient is a monotonic function of the depth, then the most unstable temperature profile is one for which the temperature gradient is a step function of the depth.
A note on the description of an attached supersonic boundary layer near a point of injection cut-off
Authors: Amr A. , Kassoy D. R.
Published: March 2006

Supersonic boundary-layer flow on a flat plate near a point of injection cut-off is considered. The goal is to develop a non-singular solution in the limit of large Reynolds number in the vicinity of the boundary-condition change. An application of Goldstein-type singular solutions shows that an interaction-type theory is required even for transverse velocity jumps on the boundary O(R− ½). The interaction analysis is developed in terms of the linearized triple-deck theory described by Smith & Stewartson (1973a). The analytically derived solution provides a continuous pressure and wall-shear distribution.
Similarity behaviour of momentumless turbulent wakes
Authors: Finson Michael L.
Published: March 2006

Similarity solutions are determined for the turbulent wake of a self-propelled body (thrust = drag). The momentumless wake is shown to behave in a manner intermediate to homogeneous grid turbulence and more familiar free-shear flows such as the drag wake or jet. In essence the decay of momentumless-wake turbulence is similar to that of grid turbulence, but proceeds at a somewhat greater rate owing to lateral diffusion. The mean velocity difference is coupled to the difference$\overline{u^2}-\overline{v^2}$between the axial and radial components of the mean-square fluctuating velocity. It is necessary to consider governing relations for various second-order turbulence quantities. Previously developed closure approximations yield far-wake decay rates that agree well with available measurements. Production of turbulent energy is negligible asymptotically; thus there is no balance between production and dissipation, and the far-wake behaviour does not become independent of the initial (near-wake) conditions. Even the radial profiles depend on the initial conditions, and there is no natural length scale with which to characterize the far wake.
Forced plumes and mixing of liquids in tanks
Authors: Germeles A. E.
Published: March 2006

We consider the mixing between two miscible liquids of slightly different density (< 10%) when one of them (cargo) is injected into a tank partially filled with the other (inventory). The injection of the cargo is such that buoyancy and inertia act in concert on the plume produced by the cargo. The two basic processes that govern the mixing of the two liquids in the tank are the entrainment of tank liquid by the plume and the tank circulation set up by this entrainment and by the plume discharge. Unlike plumes in an environment of infinite extent, the plume in this case changes its environment continuously, which, in turn, has a continuously-varying effect on the plume. A mathematical model for the mixing of the two liquids is presented, from which one can compute the tank stratification that may result when given amounts of cargo and inventory are thus mixed. Plume entrainment theory is used for the plume dynamics and a ‘filling-box’ model is used for the tank circulation. The partial differential equations of the model are integrated by an original and unique numerical method. The problem was also treated experimentally. The tank stratification is expressed in terms of a normalized density-difference variable δ. Except for some very localized large discrepancies, due to certain local effects not included in the model, computed and experimental profiles of δ agree very well, their maximum and average deviations being within 4 and 2%, respectively. It is found that values of the empirical plume parameters α and λ that are used commonly for steady plumes in environments of infinite extent are approximately right for the time-dependent plumes under consideration too.
Secondary convection in a Hele Shaw cell
Authors: Green Lloyd L. , Foster Theodore D.
Published: March 2006

A convective instability is produced by salt water diffusing onto the surface of a fresh-water layer in a Hele Shaw cell. Although the horizontal wavelength of the initial instability is small, an increase in the horizontal wavelength of the convective flow with time and depth is observed as the resulting two-dimensional convection develops. The phenomenon of wavelength variation is confirmed numerically, but quantitative observational and theoretical comparison is limited to small Rayleigh numbers. It is shown that perturbations in the density field cause horizontal pressure gradients, which in turn cause convective elements to combine.
Measurements in a two-dimensional thermal plume along a vertical adiabatic wall
Authors: Grella J. J. , Faeth G. M.
Published: March 2006

Mean velocities and temperatures were measured in a turbulent plume above a line heat source at the base of a vertical adiabatic wall. Various values of the buoyancy flux and distances above the source in the weakly buoyant regime of the flow were considered. Correlating expressions for the data were determined by assuming streamwise similarity of mean flow quantities, and a fixed entrainment constant and local skin-friction coefficient. The results yielded an entrainment constant based on the average velocity of 0·095±0·005. This value of the entrainment constant is in fair agreement with earlier work on wall plumes, but is less than half the value reported for free line plumes. Local flow properties are only weakly dependent upon the value of the skin-friction coefficient, with variations of 0-0·01 causing only a 3% change in the mean velocity and weight density defect. The results suggest that the presence of a wall, as opposed to a plane of symmetry, has a strong influence on entrainment, although the specific drag characteristics of the wall are of less importance. The reduced entrainment causes higher velocities and higher values of the weight density defect in a wall plume than in a comparable free plume.
Three-dimensional laminar compressible boundary layers with large injection
Authors: Vimala C. S. , Nath G.
Published: March 2006

The effect of large mass injection on the following three-dimensional laminar compressible boundary-layer flows is investigated by employing the method of matched asymptotic expansions: (i) swirling flow in a laminar compressible boundary layer over an axisymmetric surface with variable cross-section and (ii) laminar compressible boundary-layer flow over a yawed infinite wing in a hypersonic flow. The resulting equations are solved numerically by combining the finite-difference technique with quasi-linearization. An increase in the swirl parameter, the yaw angle or the wall temperature is found to be capable of bringing the viscous layer nearer the surface and reducing the effects of massive blowing.
Linearized buoyant motion in a closed container
Authors: Jischke M. C. , Doty R. T.
Published: March 2006

An arbitrarily-shaped, closed container completely filled with fluid is considered. It is assumed that the fluid is originally in a stably-stratified state of rest, and that at an initial instant the temperature of the container walls is impulsively changed. The ensuing unsteady laminar motion is found by solving the linearized Boussinesq equations governing buoyancy-driven flows. A ‘boundarylayer/inviscid-interior’ decomposition leads to a modified asymptotic expansion scheme of analysis. The boundary-layer concept is valid only for large values of the Rayleigh number, and, in addition, we limit the Prandtl number to order unity. It is found that the inviscid interior region heats up by means of a convection process that is driven by suction induced by the boundary layer. The inviscid, adiabatic interior responds to a special horizontal ‘average’ value of the container temperature perturbation. The boundary layer smears out, or averages, any circumferential variation in this perturbation, so that the interior, in effect, responds to an isothermal boundary in each horizontal plane. The interior temperature and vertical velocity component are expressed simply in terms of this horizontal ‘average’ container temperature. The horizontal velocity potential is governed by a Poisson equation, whose solution is developed for several specific geometries to illustrate the nature of the flow.
A model for the axial decay of a shock wave in a large abrupt area change
Authors: Sloan S. A. , Nettleton M. A.
Published: March 2006

A shock-dynamic model based on the symmetrical expansion of the critical shock is used to analyse the progressive decay of an originally planar shock wave through a large and abrupt area change. This is tested against measurements of shock strength made along the axes of area changes where the shock waves are free to expand in two or three dimensions.

The critical shock is defined as the configuration when the decaying shock wave at the axis first becomes curved. The axial shock begins to decay less than one diameter from the entrance of the area change. Differences between the experimental onset of decay and the theoretical position of the critical shock are accounted for by the non-ideal behaviour of a practical pressure transducer.

The model predicts that, when the shock wave is decaying symmetrically, there is a linear relationship between a derived function ε of the decaying shock strength and the distance from the area change. This is confirmed experimentally for all the shocks studied. The quantitative application of the results in three dimensions up to 400 mm enables accurate predictions of experimental results at 1 m for M < 2·0. Also, the model may be applied to three-dimensional results to predict accurately equivalent results in two dimensions.

The numerical values of ε are based on the equivalence of the ratio of the shock areas and the ratio of their Chisnell (1957) functions. Hence correlations between experimental results and predictions of the model are evidence that Chisnell's theory can be extended to include large and abrupt area changes.
Cross-wire anemometry in high intensity turbulence
Authors: Tutu Narinder K. , Chevray Rene
Published: March 2006

An analysis of the response of an X-probe which takes into account the axial sensitivity k, the effect of the w component of velocity and the effective rectification by the hot wire is presented. Owing to rectification points in the measured u, v ‘phase plane’ are confined within a certain sector, thus leading to distortions in the measured joint probability density functions. Numerical computations show that high turbulence intensities lead to large errors in second-order moments measured by cross-wire probes; for instance, the error in the measured correlation (over and above that due to k) can be as high as 28% when the turbulence intensity is 35%.
On the structure of pressure fluctuations in turbulent shear flow
Authors: Mulhearn P. J.
Published: March 2006

Pressure and pressure-velocity space correlations are calculated, using rapid-distortion theory, for turbulence in a uniform shear flow. It is found that pressure fluctuations remain correlated over significantly greater distances than do velocity fluctuations. When these predictions are used as a model for turbulence in free turbulent shear flows, it is found that the predicted scale of the pressure fluctuations is larger than the flow width. It is proposed that pressure fluctuations remain highly correlated right across free shear flows. Predictions from the theory are then compared with various experimental situations in which reasonable qualitative agreement is to be expected, and this is found.
A linear theory of rotating, thermally stratified, hydromagnetic flow
Authors: Loper David E.
Published: March 2006

The hydromagnetic flow of a thermally stratified fluid confined between two rotating parallel plates is studied. The flow is assumed to be linear, steady and axially symmetric. The flow is driven both mechanically and thermally and general thermal boundary conditions are applied. Attention is focused upon the mechanism controlling the interior fluid (diffusion, Ekman pumping or hydro-magnetic forces) and upon the conditions under which laminated flow (∂v/∂z ≠ 0) may occur. It is found that the occurrence of laminated flow is very sensitive to the thermal boundary conditions and is suppressed by hydromagnetic effects. For mixed boundary conditions, hydromagnetic forces control the interior and laminated flow is suppressed if α [ges ] O(1), where α2 represents the ratio of hydro-magnetic to Coriolis forces. For a constant heat flux, this occurs for a much weaker magnetic field: if α [ges ] O(E¼). For a restricted range of the parameters, a new boundary layer, called the thermomagnetic layer, in which Coriolis, thermal and hydromagnetic forces balance may occur.