bluuebunny/crossref_metadata_2025 huggingface dataset:
Surface-wave generation revisited
Authors: Miles John
Published: April 2006

The quasi-laminar model for the transfer of energy to a surface wave from a turbulent shear flow (Miles 1957) is modified to incorporate the wave-induced perturbations of the Reynolds stresses, which are related to the wave-induced velocity field through the Boussinesq closure hypothesis and the ancillary hypothesis that the eddy viscosity is conserved along streamlines. It is assumed that the basic mean velocity is U(z) = (U*/κ)log(z/z0) for sufficiently large z (elevation above the level interface) and that U(z1) [Gt ] U* for kz1 = O(1), where k is the wavenumber. The resulting vorticity-transport equation is reduced, through the neglect of diffusion, to a modification of Rayleigh's equation for wave motion in an inviscid shear flow. The energy transfer to the surface wave, which comprises independent contributions from the critical layer (where U = c, the wave speed) and the wave-induced Reynolds stresses, is calculated through a variational approximation and, independently, through matched asymptotic expansions. The critical-layer component is equivalent to that for the quasi-laminar model. The Reynolds-stress component is similar to, but differs quantitatively from, that obtained by Knight (1977, Jacobs (1987) and van Duin & Janssen (1992). The predicted energy transfer agrees with the observational data compiled by Plant (1982) for 1 [lsim ] c/U* [lsim ] 20, but the validity of the logarithmic profile for the calculation of the energy transfer in the critical layer for c/U* < 5 remains uncertain. The basic model is unreliable (for water waves) if c/U* [lsim ] 1, but this domain is of limited oceanographic importance. It is suggested that Kelvin–Helmholtz instability of air blowing over oil should provide a good experimental test of the present Reynolds-stress modelling and that this modelling may be relevant in other geophysical contexts.
Unsteady flow at a stagnation point
Authors: Riley N.
Published: April 2006

The flow at an axisymmetric stagnation point is considered when the outer, inviscid flow is oscillatory with zero mean. It is shown that following the commencement of the flow at an initial instant there is a breakdown of the solution, after a finite time, as fluid erupts from the boundary at the stagnation point. This is interpreted as the origin of the jet-like flow observed in the experiments of Amin & Riley (1990). It is demonstrated that an in-plane, torsional motion of the boundary, either steady or oscillatory, can suppress the singular behaviour.
Azimuthal instability of divergent flows
Authors: Shtern Vladimir , Hussain Fazle
Published: April 2006

We investigate a new mechanism for instability (named divergent instability), characterized by the formation of azimuthal cells, and find it to be a generic feature of three-dimensional steady axisymmetric flows of viscous incompressible fluid with radially diverging streamlines near a planar or conical surface. Four such flows are considered here: (i) Squire–Wang flow in a half-space driven by surface stresses; (ii) recirculation of fluid inside a conical meniscus; (iii) two-cell regime of free convection above a rigid cone; and (iv) Marangoni convection in a half-space induced by a point source of heat (or surfactant) placed at the liquid surface. For all these cases, bifurcation of the secondary steady solutions occurs: for each azimuthal wavenumber m = 2, 3,…, a critical Reynolds number (Re*) exists. The intent to compare with experiments led us to investigate case (iv) in more detail. The results show a non-trivial influence of the Prandtl number (Pr): instability does not occur in the range 0.05 < Pr < 1; however, outside this range, Re*(m) exists and has bounded limits as Pr tends to either zero or infinity. A nonlinear analysis shows that the primary bifurcations are supercritical and produce new stable regimes. We find that the neutral curves intersect and subcritical secondary bifurcation takes place; these suggest the presence of complex unsteady dynamics in some ranges of Re and Pr. These features agree with the experimental data of Pshenichnikov & Yatsenko (Pr = 103).
The force on a sphere in a uniform flow with small-amplitude oscillations at finite Reynolds number
Authors: Lovalenti Phillip M. , Brady John F.
Published: April 2006

The unsteady force acting on a sphere that is held fixed in a steady uniform flow with small-amplitude oscillations is evaluated to O(Re) for small Reynolds number Re. Good agreement is shown with the numerical results of Mei, Lawrence & Adrian (1991) up to Re ≈ 0.5. The analytical result is transformed by Fourier inversion to allow for an arbitrary time-dependent motion which is small relative to the steady uniform flow. This yields a history-dependent force which has an integration kernel that decays exponentially for large time.
The formation of toroidal bubbles upon the collapse of transient cavities
Authors: Best J. P.
Published: April 2006

A spectacular feature of transient cavity collapse in the neighbourhood of a rigid boundary is the formation of a high-speed liquid jet that threads the bubble and ultimately impacts upon the side of the bubble nearest to the boundary. The bubble then evolves into some toroidal form, the flow domain being doubly connected. In this work, the motion of the toroidal bubble is computed by connecting the jet tip to the side of the bubble upon which it impacts. This connection is via a cut introduced into the flow domain and across which the potential is discontinuous, the value of this discontinuity being equal to the circulation in the flow. A boundary integral algorithm is developed to account for this geometry and some example computations are presented. Consideration of the pressure field in the fluid has implications for possible damage mechanisms to structures due to nearby cavity collapse.
The near-wake of an oscillating trailing edge: mechanisms of periodic and aperiodic response
Authors: Lotfy A. , Rockwell D.
Published: April 2006

This investigation addresses the unsteady wake from a blunt trailing edge subjected to controlled perturbations. The relationship between the structure of the near wake, the surface loading on the edge, and the motion of the edge is characterized by flow visualization in conjunction with velocity and pressure measurements. The response of the near wake can be classified into two general categories: a modulated wake, characterized by ordered variations in the near-wake flow structure over a number of cycles of oscillation of the trailing edge; and a phase-locked wake, whereby the near-wake structure does not change from cycle to cycle of the edge oscillation. For the modulated wake, there are large, repetitive excursions of the near-wake vortex pattern in the stream wise direction due to coexistence of the self-excited global instability of the wake and the applied excitation. These excursions can have an amplitude two orders of magnitude larger than the amplitude of the edge motion. The duration of these excursions, in relation to the cyclic motion of the trailing edge, is deterministic. For the phase-locked wake, small changes of the edge oscillation frequency produce large changes in the phase shift of the initially formed vortex from the edge. These phase shifts are due to changes in the times required for vortex formation and departure from the near wake. The corresponding mechanisms are interpreted in terms of the crucial topological features of the near wake and a phase clock concept.
Double reflection of capillary/gravity waves by a non-uniform current: a boundary-layer theory
Authors: Trulsen Karsten , Mei Chiang C.
Published: April 2006

When a train of gravity waves encounters an opposing current, the wavelength is shortened and the waves may be reflected. If capillarity is included, the shortened waves may be reflected for a second time and experience further shortening. By this process the initially long gravity waves can be damped by viscosity quickly without breaking. In this paper a boundary-layer approximation is obtained close to the reflection points, and is matched to the ray approximations outside. This is then applied to the propagation of a wavepacket. Damping is accounted for in the ray solution and the result is compared to the undamped solution. The case where the two reflection points coalesce is also considered. It is found that as the separation between the reflection points decreases, the wavepacket appears to remain longer in the region of reflections relative to the width of this region.
Formation of solitons in transitional boundary layers: theory and experiment
Authors: Kachanov Y. S. , Ryzhov O. S. , Smith F. T.
Published: April 2006

This work brings together experimental and theoretical studies of nonlinear stages aimed at the K-regime in boundary-layer transition, and some combined theoretical and experimental results are discussed. It is shown that the initial stages in the formation of so-called spikes, observed in many experiments, may be described very well by the asymptotic theory. These flashes-spikes are shown to be (in certain regimes) possible solitons of the boundary layer and governed by the integral-differential Benjamin-Ono equation. Properties of the spike-solitons, obtained both theoretically and experimentally in the quasi-planar stages of their development, are presented. Features of the disturbance behaviour connected with the subsequent development of three-dimensionality are also discussed, as are the effects of viscosity and shorter lengthscales. The main conclusion of the work concerns the hypothesis of the possible soliton nature of the flashes-spikes (within limits), which seems reliably corroborated by the good agreement found between the theory and the experimental data.
Axially invariant laminar flow in helical pipes with a finite pitch
Authors: Liu Shijie , Masliyah Jacob H.
Published: April 2006

Steady axially invariant (fully developed) incompressible laminar flow of a Newtonian fluid in helical pipes of constant circular cross-section with arbitrary pitch and arbitrary radius of coil is studied. A loose-coiling analysis leads to two dominant parameters, namely Dean number, Dn = Reλ½, and Germano number, Gn = Reη, where Re is the Reynolds number, λ is the normalized curvature ratio and η is the normalized torsion. The Germano number is embedded in the body-centred azimuthal velocity which appears as a group in the governing equations. When studying Gn effects on the helical flow in terms of the secondary flow pattern or the secondary flow structure viewed in the generic (non-orthogonal) coordinate system of large Dn, a third dimensionless group emerges, γ = η/(λDn)½. For Dn < 20, the group γ* = Gn Dn-2 = η/(λRe) takes the place of γ.

Numerical simulations with the full Navier-Stokes equations confirmed the theoretical findings. It is revealed that the effect of torsion on the helical flow can be neglected when γ ≤ 0.01 for moderate Dn. The critical value for which the secondary flow pattern changes from two vortices to one vortex is γ* > 0.039 for Dn < 20 and γ > 0.2 for Dn ≥ 20. For flows with fixed high Dean number and A, increasing the torsion has the effect of changing the relative position of the secondary flow vortices and the eventual formation of a flow having a Poiseuille-type axial velocity with a superimposed swirling flow. In the orthogonal coordinate system, however, the secondary flow generally has two vortices with sources and sinks. In the small-γ limit or when Dn is very small, the secondary flow is of the usual two-vortex type when viewed in the orthogonal coordinate system. In the large-γ limit, the appearance of the secondary flow in the orthogonal coordinate system is also two-vortex like but its orientation is inclined towards the upper wall. The flow friction factor is correlated to account for Dn, A and γ effects for Dn ≤ 5000 and γ < 0.1.
The hydraulics of a stratified fluid flowing through a contraction
Authors: Armi Laurence , Williams Richard
Published: April 2006

The steady hydraulics of a continuously stratified fluid flowing from a stagnant reservoir through a horizontal contraction was studied experimentally and theoretically. As the channel narrows, the flow accelerates through a succession of virtual controls, at each of which the flow passes from sub-critical to supercritical with respect to a particular wave mode. When the narrowest section acts as a control, the flow is asymmetric about the narrowest section, supercritical in the divergent section and self- similar throughout the channel. With increased flow rate a new enclosed self-similar solution was found with level isopycnals and velocity uniform with depth. This flow is only symmetric in the immediate neighbourhood of the narrowest section, and in the divergent section remains supercritical with respect to higher internal modes, has separation isopycnals and splits into one or more jets separated by regions of stagnant, constant-density fluid. Flows which are subcritical with respect to lowest modes can also be asymmetric about the narrowest section for higher internal modes. The experiments are interpreted using steady, inviscid hydraulic theory. Solutions require separation isopycnals and regions of stationary, constant-density fluid in the divergent section.
An experimental study of laminar plumes
Authors: Moses Elisha , Zocchi Giovanni , Libchaberii Albert
Published: April 2006

We present an experimental study of the scaling laws for the front (or cap) of an isolated, laminar starting plume. The scaling relations are formulated and measured experimentally over a range of power, fluids, and heaters. The results are that the cap rises at constant velocity, grows diffusively in width, and its temperature depends inversely on height. This extends analytic results by Batchelor (1954) for the column (stem) below the front. The source size determines initial conditions for the cap, but does not affect it in the far field. The shape of the front is fitted by a model of potential flow. The interaction between plume caps is complex, but with simple underlying dynamics. We conjecture that some of our conclusions can be applied to a distribution of plumes, as in soft turbulent convection.
Thin liquid layers supported by steady air-flow surface traction
Authors: King A. C. , Tuck E. O.
Published: April 2006

Upward flow of air can support a thin layer of liquid on a plane wall against gravity. Such apparently stationary layers are for example sometimes seen on the windscreen of a car travelling at high speed in rain. We solve here the two-dimensional case of a layer whose length is finite, but significantly greater than the meniscus length. The flow is steady, with a fixed layer boundary, inside which there is a steadily circulating viscous liquid, and outside which the air exerts a traction which is assumed to have a known (small) constant drag coefficientCD. The air also exerts a non-uniform pressure on the liquid layer, of a magnitude determined by the shape of the layer, and the relationship between these two quantities can be obtained by thin-airfoil theory. In the lubrication approximation, the problem can be reduced to a nonlinear singular integro-differential equation to determine the unknown shape of the layer boundary. This equation is solved numerically for various (small) wall angles, for cases where the effect of surface tension is confined to a small meniscus region near the layer's leading edge. The numerical results indicate that solutions exist only for walls whose inclination is less than 0.70 C½D, and, for a range of inclinations below that maximum value, that two distinct steady solutions can exist at each inclination.
Singularity formation during Rayleigh–Taylor instability
Authors: Baker Gregory , Caflisch Russel E. , Siegel Michael
Published: April 2006

During the motion of a fluid interface undergoing Rayleigh-Taylor instability, vorticity is generated on the interface baronclinically. This vorticity is then subject to Kelvin-Helmholtz instability. For the related problem of evolution of a nearly flat vortex sheet without density stratification (and with viscosity and surface tension neglected), Kelvin-Helmholtz instability has been shown to lead to development of curvature singularities in the sheet. In this paper, a simple approximate theory is developed for Rayleigh-Taylor instability as a generalization of Moore's approximation for vortex sheets. For the approximate theory, a family of exact solutions is found for which singularities develop on the fluid interface. The resulting predictions for the time and type of the singularity are directly verified by numerical computation of the full equations. These computations are performed using a point vortex method, and singularities for the numerical solution are detected using a form fit for the Fourier components at high wavenumber. Excellent agreement between the theoretical predictions and the numerical results is demonstrated for small to medium values of the Atwood number A, i.e. for A between 0 and approximately 0.9. For A near 1, however, the singularities actually slow down when close to the real axis. In particular, for A = 1, the numerical evidence suggests that the singularities do not reach the real axis in finite time.
Nonlinear analysis of buoyant convection in binary solidification with application to channel formation
Authors: Amberg Gustav , Homsy G. M.
Published: April 2006

We consider the problem of nonlinear thermal-solutal convection in the mushy zone accompanying unstable directional solidification of binary systems. Attention is focused on possible nonlinear mechanisms of chimney formation leading to the occurrence of freckles in solid castings, and in particular the coupling between the convection and the resulting porosity of the mush. We make analytical progress by considering the case of small growth Péclet number, δ, small departures from the eutectic point, and infinite Lewis number. Our linear stability results indicate a small O(δ) shift in the critical Darcy-Rayleigh number, in accord with previous analyses. We find that nonlinear two-dimensional rolls may be either sub- or supercritical, depending upon a single parameter combining the magnitude of the dependence of mush permeability on solids fraction and the variations in solids fraction owing to melting or freezing. A critical value of this combined parameter is given for the transition from supercritical to subcritical rolls. Three-dimensional hexagons are found to be transcritical, with branches corresponding to upflow and lower porosity in either the centres or boundaries of the cells. These general results are discussed in relation to experimental observations and are found to be in general qualitative agreement with them.
A field experiment on the mechanics of irregular gravity waves
Authors: Boccotti P. , Barbaro G. , Mannino L.
Published: April 2006

In random wind-generated wave motion on the sea surface, extreme wave events have been shown theoretically to occur within groups with a well-defined configuration and time history that can be specified in terms of the space-time autocovariances of the surface displacement. The predictions of the theory have been tested in a field experiment in the Straits of Messina in which an array of nine wave gauges and nine pressure transducers supported by vertical piles provided space-time information on waves generated over a fetch of approximately 10 km. It was confirmed that the general configuration of the extreme wave groups measured was consistent with the theoretical predictions in terms of the measured space-time autocovariance. During the development stage of a group, as the height of the central (outstanding) wave grows to a maximum, the width of the wave front reduces to a minimum. As an individual wave passes through the group, its wavelength decreases as the wave height increases towards the apex, after which the wavelength increases again as the wave moves towards the front of the group and abates.
A vertical buoyant jet with high momentum in a long ventilated tunnel
Authors: Barnett S. J.
Published: April 2006

In this paper the flow resulting from the release of buoyant material within a long tunnel is investigated. The source fluid is discharged through a nozzle of small radius with sufficiently high flow rate to ensure that the axial lengthscale of the buoyant jet (subsequently called the ‘jet-length’) is several times the depth of the tunnel, d. The ends of the tunnel may be either open or closed and a number of ventilation points may exist along it. Consideration of a source with high momentum is an important development in confined jet flow models, as most previous models have assumed that the source has little or no initial momentum. It is found that circulation cells are driven near to the source and that the concentration within them increases to a steady-state maximum. At a distance of about 2.5d from the source the buoyancy forces are then sufficiently strong to drive a two-layered stratified counterflow. The steady-state conservation equations are analysed in order to calculate the mean flow variables. The flow past a ventilation point and the characteristics of the secondary outflow are derived, enabling the calculation of the total number of vents needed to vent the buoyant layer. The time dependence of the mean concentration in the circulation cell near to the source is also deduced. This could be used to calculate time-dependent solutions for the other mean flow variables. All of the theoretical results are compared with experimental measurements.
Streamwise vortices in heated boundary layers
Authors: Hall Philip
Published: April 2006

The nonlinear instability of the boundary layer on a heated flat plate placed in an oncoming flow is investigated. Such flows are unstable to stationary vortex instabilities and inviscid travelling wave disturbances governed by the Taylor-Goldstein equation. For small temperature differences the Taylor-Goldstein equation reduces to Rayleigh's equation. When the temperature difference between the wall and free stream is small the preferred mode of instability is a streamwise vortex. It is shown in this case that the vortex, assumed to be of small wavelength, restructures the underlying mean flow to produce a profile which can be massively unstable to inviscid travelling waves. The mean state is shown to be destabilized if the Prandtl number is less than unity.
Similarities in the structure of swirling and buoyancy-driven flows
Authors: Davidson P. A.
Published: April 2006

We look at two classes of contained flow: swirling flow and buoyancy-driven flow. We note that the strong links between these arise from the way in which vorticity is generated and propagated within each. We take advantage of this shared behaviour to investigate the structure of steady-state solutions of the governing equations. First, we look at flows with a small but finite viscosity. Here we find that, Batchelor regions apart, the steady state for each type of flow must consist of a quiescent stratified core, bounded by high-speed wall jets. (In the case of swirling flow, this is a radial stratification of angular momentum.) We then give a general, if approximate, method for finding these steady-state flow fields. This employs a momentum-integral technique for handling the boundary layers. The resulting predictions compare favourably with numerical experiments. Finally, we address the problem of inviscid steady states, where there is a well-known class of steady solutions, but where the question of the stability of these solutions remains unresolved. Starting with swirling flow, we use an energy minimization technique to show that stable solutions of arbitrary net azimuthal vorticity do indeed exist. However, the analogy with buoyancy-driven flow suggests that these solutions are all of a degenerate, stratified form. If this is so, then the energy minimization technique, which conserves vortical invariants, may mimic the stratification of temperature or angular momentum in a turbulent flow.
Effect of wind profile on the instability of wind blowing over water
Authors: Morland L. C. , Saffman P. G.
Published: April 2006

A linear stability analysis of the inviscid, parallel flow of air over water leads to an eigenvalue problem for the wave speed, which is solved numerically for air profiles typical of both laminar and turbulent flows. Comparison is made with Miles’ (1957) theory; growth rates differ from those predicted from the Miles (1957) formula but are in agreement with Conte & Miles’ (1959) computations for turbulent flow profiles. In the limit of a highly sheared wind profile the numerical computations retrieve the Kelvin-Helmholtz instability.
Flow along a horizontal plate near a free surface
Authors: Hofman Milan
Published: April 2006

The problem of flow along a horizontal semi-infinite flat plate moving in its own plane through a viscous liquid just below the free surface is considered. The method of matched asymptotic expansions is used to analyse the interaction between the free surface and the boundary layer formed on the plate. It is found that, due to viscosity, small-amplitude gravity waves on the free surface can be formed. The formulae for the resistance of the plate containing the free-surface effect and for the lift, appearing as a new phenomenon, are derived.
Instability of stratified fluid in a vertical cylinder
Authors: Batchelor G. K. , Nitsche J. M.
Published: April 2006

In a previous paper we analysed the stability to small disturbances of stationary stratified fluid which is unbounded. Various forms of the undisturbed density distribution were considered, including a sinusoidal profile and a function of the vertical coordinate z which is constant outside a central horizontal layer. Both these types of stratification are so unstable that the critical Rayleigh number is zero. In this sequel we make the study more complete and more useful by taking account of the effect of a vertical circular cylindrical boundary of radius a which is rigid and impermeable. As in the previous paper we assume that the undisturbed density distribution is steady.

The case of fluid in a vertical tube with a uniform density gradient is useful for comparison, and so we review and extend the available results, in particular obtaining growth rates for a disturbance which is neither z-independent nor axisymmetric. A numerical finite-difference method is then developed for the case in which dρ/dz = ρ0kA cos kz. When ka [Lt ] 1 the relation between growth rate and Rayleigh number approximates to that for a uniform density gradient of magnitude ρ0kA; and when ka [Gt ] 1 the tilting-sliding mechanism identified in the previous paper is relevant and the results approximate to those for an unbounded fluid, except that the smallest Rayleigh number for a neutral disturbance is not zero but is of order (ka-1. In the case of an undisturbed density which varies only in a central layer of thickness l, the same mechanism is at work when the horizontal lengthscale of the disturbance is large compared with l, resulting in high growth rates and a critical Rayleigh number which vanishes with l/a. Estimates of the growth rate are given for some particular density profiles.
A study of argon thermal plasma flow over a solid sphere
Authors: Paik Seungho , Nguyen Hoa D. , Chung Jacob N.
Published: April 2006

The phenomena of momentum and heat transfer associated with an impulsively started spherical particle in a quiescent argon thermal plasma environment is considered. The changing plasma thermodynamics and transport property effects are studied using a Chebyshev-Legendre spectral method. Steady-state solutions for the case of constant sphere surface temperature are obtained and compared with previously published results. Transient solutions with particle internal heat conduction included are also presented. Results indicate that the magnitude of the drag force increases as the plasma free-stream temperature increases, while the Nusselt number decreases with increasing free-stream temperature. Effects due to different initial particle temperatures on the transient Nusselt number and drag coefficient are demonstrated.
Overturning of nonlinear acoustic waves. Part 2 Relaxing gas dynamics
Authors: Hammerton P. W. , Crighton D. G.
Published: April 2006

We consider finite-amplitude acoustic disturbances propagating through media in which relaxation mechanisms, such as those associated with the vibration of polyatomic molecules, are significant. While the effect of these relaxation modes is to inhibit the wave steepening associated with nonlinearity, whether a particular mode is sufficient to prevent the occurrence of multi-valued solutions will depend on the form of the disturbance and on the characteristic parameters of the relaxation. Analysis of this condition is necessary in order to reveal which physical mechanisms actually determine the evolution of the wave profile. This then dictates the scaling of any embedded shock regions. Sufficient conditions for the occurrence of multi-valued solutions are obtained analytically for periodic waves, hence proving that in certain circumstances relaxation is in fact insufficient in fully describing the wave propagation. A much more precise criterion is then obtained numerically. This uses the techniques described in Part 1 for analysing the phenomenon of wave overturning using intrinsic coordinates. Illustrations are provided of the development of a harmonic signal for different classes of material parameters.
Hydrodynamic characteristics of bodies in channels
Authors: Linton C. M. , Evans D. V.
Published: April 2006

The effect of channel walls on the hydrodynamic characteristics of fixed or oscillating bodies is discussed using classical linear water wave theory. Particular attention is paid to the occurrence of trapped modes persisting local to the fixed body and which are manifested in a non-uniqueness of the corresponding forced problem at the trapped mode frequency. The general ideas are illustrated by consideration of two simple geometries for which semi-analytic solutions are available, namely a circular cylinder either partly immersed or extending throughout the water depth, and a thin vertical plate parallel to the channel walls which extends throughout the water depth. Conclusions are drawn concerning the conditions under which trapped modes may exist and their effect on the hydrodynamic characteristics of more general bodies.
Capillary–gravity waves of solitary type and envelope solitons on deep water
Authors: Longuet-Higgins Michael S.
Published: April 2006

The existence of steady solitary waves on deep water was suggested on physical grounds by Longuet-Higgins (1988) and later confirmed by numerical computation (Longuet-Higgins 1989; Vanden-Broeck & Dias 1992). Their numerical methods are accurate only for waves of finite amplitude. In this paper we show that solitary capillary-gravity waves of small amplitude are in fact a special case of envelope solitons, namely those having a carrier wave of length 2π(T/ρg)1½2 (g = gravity, T = surface tension, ρ = density). The dispersion relation $c^2 = 2(1-\frac{11}{32}\alpha^2_{\max)$ between the speed c and the maximum surface slope αmax is derived from the nonlinear Schrödinger equation for deep-water solitons (Djordjevik & Redekopp 1977) and is found to provide a good asymptote for the numerical calculations.
The structure of a supersonic turbulent boundary layer subjected to concave surface curvature
Authors: Donovan John F. , Spina Eric F. , Smits Alexander J.
Published: April 2006

This paper reports an experimental investigation of the instantaneous structure of a supersonic turbulent boundary layer (M= 2.86,Reθ= 82000) over a short region of longitudinal concave surface curvature. The radius of curvature was 12 initial boundary-layer thicknesses and the turning angle was 16°. Severe distortion of the boundary layer occurred, as evidenced by an alteration of the mean velocity profiles and an increase in wall shear stress of 125%. The large-scale organized motions in the boundary layer were significantly altered as illustrated by changes in the character of the mass flux ‘fronts’ (large gradients in the fluctuating streamwise mass flux).
Measurements of vortex pair interaction with a clean or contaminated free surface
Authors: Hirsa A. , Willmarth W. W.
Published: April 2006

Laminar vortex pairs with small Froude number were generated by a submerged delta wing at negative angle of attack or by a pair of vertically oriented, counter-rotating flaps. The vortex pairs thus generated rise and interact with the free surface. The surface and subsurface flow field was studied using flow visualization and particle image velocimetry. Initial surface deformations, striations, are shown to be caused by stretching and interaction of cross-stream vortices near the surface. With small amounts of surface contamination, contamination fronts (producing Reynolds ridges) form on the surface and secondary vorticity, generated beneath the surface beyond the fronts, rolls up to form vortices with opposite rotation outboard of the primary vortices. The circulation associated with the secondary vortices is as much as 1/3 that of the primary vortices. The secondary vortices cause the primary vortex pair to rebound from the surface. Slight surface deformations, scars, are caused by the primary and secondary vortices.
Compressibility effects on the structure of supersonic mixing layers: experimental results
Authors: Barre S. , Quine C. , Dussauge J. P.
Published: April 2006

An experiment in a supersonic mixing layer at convective Mach number Mc = 0.62 was performed to study the evolution of a flow from a turbulent boundary layer to a fully developed mixing layer. Turbulence measurements were taken and are interpreted with a diffusion model, which is well adapted to these flows. These measurements show that the level of turbulent friction varies with Mc proportionally to the spread rate. Our measurements appear to be consistent with the spreading rate of the layer and suggest that compressibility does not significantly alter the diffusion scheme at Mc = 0.62. This is also confirmed by a review of the existing data. Moreover, in the present flow, the anisotropy of the turbulent stresses seems to be affected by compressibility. The evolution of the radiated noise shows an increase corresponding to the developed part of the layer. Quantitative assessments of compressibility effects on turbulent quantities are given and are related to modifications in the structure of the flow.
Experimental study of dipolar vortices on a topographic βT-plane
Authors: Fuentes O. U. Velasco , Heijst G. J. F. Van
Published: April 2006

The behaviour of dipolar vortices in a rotating fluid with a sloping bottom (simulating the variation of the Coriolis parameter on the Earth, with the direction of steepest bottom slope corresponding with the northern direction) has been investigated in the laboratory. Dipoles were generated by moving a vertical cylinder through the fluid. Dye photographs provided qualitative information, whereas quantitative information about the evolving flow field was obtained by streak photography. Dipoles initially directed under a certain angle relative to the west–east axis showed meandering or cycloid-like trajectories. Soeme symmetries between east-travelling dipoles (ETD's) and west-travelling dipoles (WTD's) were observed. ETD's are stable in the trajectory sense: a small deviation from zonal motion results in small oscillations around the equilibrium latitude. WTD's are unstable: small initial deviations produce large displacements in northern or southern directions. This asymmetry arises because the vorticity of a dipole moving westward is anticorrelated with the ambient vorticity, while the vorticities are correlated when the dipole moves eastward. ETD's increase in size and eventually split into two independent monopoles, the rate of growth depending on the gradient of planetary vorticity. WTD's are initially more compact but owing to the large displacements in the meridional direction strong asymmetries in the circulation of the two halves are produced, resulting in a large deformation of the weaker part. The experimental observations show good qualitative agreement with analytical and numerical results obtained using a modulated point-vortex model.
Cavity collapse in a liquid with solid particles
Authors: Bourne N. K. , Field J. E.
Published: April 2006

An experimental study of the interaction of weak shock waves in a liquid with bubbles and solid particles has been conducted. Cavities were punched, and solid particles were cast, into a thin sheet of gelatine clamped between two transparent blocks. A shock of pressure 0.3 GPa was introduced by impacting the gelatine layer with a flyer plate. The subsequent collapse of the cavities was photographed using high-speed framing cameras, and waves in the gelatine were visualized using schlieren optics. Assorted cavity/particle geometries were studied. In the first, cavity and particle were aligned on an axis parallel to the incident shock front. The jet crossing the cavity was found to deviate from the perpendicular to the shock front. This deviation was towards the solid particle when separations were small and away from the particle when separations were increased. When a cavity was placed upstream of a solid particle the collapse time was reduced. Conversely, when a cavity was placed downstream of a solid particle, collapse time was increased and the closure was more symmetrical. These observations were explained in terms of wave reflections. Collapses where the cavity/particle axis was inclined to the incident shock showed features of each of the geometries described above.
The diode-array velocimeter
Authors: Devenport William J. , Smith Edward J.
Published: April 2006

Diode-array velocimetry is an optical technique for measuring turbulent flows. It involves timing the passage of seed particles through a small section of a light beam by imaging the light they scatter onto one or more photodiode arrays. The arrays have a few carefully shaped elements, the shapes and positions of which are used to control the measurement-volume geometry and thus select the measurement made. Measurement volumes sensitive to velocity, position and acceleration may be designed. Measurements in highly turbulent and reversing flows are possible.

A diode-array velocimeter (DAV) for one-component velocity measurements has been developed to demonstrate this concept. This uses a single laser beam to illuminate particles and a photodiode array with two rectangular elements to sense their motion. The sensitivity of this DAV to electrical noise in the photodiode circuitry decreases with reduction in measurement-volume size. The angle response is closely cosinusoidal to about 60°. Changes to the photodiode-array design could substantially increase this limit.

Measurements of mean velocity, normal turbulence stress and velocity skewness made with this DAV in two attached boundary-layer flows compare well with hot-wire measurements. Useful DAV measurements were made as close as 0.2 mm from the wall. DAV measurements made in a separated flow formed downstream of a fence are also presented. These show all the expected features of the separated shear layer and recirculation including the sub-boundary layer formed beneath the backflow. Histograms measured in the reversing part of this flow show a hole near zero velocity that is a consequence of the imperfections in the DAV angle response and limitations on the maximum transit time. These are not fundamental problems, however, and the hole could be minimized or eliminated by using a different photodiode array design and/or measurement strategy.
Small-scale structure in colliding off-axis vortex rings
Authors: Smith G. B. , Wei T.
Published: April 2006

Off-axis collisions of equal-strength vortex rings were experimentally examined. Two equal-strength vortices were generated which moved toward each other along parallel, but offset, trajectories. Two colour laser-induced fluorescence visualization techniques were used to observe these phenomena and gain insight into their importance in vortex interactions. The most prominent features of this interaction were rapid growth and rotation of the rings and formation of evenly spaced ringlets around the cores of the original rings. Large-scale motions are described using simple vortex induction arguments. The small scales are caused by nonlinear amplification of instabilities during the asymmetric interaction.
Dynamic behaviour of a non-propagating soliton under a periodically modulated oscillation
Authors: CHEN XUE-NONG , Wei Rong-Jue
Published: April 2006

It has been found theoretically and experimentally that a non-propagating soliton in a small rectangular water tank manifests dynamic behaviour when subjected to a modulated oscillation. A modification of the cubic Schrödinger equation was generalized for this case and analysed by the inverse-scattering perturbation method. The problem was reduced to a lower-dimensional one, i.e. to a pair of first-order ordinary differential equations for the amplitude and phase of the soliton, which were solved numerically. It was found that the soliton executes multi-periodic and chaotic motions under the periodically modulated oscillation. Corresponding experiments were carried out and both qualitative and quantitative agreement was obtained for the phenomena predicted and the parameter ranges in which they occur.
Emergence and evolution of triangular vortices
Authors: Carnevale G. F. , Kloosterziel R. C.
Published: April 2006

Laboratory observations and numerical simulations reveal that, in addition to monopoles, dipoles and tripoles, yet another stable coherent vortex may emerge from unstable isolated circular vortices. This new vortex is the finite-amplitude result of the growth of an azimuthal wavenumber-3 perturbation. It consists of a triangular core of single-signed vorticity surrounded by three semicircular satellites of oppositely signed vorticity. The stability of this triangular vortex is analysed through a series of high-resolution numerical simulations and by an investigation of point-vortex models. This new compound vortex rotates about its centre and is stable to small perturbations. If perturbed strongly enough, it undergoes an instability in which two of the outer satellites merge, resulting in the formation of an axisymmetric tripole, which subsequently breaks down into either a pair of dipoles or a dipole plus a monopole. The growth of higher-azimuthal-wavenumber perturbations leads to the formation of more intricate compound vortices with cores in the shape of squares, pentagons, etc. However, numerical simulations show that these vortices are unstable, which agrees with results from point-vortex models.
Crest instabilities of gravity waves. Part 2. Matching and asymptotic analysis
Authors: Longuet-Higgins Michael S. , Cleaver R. P. , Fox M. J. H.
Published: April 2006

In a previous study (Longuet-Higgins & Cleaver 1994) we calculated the stability of the flow near the crest of a steep, irrotational wave, the ‘almost-highest’ wave, considered as an isolated wave crest. In the present paper we consider the modification of this inner flow when it is matched to the flow in the rest of the wave, and obtain the normal-mode perturbations of the modified inner flow. It is found that there is just one exponentially growing mode. Its rate of growth β is a decreasing function of the matching parameter ε and hence a decreasing function of the wave steepness ak. When compared numerically to the rates of growth of the lowest superharmonic instability in a deep-water wave as calculated by Tanaka (1983) it is found that the present theory provides a satisfactory asymptote to the previously calculated values of the growth rate. This suggests that the instability of the lowest superharmonic is essentially due to the flow near the crest of the wave.
On the role of the outer region in the turbulent-boundary-layer bursting process
Authors: Myose ROY Y. , Blackwelder Ron F.
Published: April 2006

The dynamics and interaction of turbulent-boundary-layer eddy structures was experimentally emulated. Counter-rotating streamwise vortices and low-speed streaks emulating turbulent-boundary-layer wall eddies were generated by a Görtler instability mechanism. Large-scale motions associated with the outer region of turbulent boundary layer were emulated with — ωzspanwise vortical eddies shed by a periodic non-sinusoidal oscillation of an airfoil. The scales of the resulting eddy structures were comparable to a moderate-Reynolds-number turbulent boundary layer. Results show that the emulated wall-eddy breakdown was triggered by streamwise acceleration associated with the outer region of turbulent boundary layer. This breakdown involved violent mixing between low-speed fluid from the wall eddy and accelerated fluid associated with the outer structure. Although wall eddies can break down autonomously, the presence of and interaction with outer-region — ωzeddies hastened their breakdown. Increasing the — ωzeddy strength resulted in further hastening of the breakdown. Conversely, + ωzeddies were found to delay wall-eddy breakdown locally, with further delays resulting from stronger + ωzeddies. This suggests that the outer region of turbulent boundary layers plays a role in the bursting process.
Improved linear representation of surface waves. Part 2. Slowly varying bottoms and currents
Authors: Wright Jon , Creamer Dennis B.
Published: April 2006

We extend the results of a previous paper to fluids of finite depth. We consider the Hamiltonian theory of waves on the free surface of an incompressible fluid, and derive the canonical transformation that eliminates the leading order of nonlinearity for finite depth. As in the previous paper we propose using the Lie transformation method since it seems to include a nearly correct implementation of short waves interacting with long waves. We show how to use the Eikonal method for slowly varying currents and/or depths in combination with the nonlinear transformation. We note that nonlinear effects are more important in water of finite depth. We note that a nonlinear action conservation law can be derived.