bluuebunny/crossref_metadata_2025 huggingface dataset:
Origin of the peak-valley wave structure leading to wall turbulence
Authors: Asai Masahito , Nishioka Michio
Published: April 2006

A generation process for the three-dimensional wave which dominates the transition preceded by a Tollmien-Schlichting (T-S) wave is studied both experimentally and numerically in plane Poiseuille flow at a subcritical Reynolds number of 5000. In order to identify the origin of the three-dimensional wave in Nishioka et al.'s laboratory experiment, the corresponding spanwise mean-flow distortion and two-dimensional T-S wave modes are introduced into a parabolic flow as the initial disturbance conditions for a numerical simulation of temporally growing type. Through reproducing the actual wave development into the peak-valley structure, the simulation pinpoints the origin to be the slight spanwise mean-flow distortion in the experimental basic flow. Furthermore, the simulation clearly shows that the growth of the three-dimensional wave requires the vortex stretching effect due to the streamwise vortices, which appear under the experimental conditions only when the amplitude of the two-dimensional T-S wave is above the observed threshold.
Numerical simulations of transition in oscillatory plane channel flow
Authors: Singer Bart A. , Ferziger Joel H. , Reed Helen L.
Published: April 2006

The effect of flow oscillation on the stability of plane channel flow is studied via numerical simulation. For weak oscillation, the ratio of the Stokes layer thickness to the distance from the wall to the critical layer in steady flow provides the best normalization for the mean-flow frequency. Maximum growth rates occur when the instantaneous velocity profile has large regions of positive curvature. The effect of oscillation is generally stabilizing. However, at low frequencies, TS wave energies may vary by 106 in a cycle and irreversible secondary instability may be produced at the peak.
Linear instability of the wake behind a flat plate placed parallel to a uniform stream
Authors: Papageorgiou D. T. , Smith F. T.
Published: April 2006

The growth of linear disturbances in the high-Reynolds-number laminar wake of a flat plate aligned with a uniform stream is investigated. The theory is developed rationally by use of appropriate wake profiles which originate at the trailing edge as double Blasius distributions and thereafter satisfy the equations of motion, in contrast to previous theoretical work where model profiles are used. We also emphasize the structures and scales of the instability in order to provide a rational basis for the development of nonlinear analyses as opposed to existing ad hoc ones. Disturbances, in the near wake, respond according to the Rayleigh equation which is considered analytically for short-, long- and neutral-wave solutions. For more general stability characteristics eigensolutions must be obtained numerically. We calculate these at successive wake stations for ‘improved’ basic flow profiles which are obtained as solutions of the wake boundary-layer equations. Our numerical results indicate fairly good agreement with the asymptotic theory and some experimental data (see §7).
Velocity-derivative skewness and two-time velocity correlations of isotropic turbulence as predicted by the LET theory
Authors: Mccomb W. D. , Shanmugasundaram V. , Hutchinson P.
Published: April 2006

The local-energy-transfer (LET) theory was used to calculate freely decaying turbulence for arbitrary initial conditions over a range of microscale-based Reynolds numbers 0.5 [les ] Rλ(tf) [les ] 1009, where tf is the final time of computation. The predicted skewness factor S(Rλ) agreed closely with the results of numerical simulations at low-to-moderate Reynolds numbers and followed the same general trend at larger values of Rλ. It was also found that, for Rλ(tf) [les ] 5, the LET calculation was almost indistinguishable from that of the direct-interaction approximation (DIA), with the difference between the two theories tending to zero as Rλ(tf)∞ 0.

Two-time correlation and propagator (or response) functions were also obtained. Tests of their scaling behaviour suggest that, contrary to general belief, the convective sweeping of the energy-containing range is much less important than the Kolmogorov timescale in determining inertial-range behaviour. This result raises questions about the accepted explanation for the failure of the direct-interaction approximation, thus motivating a discussion about the relevance of random Galilean invariance (RGI). It is argued that, for a properly constructed ensemble of transformations to inertial frames, invariance in every realization necessarily implies RGI. It is suggested that the defects of the direct-interaction approximation can be understood in terms of a failure to renormalize the stirring forces.
The fluid mechanics of slide coating
Authors: Christodoulou K. N. , Scriven L. E.
Published: April 2006

Slide coating is a means of rapidly depositing multilayered liquid films of precise thickness and uniformity, as in manufacture of photographic products. Liquid is metered through one or more slots onto the inclined surface of the coating die, flows down that face and across a gap onto a fast-moving smooth surface. In this paper the steady, two-dimensional slide coating flow of a Newtonian liquid is analysed by solving the full Navier–Stokes system with the Galerkin/finite-element technique, spine parametrization of free surfaces and full Newton iteration. The lower meniscus in the gap is assumed to remain pinned at the die edge and the wetting-line singularity on the surface being coated is relieved by introducing dynamic-slip and contact-angle parameters. Results include the effects of several design and operating parameters on free-surface profiles and details of the flow field; these are presented by means of contours of kinematic and dynamic variables and local force balances over subdomains. The profiles show standing waves on the slide, rapid film thinning just before the gap, and exponential approach to the final film thickness on the web. As Reynolds number is raised and/or web speed is lowered several recirculation regions are predicted, deleterious features that have also been detected in experiments.
Long-period oscillations in a harbour induced by incident short waves
Authors: Mei Chiang C. , Agnon Yehuda
Published: April 2006

Progressive short waves with a narrow frequency band are known to be accompanied by long set-down waves travelling with the groups. In finite depth, scattering of short waves by a large structure or a varying coastline can radiate free long waves which propagate faster than the incident set-down. In a partially enclosed harbour attacked by short waves through the entrance, such free long waves can further resonate the natural modes of the harbour basin. In this paper an asymptotic theory is presented for a harbour whose horizontal dimensions are much greater than the entrance width, which is in turn much wider than the short wavelength.
On the dynamics of liquid spreading on solid surfaces
Authors: Ngan C. G. , V. E. B. Dussan
Published: April 2006

Our main objective is to identify a boundary-value problem capable of describing the dynamics of fluids having moving contact lines. A number of models have been developed over the past decade and a half for describing the dynamics of just such fluid systems. We begin by discussing the deficiencies of the methods used in some of these investigations to evaluate the parameters introduced by their models. In this study we are concerned exclusively with the formulation of a boundary-value problem which can describe the dynamics of the fluids excluding that lying instantaneously in the immediate vicinity of the moving contact line. From this perspective, many of the approaches referred to above are equivalent, that is to say they give rise to velocity fields with the same asymptotic structure near the moving contact line. Part of our objecive is to show that this asymptotic structure has only one parameter. A substantial portion of our investigation is devoted to determining whether or not the velocity field in a particular experiment has this asymptotic structure, and to measuring the value of the parameter.

More specifically, we use the shape of the fluid interface in the vicinity of the moving contact line to identify the asymptotic structure of the dynamics of the fluid. Experiments are performed in which silicone oil displaces air through a gap formed between two parallel narrowly-spaced glass microscope slides sealed along two opposing sides. Since we were unable to make direct measurements of the shape of the fluid interface close to the moving contact line, an indirect procedure has been devised for determining its shape from measurements of the apex height of the meniscus. We find that the deduced fluid interface shape compares well with the asymptotic form identified in the studies referred to above; however, systematic deviations do arise. The origin of these deviations is unclear. They could be attributed to systematic experimental error, or, to the fact that our analysis (valid only for small values of the capillary number) is inadequate at the conditions of our experiments.
Viscous and inviscid flows in a channel with a moving indentation
Authors: Ralph M. E. , Pedley T. J.
Published: April 2006

The flow in a channel with an oscillating constriction has been studied by the numerical solution of the Navier-Stokes and Euler equations. A vorticity wave is found downstream of the constriction in both viscous and inviscid flow, whether the downstream flow rate is held constant and the upstream flow is pulsatile, or vice versa. Closed eddies are predicted to form between the crests/troughs of the wave and the walls, in the Euler solutions as well as the Navier-Stokes flows, although their structures are different in the two cases.

The positions of wave crests and troughs, as determined numerically, are compared with the predictions of a small-amplitude inviscid theory (Pedley & Stephanoff 1985). The theory agrees reasonably with the Euler equation predictions at small amplitude (ε [lsim ] 0.2) as long as the downstream flow rate is held fixed; otherwise a sinusoidal displacement is superimposed on the computed crest positions. At larger amplitude (ε = 0.38) the wave crests move downstream more rapidly than predicted by the theory, because of the rapid growth of the first eddy (‘eddy A’) attached to the downstream end of the constriction. At such larger amplitudes the Navier-Stokes predictions also agree well with the Euler predictions, when the downstream flow rate is held fixed, because the wave generation process is essentially inviscid and the undisturbed vorticity distribution is the same in each case. It is quite different, however, when the upstream flow rate is fixed, as in the experiments of Pedley & Stephanoff, because of differences in the undisturbed vorticity distribution, in the growth rate of the vorticity waves and in the dynamics of eddy A. A further finite-amplitude effect of importance, especially in an inviscid fluid, is the interaction of an eddy with its images in the channel walls.
Effect of a surface shear layer on gravity and gravity–capillary waves of permanent form
Authors: Milinazzo F. A. , Saffman P. G.
Published: April 2006

Calculations are carried out of the shape of gravity and gravity–capillary waves on deep water in the presence of a thin sheet of uniform vorticity which models the effect of a wind drift layer. The dependence of the fluid speed at the wave crest is determined and compared for gravity waves with the theory of Banner & Phillips (1974). It is found that this theory underestimates the retardation due to drift and tendency to break. The retardation disappears when capillary forces are significant, but in this case it is found that there can be a significant alteration of the wave shape.
Stability of symmetric film-splitting between counter-rotating cylinders
Authors: Coyle D. J. , Macosko C. W. , Scriven L. E.
Published: April 2006

The ribbing instability, an extremely common cause of non-uniform liquid films in coating operations, is investigated both theoretically and experimentally. The Navier–Stokes system for the two-dimensional flow in symmetric film-splitting in forward roll coating is solved by finite-element analysis. Stability of the flow with respect to three-dimensional disturbances is examined by applying linear stability theory in a consistent finite-element approach, taking Fourier components in the transverse direction. The resulting generalized asymmetric eigenproblem is solved for the growth rates of disturbances as functions of wavenumber. The theory accurately predicts the critical capillary number and wavenumber at the transition to large-amplitude ribs. A sensitive experimental technique for detecting the ribs was developed that relies on low-angle reflection of a focused strip of white light off the meniscus between the rolls. This allowed detection of much smaller amplitude ribs, and much smaller critical capillary numbers were measured. The results indicate that the transition to ribbing is an imperfect bifurcation due to end effects, and clarify earlier discordances in the literature.
On the directly generated resonant standing waves in a rectangular tank
Authors: Shemer Lev
Published: April 2006

A numerical study based on the nonlinear Schrödinger equation, as applied to nonlinear resonant standing waves excited directly by a wavemaker in a rectangular tank, is presented. The stationary solutions of the problem serve as a starting point of the investigation. Bifurcations from a single steady state to multiple stationary solutions are obtained for several values of damping coefficients along the tank and at the wavemaker. The stability of the latter solutions is tested. Limit-cycle or fixed-point solutions are obtained. The results of the numerical study are discussed in connection with experimental data. The necessity of incorporation of dissipation at the wavemaker in the theoretical model in order to obtain qualitative agreement with experiment is demonstrated.
Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity
Authors: Nagata M.
Published: April 2006

Finite-amplitude solutions of plane Couette flow are discovered. They take a steady three-dimensional form. The solutions are obtained numerically by extending the bifurcation problem of a circular Couette system between co-rotating cylinders with a narrow gap to the case with zero average rotation rate.
Self-similar viscous gravity currents: phase-plane formalism
Authors: Gratton Julio , Minotti Fernando
Published: April 2006

A theoretical model for the spreading of viscous gravity currents over a rigid horizontal surface is derived, based on a lubrication theory approximation. The complete family of self-similar solutions of the governing equations is investigated by means of a phase-plane formalism developed in analogy to that of gas dynamics. The currents are represented by integral curves in the plane of two phase variables, Z and V, which are related to the depth and the average horizontal velocity of the fluid. Each integral curve corresponds to a certain self-similar viscous gravity current satisfying a particular set of initial and/or boundary conditions, and is obtained by solving a first-order ordinary differential equation of the form dV/dZ = f(Z, V), where f is a rational function. All conceivable self-similar currents can thus be obtained. A detailed analysis of the properties of the integral curves is presented, and asymptotic formulae describing the behaviour of the physical quantities near the singularities of the phase plane corresponding to sources, sinks, and current fronts are given. The derivation of self-similar solutions from the formalism is illustrated by several examples which include, in addition to the similarity flows studied by other authors, many other novel ones such as the extension to viscous flows of the classical problem of the breaking of a dam, the flows over plates with borders, as well as others. A self-similar solution of the second kind describing the axisymmetric collapse of a current towards the origin is obtained. The scaling laws for these flows are derived. Steady flows and progressive wave solutions are also studied and their connection to self-similar flows is discussed. The mathematical analogy between viscous gravity currents and other physical phenomena such as nonlinear heat conduction, nonlinear diffusion, and ground water motion is commented on.
Spanwise structure in the near-wall region of a turbulent boundary layer
Authors: Antonia R. A. , Bisset D. K.
Published: April 2006

The behaviour of the stream wise velocityuin the near-wall region of a turbulent boundary layer is obtained by analysing the data from an array of hot wires aligned in the span wise direction. Conventional and conditional statistics are presented, relative to the occurrence of bursts and sweeps detected using a modifiedu-level method. Sweeps have an average stream wise length which is twice as large as that of bursts while the average span wise extent of sweeps is about 25% larger than that of bursts. Both instantaneous and conditionally averaged information is presented and discussed in the context of bursts and sweeps in the (x, z)-plane. Dependence ony+is significant, and important differences are observed between instantaneous and conditionally averaged results. Conventional and conditional statistics of the velocity derivatives ∂u/∂xand ∂u/∂zprovide some insight into the anisotropy of the mean-square velocity derivatives in the near-wall region. Conditionally averaged patterns ofucompare favourably with the numerical simulations of Kim (1985) in the near-wall region of a turbulent channel flow, at a comparable Reynolds number.
On the Lagrangian description of unsteady boundary-layer separation. Part 1. General theory
Authors: Van Dommelen Leon L. , Cowley Stephen J.
Published: April 2006

Although unsteady, high-Reynolds-number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary-layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady three-dimensional separating flows follow and depend on the symmetry properties of the flow (e.g. line symmetry, axial symmetry). In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi two-dimensional with a displacement thickness in the form of a crescent-shaped ridge. Physically the singularities can be understood in terms of the behaviour of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.
Experimental investigation of three-dimensional turbulent boundary layers on ‘infinite’ swept curved wings
Authors: Baskaran V. , Pontikis Y. G. , Bradshaw P.
Published: April 2006

Mean flow and turbulence measurements have been made in three-dimensional turbulent boundary layers in curved ducts, simulating adverse pressure gradients on two ‘infinite’ swept curved wing surfaces with concave and convex curvature respectively. The ratio of the initial boundary-layer thickness to the surface radius of curvature in both cases is approximately 0.01, the value used in the earlier two-dimensional turbulent boundary-layer studies on the effects of concave and convex curvature by Hoffmann, Muck & Bradshaw (1985) and Muck, Hoffmann & Bradshaw (1985) respectively. The pressure-driven crossflow has nearly the same streamwise distribution as in the ‘infinite’ swept flat-surface experiment of Bradshaw & Pontikos (1985), which used a similar duct. The results of the present study show that the coupled effects of mean flow three-dimensionality and prolonged mild surface curvature of either sign have rather a weak influence on the turbulence structure, unlike the significant influence of the above extra strain rates when applied individually. In the concave case, the effect of the crossflow appears to oppose the destabilizing effect of curvature in addition to suppressing spanwise wavy inhomogeneities In contrast, the weak combined influence of convex curvature and crossflow, both of which, separately, tend to attenuate turbulence, implies that the interaction between the two effects is grossly nonlinear. Implications of the present results for turbulence modelling are briefly discussed.
The complete second-order diffraction solution for an axisymmetric body Part 2. Bichromatic incident waves and body motions
Authors: Kim Moo-Hyun , Yue Dick K. P.
Published: April 2006

In Part 1 (Kim & Yue 1989), we considered the second-order diffraction of a plane monochromatic incident wave by an axisymmetric body. A ring-source integral equation method in conjunction with a novel analytic free-surface integration in the entire local-wave-free domain was developed. To generalize the second-order theory to irregular waves, say described by a continuous spectrum, we consider in this paper the general second-order wave–body interactions in the presence of bichromatic incident waves and the resulting sum- and difference-frequency problems. For completeness, we also include the radiation problem and second-order motions of freely floating or elastically moored bodies. As in Part 1, the second-order sum- and difference-frequency potentials are obtained explicitly, revealing a number of interesting local behaviours of the second-order pressure. For illustration, the quadratic transfer functions (QTF's) for the sum- and difference-frequency wave excitation and body response obtained from the present complete theory are compared to those of existing approximation methods for a number of simple geometries. It is found that contributions from the second-order potentials, typically neglected, can dominate the total load in many cases.
Unsteady three-dimensional marginal separation, including breakdown
Authors: Duck Peter W.
Published: April 2006

We consider a situation involving a three-dimensional marginal separation, where a (steady) boundary-layer flow is on the verge of separating at a point (located along a line of symmetry/centreline). At this point we include a ‘triple-deck’, thereby permitting a small amount of interaction to occur. Unsteadiness is included within this interaction region through some external means. It is shown that the problem reduces to the solution of a nonlinear, unsteady, partial integro system, which is solved numerically by means of time-marching together with a pseudo-spectral method spatially. A number of solutions to this system are presented which strongly suggest that a breakdown of this system may occur, at a finite spatial position, at a finite time. The structure and details of this breakdown are then described.
The hydrodynamic stability of boundary-layer flow over a class of anisotropic compliant walls
Authors: Yeo K. S.
Published: April 2006

This paper examines the linear stability of zero-pressure-gradient boundary-layer flow over a class of anisotropically responding compliant walls. The anisotropic wall behaviour is derived from a material anisotropy which is characterized by relatively high tensile and compressive strength along a certain direction, termed the fibre axis. When the material stiffness along the fibre axis is sufficiently high, the resulting correlation between the horizontal and the vertical components of wall displacement induces at the flow–wall interface a Reynolds shear stress of a sign that is predetermined by the angle with which the fibre axis makes with the direction of the flow. The notion that anisotropic surface response could be employed to produce turbulent Reynolds shear stresses of predetermined sign at a surface was first explored by Grosskreutz (1971) in an experimental study on turbulent drag reduction. The present paper examines the implications of this interesting idea in the context of two-dimensional flow stability over anisotropic compliant walls. The study covers single- and two-layer compliant walls using the methodology described in Yeo (1988). The effects of wall anisotropy, as determined by the orientation of the fibre axis and the material stiffness along the fibre axis, on flow stability are examined for a variety of walls. The potential of some anisotropic compliant walls for delaying laminar–turbulent transition is investigated, and the contribution of the anisotropy to transition delay is appraised.
The effects of surfactants on drop deformation and breakup
Authors: Stone H. A. , Leal L. G.
Published: April 2006

The effects of surface-active agents on drop deformation and breakup in extensional flows at low Reynolds numbers are described. In this free-boundary problem, determination of the interfacial velocity requires knowledge of the distribution of surfactant, which, in turn, requires knowledge of the interfacial velocity field. We account for this explicit coupling of the unknown drop shape and the evolving surfactant distribution. An analytical result valid for nearly spherical distortions is presented first. Finite drop deformation is studied numerically using the boundary-integral method in conjunction with the time-dependent convective–diffusion equation for surfactant transport. This procedure accurately follows interfacial tension variations, produced by non-uniform surfactant distribution, on the evolving interface. The numerical method allows for an arbitrary equation of state relating interfacial tension to the local concentration of surfactant, although calculations are presented only for the common linear equation of state. Also, only the case of insoluble surfactant is studied.

The analytical and numerical results indicate that at low capillary numbers the presence of surfactant causes larger deformation than would occur for a drop with a constant interfacial tension equal to the initial equilibrium value. The increased deformation occurs owing to surfactant being swept to the end of the drop where it acts to locally lower the interfacial tension, which therefore requires increased deformation to satisfy the normal stress balance. However, at larger capillary numbers and finite deformations, this convective effect competes with ‘dilution’ of the surfactant due to interfacial area increases. These two different effects of surface-active material are illustrated and discussed and their influence on the critical capillary number for breakup is presented.
The effect of buoyancy on vortex shedding in the near wake of a circular cylinder
Authors: Chang Keun-Shik , Sa Jong-Youb
Published: April 2006

The phenomenon of vortex shedding from a heated/cooled circular cylinder has been investigated numerically in the mixed natural and forced convection regimes. Accuracy of the computation was achieved by the fourth-order Hermitian relation applied to the contravariant velocity components in the convection terms of the vorticity transport equation, and by the far-boundary stream-function condition of an integral-series form developed by the authors. Purely periodic flows at Re = 100, efficiently established through the use of a direct elliptic solver called the SEVP, was found to degenerate into a steady twin-vortex pattern at the critical Grashof number 1500, confirming an earlier experimental observation identified as ‘breakdown of the Kármán vortex street’. Various other buoyancy effects about the heated/cooled cylinder are discussed by means of the flow patterns, the Nusselt number and the drag coefficient curves.
Inviscid–viscous interaction on triple-deck scales in a hypersonic flow with strong wall cooling
Authors: Brown S. N. , Cheng H. K. , Lee C. J.
Published: April 2006

Inviscid–viscous interaction in a high supersonic flow is studied on the triple-deck scales to delineate the wall-temperature influence on the flow structure in a region near a laminar separation. A critical wall-temperature rangeO(Tw*) is identified, in which the pressure–displacement relation governing the lower deck departs from that of the classical (Stewartson, Messiter, Neiland) formulation, and below which the pressure–displacement relation undergoes still greater changes along with drastic scale changes in the triple deck. The reduced lower-deck problem falls into three domains: (i) supercritical (Tw* [Lt ]Tw), (ii) transcritical (Tw=O(Tw*)) and (iii) subcritical (Tw[Lt ]Tw*). Readily identified is a parameter domain overlapping with the Newtonian triple-deck theory of Brown, Stewartson & Williams (1975), even though the assumption of a specific-heat ratio approaching unity is not required here. Computational study of the compressive free-interaction solutions and solutions for a sharp-corner ramp are made for the three wall-temperature ranges. Finite-difference equations for primitive variables are solved by iterations, employing Newton linearization and a large-band matrix solver. Also treated in the program is the sharp-corner effect through the introduction of proper jump conditions. Comparison with existing numerical results in the supercriticalTwrange reveals a smaller separation bubble and a more pronounced corner behaviour in the present numerical solution. Unlike an earlier comparison with solutions by interactive-boundary-layer methods for ramp-induced pressure with separation, the IBL results do approach closely the triple-deck solution atRe= 108in a Mach-three flow, and the differences atRe= 106may be attributed in part to the transcritical temperature effect. Examination of the numerical solutions indicates that separation and reattachment on a compressive ramp cannot be effectively eliminated/delayed by lowering the wall temperature, but loweringTwdrastically reduces the triple-deck dimension, and hence the degree of upstream influence.
The structure of two-dimensional separation
Authors: Pauley Laura L. , Moin Parviz , Reynolds William C.
Published: April 2006

The separation of a two-dimensional laminar boundary layer under the influence of a suddenly imposed external adverse pressure gradient was studied by time-accurate numerical solutions of the Navier–Stokes equations. It was found that a strong adverse pressure gradient created periodic vortex shedding from the separation. The general features of the time-averaged results were similar to experimental results for laminar separation bubbles. Comparisons were made with the ‘steady’ separation experiments of Gaster (1966). It was found that his ‘bursting’ occurs under the same conditions as our periodic shedding, suggesting that bursting is actually periodic shedding which has been time-averaged. The Strouhal number based on the shedding frequency, local free-stream velocity, and boundary-layer momentum thickness at separation was independent of the Reynolds number and the pressure gradient. A criterion for onset of shedding was established. The shedding frequency was the same as that predicted for the most amplified linear inviscid instability of the separated shear layer.
Turbulence modulation in homogeneous dilute particle-laden flows
Authors: Parthasarathy R. N. , Faeth G. M.
Published: April 2006

Continuous-phase properties were studied for homogeneous dilute particle-laden flows caused by nearly monodisperse glass particles falling in a stagnant water bath. Test conditions included 0.5, 1.0 and 2.0 mm diameter particles (yielding particle Reynolds numbers based on terminal velocities of 38, 156 and 545) with particle volume fractions less than 0.01%. Measurements included mean and fluctuating velocities, as well as temporal spectra and spatial correlations of velocity fluctuations in the streamwise and cross-stream directions, using a two-point phase-discriminating laser velocimeter. Flow properties were also analysed using a stochastic method involving linear superposition of randomly-arriving particle velocity fields.

For present test conditions, liquid velocity fluctuations varied solely as a function of the rate of dissipation of particle energy in the liquid. The flows were highly anisotropic with streamwise velocity fluctuations being roughly twice cross-stream velocity fluctuations. Correlation coefficients and temporal spectra were independent of both particle size and the rate of dissipation of particle energy in the liquid. The temporal spectra indicated a large range of frequencies even though particle Reynolds numbers were relatively low, since both mean and fluctuating velocities in the particle wakes contributed to the spectra because particle arrivals were random. The theory predicted many of the features of the flows reasonably well but additional information concerning the mean and turbulent structure of the wakes of freely moving particles having moderate Reynolds numbers in turbulent environments is needed to address deficiencies in predictions of integral scales and streamwise spatial correlations.
The entrainment of bubbles by drop impacts
Authors: Pumphrey Hugh C. , Elmore Paul A.
Published: April 2006

Various processes are described by which a drop of water, impacting on a water surface, may entrain a bubble. There are: (i) irregular entrainment, in which the complex details of a splash entrain bubbles; (ii) regular entrainment, in which the crater formed by the drop impact develops in a predictable way to form a single bubble; (iii) entrainment of large bubbles, in which most of the volume of the crater is trapped as a bubble; and (iv) Mesler entrainment, in which many very small bubbles are trapped in the very early stages of the impact process; possibly between wave crests of capillary waves which develop on the drop and on the water surface. This last process is different from the preceding three in that it produces very little sound. All of the processes except the third one have been described individually in the literature; here we present them together for comparison. The regular entrainment process is discussed in the greatest detail and some new experimental results are presented which concern the size and nature of the entrained bubbles. The significance of the regular and irregular entrainment processes to the generation of underwater sound by rain is discussed.
Coalescence and separation in binary collisions of liquid drops
Authors: Ashgriz N. , Poo J. Y.
Published: April 2006

An extensive experimental investigation of the binary collision dynamics of water drops for size ratios of 1. 0.75, and 0.5, for the Weber-number range of 1 to 100, and for all impact parameters is reported. Two different types of separating collisions, namely reflexive and stretching separations, are identified. Reflexive separation is found to occur for near head-on collisions, while stretching separation occurs for large-impact-parameter collisions. The boundaries between both of the separating collisions and coalescence collision are found experimentally. Theoretical models for predictions of the reflexive and stretching separation are also given.
An angular spectrum model for propagation of Stokes waves
Authors: Suh Kyung Duck , Dalrymple Robert A. , Kirby James T.
Published: April 2006

An angular spectrum model for predicting the transformation of Stokes waves on a mildly varying topography is developed, including refraction, diffraction, shoaling and nonlinear wave interactions. The equations governing the water-wave motion are perturbed using the method of multiple scales and Stokes expansions for the velocity potential and free-surface displacement. The first-order solution is expressed as an angular spectrum, or directional modes, of the wave field propagating on a beach with straight iso-baths whose depth is given by laterally averaged depths. The equations for the evolution of the angular spectrum due to the effects of bottom variation and cubic resonant interaction are obtained from the higher-order problems. Comparison of the present model with existing models is made for some simple cases. Numerical examples of the time-independent version of the model are presented for laboratory experiments for wave diffraction behind a breakwater gap and wave focusing over submerged shoals: an elliptic shoal on a sloping beach and a circular shoal on a flat bottom.
Liquid-metal flow in a backward elbow in the plane of a strong magnetic field
Authors: Moon T. J. , Hua T. Q. , Walker J. S.
Published: April 2006

This paper treats a liquid-metal flow through a sharp elbow connecting two constant-area, rectangular ducts with thin metal walls. There is a uniform, strong magnetic field in the plane of the ducts’ centrelines, and the velocity component normal to the magnetic field is in opposite directions upstream and downstream of the elbow. The magnetic field is sufficiently strong that inertial effects are negligible everywhere and viscous effects are confined to boundary layers and to an interior layer lying along the magnetic field lines through the inside corner of the elbow. The interior layer involves large velocities parallel to the magnetic field and carries roughly half of the flow between the upstream and downstream ducts for the case considered.
On cell formation in vortex streets
Authors: Noack Bernd R. , Ohle Frank , Eckelmann Helmut
Published: April 2006

A simple, phenomenological model is proposed for the formation of spanwise cells behind slender bodies of revolution in crosswise, uniform or non-uniform oncoming flow. The model yields estimates for the position of the cells, their frequencies, their amplitudes of oscillation along the span, and the local shedding angle. The qualitative features of the solutions of this theory agree well with experiments. A quantitative comparison with experiments for a slender cone is presented.
A theoretical study on drop impact sound and rain noise
Authors: Guo Y. P. , Williams J. E. Ffowcs
Published: April 2006

This paper examines the sound waves generated when a spherical water drop impacts upon an initially quiescent water surface. The pressure fluctuations and the acoustic energy radiated by the initial impact are calculated analytically. It is shown that the rapid momentum exchange between the fluid in the falling drop and that in the main water body causes the radiation of compressive waves. These waves are radiated in the form of a wave packet with a densely packed edge which is heard in the far field as a noisy shock-like pulse followed by a quickly decreasing tail. The wave packet carries with it sound energy proportional to the kinetic energy of the falling drop and to the cube of the impact Mach number. Applications of these analytic results to the study of noise from natural rain are discussed, and an illustrative example is given where the noise level due to rain showers is linearly related to the rainfall rate, which is shown to be consistent with observations.
The viscous-diffusion nonlinear critical layer in a stratified shear flow
Authors: Troitskaya Yu. I.
Published: April 2006

Stationary finite-amplitude wave disturbances in a stratified shear flow with Richardson number larger than ¼ are investigated for large Reynolds numbers when viscosity and thermal conductivity, as well as nonlinearity, are essential factors in the critical layer. The jumps across the critical layer in average vorticity, reflection and transmission coefficients are calculated as functions of the local Reynolds number determined by the amplitude of the incident wave. With the increase of the incident wave amplitude the asymptotic value of the Richardson number on the same side of critical layer as the incident wave tends to 1/4 the reflection coefficient tends to unity and the transmission coefficient to zero.
Propagation of barotropic vortices over topography in a rotating tank
Authors: Carnevale G. F. , Kloosterziel R. C. , Van Heijst G. J. F.
Published: April 2006

A small-scale cyclonic vortex in a relatively broad valley tends to climb up and out of the valley in a cyclonic spiral about the centre, and when over a relatively broad hill it tends to climb toward the top in an anticyclonic spiral around the peak. This phenomenon is examined here through two-dimensional numerical simulations and rotating-tank experiments. The basic mechanism involved is shown to be the same as that which accounts for the northwest propagation of cyclones on a β-plane. This inviscid nonlinear effect is also shown to be responsible for the observed translationary motion of barotropic vortices in a free-surface rotating tank. The behaviour of isolated vortices is contrasted with that of vortices with non-vanishing circulation.
Dispersion of a passive solute in non-ergodic transport by steady velocity fields in heterogeneous formations
Authors: Dagan Gedeon
Published: April 2006

An inert solute is convected by a steady random velocity field, which is associated with flow through a heterogeneous porous formation. The log conductivity and the velocity are stationary random space functions. The log conductivity Y is assumed to be normal, with an isotropic two-point correlation of variance σY2 and of finite integral scale I. The solute cloud is of a finite input zone of lengthscale l. The transport is characterized with the aid of the spatial moments of the solute body. The effective dispersion coefficient is defined as half of the rate of change with time of the second spatial moment with respect to the centroid. Under the ergodic hypothesis, which is bound to be satisfied for l/I [Gt ] 1, the centroid moves with the mean velocity U and the longitudinal dispersion coefficient [dscr ]L tends to its constant, Fickian, limit. Under a Lagrangian first-order analysis in σY2 it has been found that [dscr ]L = σY2UI.

This study addresses the computation of the effective longitudinal dispersion coefficient for a finite input zone, for which ergodic conditions may not be satisfied. In this case the centroid trajectory and the second spatial moments are random variables. In line with a previous work (Dagan 1990) the effective dispersion coefficient DL is defined as half the rate of change of the expected value of the second spatial moment for large transport time. The aim of the study is to derive DL and its dependence upon l/I and in particular to determine the conditions under which it tends to the ergodic limit [dscr ]L. The computation is carried out separately for a thin body aligned with the mean flow and one transverse to it. In the first case it is found that DL is equal to zero, i.e. the streamlined body does not disperse in the mean. This result is explained by the correlation between the trajectories of the leading and trailing edges, respectively, once the latter reaches the position of the first. The relatively modest increase of the mean second spatial moment is effectively computed. In the case of a thin body initially transverse to the mean flow, DL may reach the ergodic limit [dscr ]L for a ratio l/I of the order 102. For smaller values, DL is found to be bounded from above, and its maximum depends on l but not on I. The uncertainty caused by the randomness of the velocity field is manifested in the trajectory of the centroid rather than in the effective dispersion.
Reaction in a scalar mixing layer
Authors: Bilger R. W. , Saetran L. R. , Krishnamoorthy L. V.
Published: April 2006

Reaction in a scalar mixing layer in grid-generated turbulence is studied experimentally by doping half of the flow with nitric oxide and the other half with ozone. The flow conditions and concentrations are such that the chemical reaction is passive and the flow and chemical timescales are of the same order. Conserved scalar theory for such flows is outlined and further developed; it is used as a basis for presentation of the experimental results. Continuous measurements of concentration are limited in their spatial and temporal resolution but capture sufficient of their spectra for adequate second-order correlations to be made. Two components of velocity have been measured simultaneously with hot-wire anemometry. Conserved scalar mixing results, deduced from reacting and non-reacting measurements of concentration, show the independence of concentration level and concentration ratio expected for passive reacting flow. The results are subject to several limitations due to the necessary experimental compromises, but they agree generally with measurements made in thermal mixing layers. Reactive scalar statistics are consistent with the realizability constraints obtainable from conserved scalar theory where such constraints apply, and otherwise are generally found to lie between the conserved scalar theory limits for frozen and very fast chemistry. It is suggested that Toor's (1969) closure for the mean chemical reaction rate could be improved by interpolating between the frozen and equilibrium values for the covariance. The turbulent fluxes of the reactive scalars are found to approximately obey the gradient model but the value of the diffusivity is found to depend on the Damköhler number.
A numerical study of flow around an impulsively started circular cylinder by a deterministic vortex method
Authors: Chang Chien-Cheng , Chern Ruey-Ling
Published: April 2006

Impulsively started flow around a circular cylinder at various Reynolds numbers is studied by a deterministic hybrid vortex method. The key feature of the method consists in solving the viscous vorticity equation by interlacing a finite-difference method for diffusion and a vortex-in-cell method for convection. The vorticity is updated along the surface of the cylinder to satisfy the no-slip condition. The present method is basically different from previous applications of vortex methods, which are primarily in the context of random vortex algorithms. The Reynolds numbers of the flows under investigation range from 300 to 106. Numerical results are compared with analytical solutions at small times, and compared with finite-difference solutions and flow visualization results at relatively long times. Satisfactory agreement is found in the evolutions of the separation angles, wake lengths, surface pressure and drag coefficients, streamline patterns, and some velocities on the axis of symmetry behind the circular cylinder. The present hybrid vortex method is highly stable and suffers from little numerical diffusivity, yielding convincing numerical results for unsteady vortical flows at moderately high Reynolds numbers.
Unsteady drag on a sphere at finite Reynolds number with small fluctuations in the free-stream velocity
Authors: Mei Renwei , Lawrence Christopher J. , Adrian Ronald J.
Published: April 2006

Unsteady flow over a stationary sphere with small fluctuations in the free-stream velocity is considered at finite Reynolds number using a finite-difference method. The dependence of the unsteady drag on the frequency of the fluctuations is examined at various Reynolds numbers. It is found that the classical Stokes solution of the unsteady Stokes equation does not correctly describe the behaviour of the unsteady drag at low frequency. Numerical results indicate that the force increases linearly with frequency when the frequency is very small instead of increasing linearly with the square root of the frequency as the classical Stokes solution predicts. This implies that the force has a much shorter memory in the time domain. The incorrect behaviour of the Basset force at large times may explain the unphysical results found by Reeks & Mckee (1984) wherein for a particle introduced to a turbulent flow the initial velocity difference between the particle and fluid has a finite contribution to the long-time particle diffusivity. The added mass component of the force at finite Reynolds number is found to be the same as predicted by creeping flow and potential theories. Effects of Reynolds number on the unsteady drag due to the fluctuating free-stream velocity are presented. The implications for particle motion in turbulence are discussed.