bluuebunny/crossref_metadata_2025 huggingface dataset:
Self-diffusion in sheared suspensions
Authors: Morris Jeffrey F. , Brady John F.
Published: April 2006

Self-diffusion in a suspension of spherical particles in steady linear shear flow is investigated by following the time evolution of the correlation of number density fluctuations. Expressions are presented for the evaluation of the self-diffusivity in a suspension which is either raacroscopically quiescent or in linear flow at arbitrary Peclet number $Pe = \dot{\gamma}a^2/2D$, where $\dot{\gamma}$ is the shear rate, a is the particle radius, and D = kBT/6πa is the diffusion coefficient of an isolated particle. Here, kB is Boltzmann's constant, T is the absolute temperature, and η is the viscosity of the suspending fluid. The short-time self-diffusion tensor is given by kBT times the microstructural average of the hydrodynamic mobility of a particle, and depends on the volume fraction $\phi = \frac{4}{3}\pi a^3n$ and Pe only when hydrodynamic interactions are considered. As a tagged particle moves through the suspension, it perturbs the average microstructure, and the long-time self-diffusion tensor, D∞s, is given by the sum of D0s and the correlation of the flux of a tagged particle with this perturbation. In a flowing suspension both D0s and D∞ are anisotropic, in general, with the anisotropy of D0s due solely to that of the steady microstructure. The influence of flow upon D∞s is more involved, having three parts: the first is due to the non-equilibrium microstructure, the second is due to the perturbation to the microstructure caused by the motion of a tagged particle, and the third is by providing a mechanism for diffusion that is absent in a quiescent suspension through correlation of hydrodynamic velocity fluctuations.

The self-diffusivity in a simply sheared suspension of identical hard spheres is determined to O(øPe3/2) for Pe ≤ 1 and ø ≤ 1, both with and without hydro-dynamic interactions between the particles. The leading dependence upon flow of D0s is 0.22DøPeÊ, where Ê is the rate-of-strain tensor made dimensionless with $\dot{\gamma}$. Regardless of whether or not the particles interact hydrodynamically, flow influences D∞s at O(øPe) and O(øPe3/2). In the absence of hydrodynamics, the leading correction is proportional to øPeDÊ. The correction of O(øPe3/2), which results from a singular advection-diffusion problem, is proportional, in the absence of hydrodynamic interactions, to øPe3/2DI; when hydrodynamics are included, the correction is given by two terms, one proportional to Ê, and the second a non-isotropic tensor.

At high ø a scaling theory based on the approach of Brady (1994) is used to approximate D∞s. For weak flows the long-time self-diffusivity factors into the product of the long-time self-diffusivity in the absence of flow and a non-dimensional function of $\bar{P}e = \dot{\gamma}a^2/2D^s_0(\phi)$. At small $\bar{P}e$ the dependence on $\bar{P}e$ is the same as at low ø.
The generation of Tollmien-Schlichting waves by free-stream turbulence
Authors: Duck P. W. , Ruban A. I. , Zhikharev C. N.
Published: April 2006

The phenomenon of Tollmien-Schlichting wave generation in a boundary layer by free-stream turbulence is analysed theoretically by means of asymptotic solution of the Navier-Stokes equations at large Reynolds numbers (Re → ∞). For simplicity the basic flow is taken to be the Blasius boundary layer over a flat plate. Free-stream turbulence is taken to be uniform and thus may be represented by a superposition of vorticity waves. Interaction of these waves with the flat plate is investigated first. It is shown that apart from the conventional viscous boundary layer of thickness O(Re−1/2), a ‘vorticity deformation layer’ of thickness O(Re−1/4) forms along the flat-plate surface. Equations to describe the vorticity deformation process are derived, based on multiscale asymptotic techniques, and solved numerically. As a result it is shown that a strong singularity (in the form of a shock-like distribution in the wall vorticity) forms in the flow at some distance downstream of the leading edge, on the surface of the flat plate. This is likely to provoke abrupt transition in the boundary layer. With decreasing amplitude of free-stream turbulence perturbations, the singular point moves far away from the leading edge of the flat plate, and any roughness on the surface may cause Tollmien-Schlichting wave generation in the boundary layer. The theory describing the generation process is constructed on the basis of the ‘triple-deck’ concept of the boundary-layer interaction with the external inviscid flow. As a result, an explicit formula for the amplitude of Tollmien-Schlichting waves is obtained.
Interactions of two jets in a channel: solution multiplicity and linear stability
Authors: Goodwin Ralph T. , Schowalter William R.
Published: April 2006

The steady, two-dimensional, isothermal flow of an incompressible Newtonian fluid in a semi-infinite channel is modelled using a finite-element method. The flow is driven by injecting two identical jets through symmetrically placed slit-like nozzles into the otherwise closed end of the channel. Multiple steady-state solutions are observed for Reynolds numbers greater than 18.8, where seven solutions have been found. Six of these solutions exist on branches that are not connected to the Stokes flow solution via continuation in the Reynolds number. Further bifurcations of these solutions has led to the discovery of 17 solutions at a Reynolds number of 40. A two-dimensional linear stability analysis of the solution branches shows that for Reynolds numbers in the range of 18.8 to 26.8 there are three stable solutions. One solution is symmetric about the channel centreline while the other two stable solutions are a pair of mirror-image asymmetric flows. For Reynolds numbers in the range 26.8 to 40, there are four known stable solutions consisting of two asymmetric solutions and their mirror-images.
Stokesian Dynamics simulation of Brownian suspensions
Authors: Phung Thanh N. , Brady John F. , Bossis Georges
Published: April 2006

The non-equilibrium behaviour of concentrated colloidal dispersions is studied by Stokesian Dynamics, a general molecular-dynamics-like technique for simulating particles suspended in a viscous fluid. The simulations are of a suspension of monodisperse Brownian hard spheres in simple shear flow as a function of the Péclet number, Pe, which measures the relative importance of shear and Brownian forces. Three clearly defined regions of behaviour are revealed. There is first a Brownian-motion-dominated regime (Pe ≤ 1) where departures from equilibrium in structure and diffusion are small, but the suspension viscosity shear thins dramatically. When the Brownian and hydrodynamic forces balance (Pe ≈ 10), the dispersion forms a new ‘phase’ with the particles aligned in ‘strings’ along the flow direction and the strings are arranged hexagonally. This flow-induced ordering persists over a range of Pe and, while the structure and diffusivity now vary considerably, the rheology remains unchanged. Finally, there is a hydrodynamically dominated regime (Pe > 200) with a dramatic change in the long-time self-diffusivity and the rheology. Here, as the Péclet number increases the suspension shear thickens owing to the formation of large clusters. The simulation results are shown to agree well with experiment.
Non-Gaussian scalar statistics in homogeneous turbulence
Authors: Jaberi F. A. , Miller R. S. , Madnia C. K. , Givi P.
Published: April 2006

Results are presented of numerical simulations of passive scalar mixing in homogeneous, incompressible turbulent flows. These results are generated via the Linear Eddy Model (LEM) and Direct Numerical Simulation (DNS) of turbulent flows under a variety of different conditions. The nature of mixing and its response to the turbulence field is examined and the single-point probability density function (p.d.f.) of the scalar amplitude and the p.d.f.s of the scalar spatial-derivatives are constructed. It is shown that both Gaussian and exponential scalar p.d.f.s emerge depending on the parameters of the simulations and the initial conditions of the scalar field. Aided by the analyses of data, several reasons are identified for the non-Gaussian behaviour of the scalar amplitude. In particular, two mechanisms are identified for causing exponential p.d.f.s: (i) a non-uniform action of advection on the large and the small scalar scales, (ii) the nonlinear interaction of the scalar and the velocity fluctuations at small scales. In the absence of a constant non-zero mean scalar gradient, the behaviour of the scalar p.d.f. is very sensitive to the initial conditions. In the presence of this gradient, an exponential p.d.f. is not sustained regardless of initial conditions. The numerical results pertaining to the small-scale intermittency (non-Gaussian scalar derivatives) are in accord with laboratory experimental results. The statistics of the scalar derivatives and those of the velocity-scalar fluctuations are also in accord with laboratory measured results.
Simple shear flows of dense gas-solid suspensions at finite Stokes numbers
Authors: Sangani Ashok S. , Mo Guobiao , Tsao Heng-Kwong , Koch Donald L.
Published: April 2006

We examine the problem of determining the particle-phase velocity variance and rhe-ology of sheared gas-solid suspensions at small Reynolds numbers and finite Stokes numbers. Our numerical simulations take into account the Stokes flow interactions among particles except for pairs of particles with a minimum gap width comparable to or smaller than the mean free path of the gas molecules for which the usual lubrication approximation breaks down and particle collisions occur in a finite time. The simulation results are compared to the predictions of two theories. The first is an asymptotic theory for large Stokes numberStand nearly elastic collisions, i.e.St[Gt ] 1 and 0 ≤ 1 -e[Lt ] 1,ebeing the coefficient of restitution. In this limit, the particle velocity distribution is close to an isotropic Maxwellian and the velocity variance is determined by equating the energy input in shearing the suspension to the energy dissipation by inelastic collisions and viscous effects. The latter are estimated by solving the Stokes equations of motion in suspensions with the hard-sphere equilibrium spatial and velocity distribution while the shear energy input and energy dissipation by inelastic effects are estimated using the standard granular flow theory (i.e.St= ∞). The second is an approximate theory based on Grad's moments method for whichStand 1 –eareO(1). The two theories agree well with each other at higher values of volume fraction ϕ of particles over a surprisingly large range of values ofSt.For smaller ϕ however, the two theories deviate significantly except at sufficiently largeSt.A detailed comparison shows that the predictions of the approximate theory based on Grad's method are in excellent agreement with the results of numerical simulations.
Low Reynolds number fully developed two-dimensional turbulent channel flow with system rotation
Authors: Nakabayashi Koichi , Kitoh Osami
Published: April 2006

Theoretical and experimental studies have been performed on fully developed twodimensional turbulent channel flows in the low Reynolds number range that are subjected to system rotation. The turbulence is affected by the Coriolis force and the low Reynolds number simultaneously. Using dimensional analysis, the relevant parameters of this flow are found to be Reynolds number Re* = u*D/v (u* is the friction velocity, D the channel half-width) and Ωv/u2* (Ω is the angular velocity of the channel) for the inner region, and Re* and ΩD/u* for the core region. Employing these parameters, changes of skin friction coefficients and velocity profiles compared to nonrotating flow can be reasonably well understood. A Coriolis region where the Coriolis force effect predominates is shown to exist in addition to conventional regions such as viscous and buffer regions. A flow regime diagram that indicates ranges of these regions as a function of Re* and |Ω|v/u2* is given from which the overall flow structure in a rotating channel can be obtained.

Experiments have been made in the range of 56 ≤ Re* ≤ 310 and -0.0057 ≤ Ωv/u2* ≤ 0.0030 (these values correspond to Re = 2UmD/v from 1700 to 10000 and rotation number R0 = 2|Ω|D/Um up to 0.055; Um is bulk mean velocity). The characteristic features of velocity profiles and the variation of skin friction coefficients are discussed in relation to the theoretical considerations.
A comparison of numerical predictions and experimental measurements of the internal kinematics of a deep-water plunging wave
Authors: Skyner David
Published: April 2006

A deep-water long-crested breaking wave is generated from a time-stepping numerical model, then replicated in a wave flume. The numerical model is based on the boundary integral method and measurements of the internal kinematics are made during the breaking process with Particle Image Velocimetry (PIV). Velocity measurements are obtained throughout the wave crest, including the plunging spout. After a small shift of the numerical data to match the surface profiles, the predicted and measured kinematics are found to be in good agreement, within the limits of experimental error.
On the spatial evolution of centrifugal instabilities within curved incompressible mixing layers
Authors: Otto S. R. , Jackson T. L. , Hu F. Q.
Published: April 2006

It is known that certain configurations which possess curvature are prone to a class of instabilities which their ‘flat’ counterparts will not support. The main thrust of the study of these centrifugal instabilities has concentrated on curved solid boundaries and their effect on the fluid motion. In this article attention is shifted towards a fluid-fluid interface observed within a curved incompressible mixing layer. Experimental evidence is available to support the conjecture that this situation may be subject to centrifugal instabilities. The evolution of modes with wavelengths comparable with the layer's thickness is considered within moderately curved mixing layers. The high Taylor/Görtler number régime is also discussed which characterizes the ultimate fate of the modes.
Receptivity of pipe Poiseuille flow
Authors: Tumin Anatoli
Published: April 2006

The receptivity problem is considered for pipe flow with periodic blow–suction through a narrow gap in the pipe wall. Axisymmetric and non-axisymmetric modes (1, 2, and 3) are analysed. The method of solution is based on global eigenvalue analysis for spatially growing disturbances in circular pipe Poiseuille flow. The numerical procedure is formulated in terms of the collocation method with the Chebyshev polynomials application. The receptivity problem is solved with an expansion of the solution in a biorthogonal eigenfunction system, and it was found that there is an excitation of many eigenmodes, which should be taken into account. The result explains the non-similar character of the amplitude distribution in the downstream direction that was observed in experiments.
The suppression of short waves by a train of long waves
Authors: Balk A. M.
Published: April 2006

It is shown that a train of long waves can suppress a short-wave field due to four-wave resonance interactions. These interactions lead to the diffusion (in Fourier space) of the wave action of the short-wave field, so that the wave action is transported to the regions of higher wavenumbers, where it dissipates more effectively. The diffusion equation is derived.
Vortical structure morphology in the initial region of a forced mixing layer: roll-up and pairing
Authors: Leboeuf Richard L. , Mehta Rabindra D.
Published: April 2006

Detailed three-dimensional phase-averaged measurements of the spanwise and streamwise vorticity formation and evolution in a forced mixing layer have been obtained. A plane two-stream mixing layer with a velocity ratio (U2/U1) of 0.6, a maximum Reynolds number (Reδ) of about 3150 and laminar initial boundary layers was generated in a mixing layer wind tunnel. Acoustic forcing, consisting of a fundamental roll-up frequency and its subharmonic, was used to phase-lock the initial development and first pairing of the spanwise vortical structures. For the first time, phase-averaged measurements of all three velocity components have been obtained on a three-dimensional grid, yielding the spanwise and streamwise vorticity distributions without invoking Taylor's hypothesis. The phase-averaged results show that the streamwise vorticity first appears in the form of ‘ribs’ just upstream of the first spanwise vortex roll-up. At the same time, the first spanwise roller becomes kinked, thus also contributing to the streamwise vorticity. As a result, in cross-stream cuts through the spanwise rollers, the streamwise vorticity appears in a ‘three-tier’ arrangement with opposite-signed vorticity in the centre. In terms of phase-averaged quantities, the maximum streamwise vorticity in the initial ribs is equivalent to about 10–15% of the peak spanwise vorticity and the streamwise rib circulation is equivalent to about 5–10% of the spanwise circulation. Further downstream, the peak streamwise vorticity decreases with increasing distance, while the average circulation remains approximately constant. Downstream of the pairing, the streamwise vorticity levels in the spanwise rollers are reduced. However, the spanwise spacing of the streamwise vortices does not increase within the measurement domain. Phase-averaged Reynolds stress measurements show that relatively high stress levels (periodic and random) were generated in the cores of the spanwise vortices.
The onset of instability in unsteady boundary-layer separation
Authors: Cassel K. W. , Smith F. T. , Walker J. D. A.
Published: April 2006

The process of unsteady two-dimensional boundary-layer separation at high Reynolds number is considered. Solutions of the unsteady non-interactive boundary-layer equations are known to develop a generic separation singularity in regions where the pressure gradient is prescribed and adverse. As the boundary layer starts to separate from the surface, however, the external pressure distribution is altered through viscous—inviscid interaction just prior to the formation of the separation singularity; hitherto this has been referred to as the first interactive stage. A numerical solution of this stage is obtained here in Lagrangian coordinates. The solution is shown to exhibit a high-frequency inviscid instability resulting in an immediate finite-time breakdown of this stage. The presence of the instability is confirmed through a linear stability analysis. The implications for the theoretical description of unsteady boundary-layer separation are discussed, and it is suggested that the onset of interaction may occur much sooner than previously thought.
An example of non-uniqueness in the two-dimensional linear water wave problem
Authors: McIver M.
Published: April 2006

An example of non-uniqueness in the two-dimensional, linear water wave problem is obtained by constructing a potential which does not radiate any waves to infinity and whose streamline pattern represents the flow around two surface-piercing bodies. The potential is constructed from two wave sources which are positioned in the free surface in such a way that the waves radiated from each source cancel at infinity. A numerical calculation of the streamline pattern indicates that there are at least two streamlines which represent surface-piercing bodies, each of which encloses a source point. A proof of the existence of these lines is then given.
Multi-mode resonances in fluids
Authors: Ockendon H. , Ockendon J. R. , Waterhouse D. D.
Published: April 2006

When a lightly damped fluid resonator is forced near its fundamental frequency, the most usual response is one in which the fluid oscillates in the corresponding eigenmode with an amplitude response similar to that of a Duffing oscillator. Examples are the sloshing of a horizontally oscillated tank or acoustic oscillations in a resonator of general shape. However, multiple eigenmodes can be excited if the spectrum is either commensurate or degenerate and both acoustic resonance and the sloshing of shallow water in a nearly square container exemplify both these exceptional cases. In this paper we investigate how the response of such systems depends on geometry and dispersion.
The motion of a solid sphere suspended by a Newtonian or viscoelastic jet
Authors: Feng J. , Joseph D. D.
Published: April 2006

This paper describes experimental observations of a solid sphere suspended by a vertical or inclined jet. A laminar Newtonian jet is able to suspend a sphere only through viscous entrainment at low Reynolds numbers (Re ~ 10). A turbulent Newtonian jet (Re ~ 104) attracts a sphere that is sufficiently large but rejects smaller ones. The Coanda effect is responsible for steady suspension of solid spheres even in highly slanted jets. Anomalous rotation, opposite to the direction of the local shear, occurs under certain conditions, and its physical mechanism cannot be explained based on available information. A viscoelastic laminar jet is narrower than a comparable Newtonian one and it can suspend spheres at Reynolds numbers in the hundreds, precisely the Re range in which a Newtonian jet fails to suspend a sphere. It is suggested that the contrast between laminar Newtonian and viscoelastic jets may be related to a reversal in the pressure distribution on the surface of the sphere caused by non-Newtonian normal stresses. Flow visualization provides insights into the flow field in the jet and around the solid sphere.
Experimental studies of vortex disconnection and connection at a free surface
Authors: Gharib Morteza , Weigand Alexander
Published: April 2006

An experimental study is presented that examines the interaction of a vortex ring with a free surface. The main objective of this study is to identify the physical mechanisms that are responsible for the self-disconnection of vortex filaments in the near-surface region and the subsequent connection of disconnected vortex elements to the free surface. The understanding of those mechanisms is essential for the identification and estimation of the appropriate spatial and temporal scales of the disconnection and connection process. In this regard, the velocity and vorticity fields of an obliquely approaching laminar vortex ring with a Reynolds number of 1150 were mapped by using Digital Particle Image Velocimetry (DPIV). The evolution of the near-surface vorticity field indicates that the connection process starts in the side regions of the approaching vortex ring where surface-normal vorticity already exists in the bulk. A local strain rate analysis was conducted to support this conclusion. Disconnection in the near-surface tip region of the vortex ring occurs because of the removal of surfaceparallel vorticity by the viscous flux of vorticity through the surface. Temporal and spatial mapping of the vorticity field at the surface and in the perpendicular plane of symmetry shows that the viscous flux is balanced by a local deceleration of the flow at the surface. It is found that the observed timescales of the disconnection and connection process scale with the near-surface vorticity gradient rather than with the core diameter of the vortex ring.
Unsteadiness and convective instabilities in two-dimensional flow over a backward-facing step
Authors: Kaiktsis Lambros , Em Karniadakis George , Orszag Steven A.
Published: April 2006

A systematic study of the stability of the two-dimensional flow over a backward-facing step with a nominal expansion ratio of 2 is presented up to Reynolds numberRe= 2500 using direct numerical simulation as well as local and global stability analysis. Three different spectral element computer codes are used for the simulations. The stability analysis is performed both locally (at a number of streamwise locations) and globally (on the entire field) by computing the leading eigenvalues of a base flow state. The distinction is made between convectively and absolutely unstable mean flow. In two dimensions, it is shown that all the asymptotic flow states up toRe= 2500 are time-independent in the absence of any external excitation, whereas the flow is convectively unstable, in a large portion of the flow domain, for Reynolds numbers in the range 700 [les ]Re[les ] 2500. Consequently, upstream generated small disturbances propagate downstream at exponentially amplified amplitude with a space-dependent speed. For small excitation disturbances, the amplitude of the resulting waveform is proportional to the disturbance amplitude. However, selective sustained external excitation (even at small amplitudes) can alter the behaviour of the system and lead to time-dependent flow. Two different types of excitation are imposed at the inflow: (i) monochromatic waves with frequency chosen to be either close to or very far from the shear layer frequency; and (ii) random noise. It is found that for small-amplitude monochromatic excitation the flow acquires a time-periodic behaviour if perturbed close to the shear layer frequency, whereas the flow remains unaffected for high values of the excitation frequency. On the other hand, for the random noise as input, an unsteady behaviour is obtained with a fundamental frequency close to the shear layer frequency.
The influence of wall cooling on hypersonic boundary-layer separation and stability
Authors: Cassel K. W. , Ruban A. I. , Walker J. D. A.
Published: April 2006

The effect of wall cooling on hypersonic boundary-layer separation near a compression ramp is considered. Two cases are identified corresponding to the value of the average Mach number $\overline{M}$ across the upstream boundary layer approaching the compression ramp. The flow is referred to as supercritical for $\overline > 1$ and subcritical for $\overline{M} < 1$. The interaction is described by triple-deck theory, and numerical results are given for both cases for various ramp angles and levels of wall cooling. The effect of wall cooling on the absolute instability described recently by Cassel, Ruban & Walker (1995) for an uncooled wall is of particular interest; a stabilizing effect is observed for supercritical boundary layers, but a strong destabilizing influence occurs in the subcritical case. Wall cooling also influences the location and size of the separated region. For supercritical flow, progressive wall cooling reduces the size of the recirculating-flow region, the separation point moves downstream, and upstream influence is diminished. In contrast for the subcritical case downstream influence is reduced with increased cooling. In either situation, a sufficient level of wall cooling eliminates separation altogether for the ramp angles considered. The present numerical results closely confirm the strong wall cooling theory of Kerimbekov, Ruban & Walker (1994).
Subharmonic resonance of short internal standing waves by progressive surface waves
Authors: Hill D. F. , Foda M. A.
Published: April 2006

Experimental evidence and a theoretical formulation describing the interaction between a progressive surface wave and a nearly standing subharmonic internal wave in a two-layer system are presented. Laboratory investigations into the dynamics of an interface between water and a fluidized sediment bed reveal that progressive surface waves can excite short standing waves at this interface. The corresponding theoretical analysis is second order and specifically considers the case where the internal wave, composed of two oppositely travelling harmonics, is much shorter than the surface wave. Furthermore, the analysis is limited to the case where the internal waves are small, so that only the initial growth is described. Approximate solution to the nonlinear boundary value problem is facilitated through a perturbation expansion in surface wave steepness. When certain resonance conditions are imposed, quadratic interactions between any two of the harmonics are in phase with the third, yielding a resonant triad. At the second order, evolution equations are derived for the internal wave amplitudes. Solution of these equations in the inviscid limit reveals that, at this order, the growth rates for the internal waves are purely imaginary. The introduction of viscosity into the analysis has the effect of modifying the evolution equations so that the growth rates are complex. As a result, the amplitudes of the internal waves are found to grow exponentially in time. Physically, the viscosity has the effect of adjusting the phase of the pressure so that there is net work done on the internal waves. The growth rates are, in addition, shown to be functions of the density ratio of the two fluids, the fluid layer depths, and the surface wave conditions.
A mechanism for rivulet formation in heated falling films
Authors: Joo S. W. , Davis S. H. , Bankoff S. G.
Published: April 2006

We consider a long-wave evolution equation that governs a draining film on a heated plate and hence is capable of describing both surface-wave and thermocapillary instabilities. When the flow and heat transfer rates are moderate, we show, via weakly nonlinear analysis of a truncated system and numerical simulation of the full nonlinear evolution equation, that coupled temporal instabilities can create surface deformations that lead to an array of rivulets aligned with the flow. This work thus demonstrates a mechanism of rivulet formation based solely on instability phenomena.
Shear-induced radial segregation in bidisperse suspensions
Authors: Krishnan Gokul P. , Beimfohr Shannon , Leighton David T.
Published: April 2006

In this paper, we discuss experimental evidence for radial particle segregation in a parallel-plate geometry. The motion of coloured tracer particles of a size different from the bulk suspension is followed as a function of time. The tracer particles are seen to experience a constant drift velocity independent of their radial position. This is in addition to the random-walk motion arising from their interactions with other particles in the suspension. These observations are found to be consistent with the shear-induced migration model of Leighton & Acrivos (1987 a,b) as well as the tracer diffusivity measurements of Phan & Leighton (1996). In the experiments of Abbott et al. (1991), it was observed that larger particles migrated radially outward to regions of lower shear stress in a wide-gap Couette device. In our experiments large tracers were also observed to migrate radially outward. In this case, however, the radial migration resulted in migration to regions of higher shear stress, contrary to expectations. This apparent discrepancy is explained in terms of a model that incorporates both the stress-induced migration of earlier studies and a curvature-induced migration flux (which in turn is shear-induced) as an opposing effect.
Taylor—Couette instability of travelling waves with a continuous spectrum
Authors: Moulic S. Ghosh , Yao L. S.
Published: April 2006

The nonlinear evolution of a continuous spectrum of travelling waves resulting from the growth of unstable disturbances in circular Couette flow has been investigated. Numerical solution of the governing integro-differential equations for different initial conditions shows that the equilibrium states of Taylor-vortex, wavy-vortex or spiralvortex flows are not unique, but depend on the initial disturbance. The presence of multiple solutions at a fixed Reynolds number for a given Taylor–Couette geometry has been known since Coles’ seminal contribution in 1965. The current study indicates that the equilibrium state of flows on a stable bifurcation branch is a natural consequence of nonlinear wave resonance and is dependent on the initial conditions. The resulting wavenumber can take any value within an accessible finite band. Since such multiple solutions have also been found numerically for mixed-convection flows and experimentally for several other flows, there is evidence to support the conclusion that a non-uniqueness in the sense of Coles is a generic property for all fluid flows.
The flow field due to a body in impulsive motion
Authors: Mei Renwei , Lawrence Christopher J.
Published: April 2006

An asymptotic analysis for the long-time unsteady laminar far wake of a bluff body due to a step change in its travelling velocity from U1 to U2 is presented. For U1 [ges ] 0 and U2 > 0, the laminar wake consists of a new wake of volume flux Q2 corresponding to the current velocity U2, an old wake of volume flux Q1 corresponding to the original velocity U1, and a transition zone that connects these two wakes. The transition zone acts as a sink (or a source) of volume flux (Q2 – Q1) and is moving away from the body at speed U2. Streamwise diffusion is negligible in the new and old wakes but a matched asymptotic expansion that retains the streamwise diffusion is required to determine the vorticity transport in the transition zone. A source of volume flux Q2 located near the body needs to be superposed on the unsteady wake to form the global flow field around the body. The asymptotic predictions for the unsteady wake velocity, unsteady wake vorticity, and the global flow field around the body agree well with finite difference solutions for flow over a sphere at finite Reynolds numbers. The long-time unsteady flow structures due to a sudden stop (U2 = 0) and an impulsive reverse (U1U2 < 0) of the body are analysed in detail based on the asymptotic solutions for the unsteady wakes and the finite difference solutions. The elucidation of the long-time behaviour of such unsteady flows provides a framework for understanding the long-time particle dynamics at finite Reynolds number.
A full-scale numerical study of interfacial instabilities in thin-film flows
Authors: Ramaswamy B. , Chippada S. , Joo S. W.
Published: April 2006

Surface wave instabilities in a two-dimensional thin draining film are studied by a direct numerical simulation of the full nonlinear system. A finite element method is used with an arbitrary Lagrangian–Eulerian formulation to handle the moving boundary problem. Both temporal and spatial stability analysis of the finite-amplitude nonlinear wave regimes are done. As the wavenumber is decreased below the linear cut-off wavenumber, supercritical sinusoidal waves occur as reported earlier from weakly nonlinear analysis and experiments. Further reduction in wavenumber makes the Fourier spectrum broad-banded resulting in solitary humps. This transition from nearly sinusoidal permanent waveforms to solitary humps is found to go through a quasi-periodic regime. The phase boundaries for this quasi-periodic regime have been determined through extensive numerical parametric search. Complex wave interaction processes such as wave merging and wave splitting are discussed. In the exhaustive numerical simulations performed in this paper, no wave-breaking tendency was observed, and it is speculated that the complex wave-interaction processes such as wave merging and wave splitting curb the tendency of the film to break.
Magnetohydrodynamic flow in a right-angle bend in a strong magnetic field
Authors: Stieglitz R. , Barleon L. , BüHler L. , Molokov S.
Published: April 2006

The magnetohydrodynamic (MHD) flow through sharp 90° bends of rectangular cross-section, in which the flow turns from a direction almost perpendicular to the magnetic field to a direction almost aligned with the magnetic field, is investigated experimentally for high values of the Hartmann number M and of the interaction parameter N. The bend flow is characterized by strong three-dimensional effects causing a large pressure drop and large deformations in the velocity profile. Since such bends are basic elements of fusion reactors, the scaling laws of magnetohydrodynamic bends flows with the main flow parameters such as M and N as well as the sensitivity to small magnetic field inclinations are of major importance. The obtained experimental results are compared to those of an asymptotic theory.

In the case where one branch of the bend is perfectly aligned with the magnetic field good agreement between the results obtained by the asymptotic model and by the experiments was found at high M ≈ 8 × 10 and N ≈ 105 for pressure as well as for electric potentials on the duct surface. At lower values of N a significant influence of inertia has been detected. The pressure drop due to inertial effects was found to scale with N−1/3. The same – 1/3-power dependency on N has been found in the vicinity of the bend for the electric potentials at walls aligned with the magnetic field. At walls with a significant normal component of the field an influence neither of the Hartmann number nor of the interaction parameter has been found. This suggests that the inertial part of the pressure drop arises from inertial side layers, whereas the core flow remains inertialess and inviscid. A variation of the Hartmann number is of negligible influence compared to inertia effects with respect to pressure drop and surface potential distribution. The viscous part of the pressure drop scales with M−½.

Changes of the magnetic field orientation with respect to the bend lead in general to different flow patterns in the duct, because the electric current paths are changed. The inertia–electromagnetic interaction determines the magnitude of the inertial part of the pressure drop, which scales with N−1/3 for any magnetic field orientation. The dependence of the pressure drop on M remains proportional to M−½. With increasing M and N the measured data tend to those predicted by the asymptotic model. Local measurements within the liquid metal exhibit discrepancies with the model predictions for which no adequate explanation has been found. But they show that below a critical interaction parameter flow regions exist in which the flow is time dependent. These regions are highly localized, whereas the flow in the rest of the bend remains steady.
Nonlinear dynamics of vorticity waves in the coastal zone
Authors: Shrira Victor I. , Voronovich Vyacheslav V.
Published: April 2006

Vorticity waves are wave-like motions occurring in various types of shear flows. We study the dynamics of these motions in alongshore shear currents in situations where it can be described within weakly nonlinear asymptotic theory. The principal mechanism of vorticity waves can be interpreted as potential vorticity conservation with the background vorticity gradient provided both by the mean current shear and the variation of depth. Under the assumption that the mean potential vorticity distibution is monotonic in the cross-shore direction, the nonlinear stage of the dynamics of weakly nonlinear vorticity waves, long in comparison with the current cross-shore scale, is found to be governed by an evolution equation of the generalized Benjamin–Ono type. The dispersive terms are given by an integro-differential operator with the kernel determined by the large-scale cross-shore depth and current dependence. The derived equations form a wide new class of nonlinear evolution equations. They all tend to the Benjamin–Ono equation in the short-wave limit, while in the long-wave limit their asymptotics depend on the specific form of the depth and current profiles. For a particular family of model bottom profiles the equations are ‘intermediate’ between Benjamin–Ono and Korteweg–de Vries equations, but are distinct from the Joseph intermediate equation. Solitary-wave solutions to the equations for these depth profiles are found to decay exponentially. Taking into account coastline inhomogeneity or/and alongshore depth variations adds a linear forcing term to the evolution equation, thus providing an effective generation mechanism for vorticity waves.
Dynamics of drop formation from a capillary in the presence of an electric field
Authors: Zhang Xiaoguang , Basaran Osman A.
Published: April 2006

This paper reports an experimental study of the effects of an externally applied electric field on the dynamics of drop formation in the dripping mode from a vertical metal capillary. The fluid issuing out of the capillary is a viscous liquid, the surrounding ambient fluid is air, and the electric field is generated by establishing a potential difference between the capillary and a horizontal, circular electrode of large radius placed downstream of the capillary outlet. By means of an ultra-high-speed video system that is capable of recording up to 12000 frames per second, special attention is paid to the dynamics of the liquid thread that connects the primary drop that is about to detach and fall from the capillary to the rest of the conical liquid mass that is hanging from it. The experiments show that as the strength of the electric field increases, the volume of the primary drop decreases whereas the maximum length attained by the thread increases. The reduction in the volume of primary drops and the increase in the length of threads occur because the effective electromechanical surface tension of the fluid interface falls as the field strength rises. For the highly conducting drops of aqueous NaCl solutions studied in this work, the increase in thread length is due solely to the rising importance of normal electric stress relative to the falling importance of surface tension. However, as the conductivity of the drop liquid decreases, the thread length is further increased on account of the stabilizing influence exerted by the increasing electric shear stress that acts on the charged liquid–gas interface. Two new phenomena are also reported that have profound implications for electrohydrodynamics and practical applications. First, it is shown that whereas the liquid thread always ruptures at its downstream end in the absence of an applied electric field or when the field strength is low, it ruptures at its upstream end when the field strength is sufficiently high. Since satellite drops are produced directly from the thread once both of its ends have ruptured, the change in the mechanism of breakup with field strength influences the dynamics and fate of satellite drops. Second, it is demonstrated that the generation of satellites, which are often undesirable in applications, can be suppressed by the judicious application of an electric field. This is accomplished by using a field of moderate strength to induce charges of the opposite sign on the nearby surfaces of the satellite drop and the liquid that remains pendant from the tube following thread rupture. At high field strengths, induced charge effects are too weak to compete with net charge effects: the satellite is repelled by the pendant drop and falls under gravity as a distinct entity.
Self-similarity of decaying two-dimensional turbulence
Authors: Bartello Peter , Warn Tom
Published: April 2006

Simulations of decaying two-dimensional turbulence suggest that the one-point vorticity density has the self-similar form
$P_\omega \sim t\;\;f(\omega t)$

implied by Batchelor's (1969) similarity hypothesis, except in the tails. Specifically, similarity holds for |ω| < ωm, while pω falls off rapidly above. The upper bound of the similarity range, ωm, is also nearly conserved in high-Reynolds-number hyperviscosity simulations and appears to be related to the average amplitude of the most intense vortices (McWilliams 1990), which was an important ingredient in the vortex scaling theory of Carnevale et al. (1991).

The universal function f also appears to be hyperbolic, i.e.
$f(x) \sim c/2\vert x \vert^{1+q_c}$
for |x| > x*, where qc = 0.4 and x* = 70, which along with the truncated similarity form implies a phase transition in the vorticity moments
$\langle \vert \omega\vert ^q\rangle \sim \left\{\begin{array}{ll}
c_q t^{-q}, & -1 < q < q_c\cr
c(q - q_c)^{-1} \omega _m^{q-q_c} t^{-q_c} & q > q_c,
\end{array}\right.$
between the self-similar 'background sea' and the coherent vortices. Here Cq and c are universal. Low-order moments are therefore consistent with Batchelor's similarity hypothesis whereas high-order moments are similar to those predicted by Carnevale et al. (1991). A self-similar but less well-founded expression for the energy spectrum is also proposed.

It is also argued that ωc = x*/t represents 'mean sea-level', i.e. the (average) threshold separating the vortices and the sea, and that there is a spectrum of vortices with amplitudes in the range (ωs,ωm). The total area occupied by vortices is also found to remain constant in time, with losses due to mergers of large-amplitude vortices being balanced by gains due to production of weak vortices. By contrast, the area occupied by vortices above afixed threshold decays in time as observed by McWilliams (1990).
Experimental studies of a distorted turbulent spot in a three-dimensional flow
Authors: Jahanmiri M. , Prabhu A. , Narasimha R.
Published: April 2006

We report here on the results of a series of experiments carried out on a turbulent spot in a distorted duct to study the effects of a divergence with straight streamlines preceded by a short stretch of transverse streamline curvature, both in the absence of any pressure gradient. It is found that the distortion produces substantial asymmetry in the spot: the angles at which the spot cuts across the local streamlines are altered dramatically (in contradiction of a hypothesis commonly made in transition zone modelling), and the Tollmien–Schlichting waves that accompany the wing tips of the spot are much stronger on the outside of the bend than on the inside. However there is no strong effect on the internal structure of the spot and the eddies therein, or on such propagation characteristics as overall spread rate and the celerities of the leading and trailing edges. Both lateral streamline curvature and non-homogeneity of the laminar boundary layer into which the spot propagates are shown to be strong factors responsible for the observed asymmetry. It is concluded that these factors produce chiefly a geometric distortion of the coherent structure in the spot, but do not otherwise affect its dynamics in any significant way.
A numerical study of the rheological properties of suspensions of rigid, non-Brownian fibres
Authors: Mackaplow Michael B. , Shaqfeh Eric S. G.
Published: April 2006

Using techniques developed in our previous publication (Mackaplow et al. 1994), we complete a comprehensive set of numerical simulations of the volume-averaged stress tensor in a suspension of rigid, non-Brownian slender fibres at zero Reynolds number. In our problem formulation, we use slender-body theory to develop a set of integral equations to describe the interfibre hydrodynamic interactions at all orders. These integral equations are solved for a large number of interacting fibres in a periodically extended box. The simulations thus developed are an accurate representation of the suspensions at concentrations up to and including the semidilute regime. Thus, large changes in the suspensions properties can be obtained. The Theological properties of suspensions with concentrations ranging from the dilute regime, through the dilute/semi-dilute transition, and into the semi-dilute regime, are surprisingly well predicted by a dilute theory that takes into account two-body interactions. The accuracy of our simulations is verified by their ability to reproduce published suspension extensional and shear viscosity data for a variety of fibre aspect ratios and orientation distributions, as well as a wide range of suspension concentrations.
Living in the Shadow of Death: Gangs, Violence and Social Order in Urban Nicaragua, 1996–2002
Authors: RODGERS DENNIS
Published: April 2006

This article explores the dynamics of the youth gang (pandilla) phenomenon in contemporary urban Nicaragua, drawing on longitudinal ethnographic research conducted with a Managua pandilla in 1996–97 and in 2002. Pandillas and their violent practices are conceived as constituting a form of local social structuration in the face of broader conditions of high crime, insecurity, and socio-political breakdown. This form of ‘street-level politics’ changed significantly between 1997 and 2002, however, evolving from a form of collective social violence to a more individually and economically motivated type of brutality. This transformation is related to wider structural processes, which are described as coming together and precipitating a form of ‘social death’ in contemporary Nicaragua.