Volume 15, Issue 8, August 2003
 LETTERS


Suppression of the Richtmyer–Meshkov instability in the presence of a magnetic field
View Description Hide DescriptionWe present numerical evidence from two dimensional simulations that the growth of the Richtmyer–Meshkov instability is suppressed in the presence of a magnetic field. A bifurcation occurs during the refraction of the incident shock on the density interface which transports baroclinically generated vorticity away from the interface to a pair of slow or intermediate magnetosonic shocks. Consequently, the density interface is devoid of vorticity and its growth and associated mixing is completely suppressed.

On threedimensional quasiperiodic Floquet instabilities of twodimensional bluff body wakes
View Description Hide DescriptionPrevious studies dealing with Floquet secondary stability analysis of the wakes of circular and square crosssection cylinders have shown that there are two synchronous instability modes, with long (mode A) and short (mode B) spanwise wavelengths. At intermediate wavelengths another mode arises, which reaches criticality at Reynolds numbers higher than modes A or B. Here we concentrate on these intermediatewave number modes for the wakes of circular and square cylinders. It is found that in both cases these modes possess complexconjugate pair Floquet multipliers, and can be combined to produce either standing or traveling waves. Both these states are quasiperiodic.

The filtering analog of the variational multiscale method in largeeddy simulation
View Description Hide DescriptionThe variational multiscale method introduced by Hughes et al. [Comput. Visual. Sci. 3, 47 (2000)] is extended to the classic filtering approach in largeeddy simulation. The role of the Germano identity in the formulation is precisely indicated. Multiscale methods based on standard eddyviscosity models are related to (anisotropic) hyperviscosity models under certain conditions. Several models are tested and found to be as accurate as the standard dynamic model, while the implementations are more simple. Finally, the turbulent stress tensor is reformulated, such that filter and derivative in the filtered equations can be treated as a single operator.
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 ARTICLES


Scaling in threedimensional and quasitwodimensional rotating turbulent flows
View Description Hide DescriptionWe have made velocitytime seriesmeasurements (using hot film probes) and velocity field measurements (using particle imagevelocimetry) on turbulent flow in a rotating annulus. For low annulus rotation rates the Rossby number was of order unity and the flow was threedimensional (3D), but at high rotation rates the Rossby number was only about 0.1, comparable to the value for oceans and the atmosphere on large length scales. The low Rossby number (quasigeostrophic) flow was nearly twodimensional (2D), as expected from the Taylor–Proudman theorem. For the 3D flow we found that the probability distribution function (PDF) for velocity differences along the direction of the flow, was Gaussian for large separations d and nonGaussian (with exponential tails) for small d, as has been found for nonrotating turbulent flows. However, for low Rossby number flow, the PDF was selfsimilar (independent of d) and nonGaussian. The exponents characterizing the structure functions, were obtained by the extended selfsimilarity method. For 3D flow the exponents departed from with increasing p, as has been found for turbulence in nonrotating flows, while for the quasi2D turbulent flow, the exponents increased linearly with p, as expected for a selfsimilar flow. We applied the βtest of the hierarchical structure model [She and Lévêque, Phys. Rev. Lett. 72, 336 (1994)] and found that β remained constant at as the rotation was increased from the 3D to the 2D regime; this indicates that both the quasi2D and 3D flows are highly intermittent. The PIVimages provided another indication of the intermittency—both the quasi2D and 3D flows had coherent vortices which could be distinguished from the background flow. We also applied the γtest of the hierarchical structure model and found that γ increased from 0.18 for the 3D flow to 0.34 for the quasi2D flow; the latter value is in accord with expectation for selfsimilar turbulence. We conclude that our rotating 3D flow is similar to nonrotating turbulent flows, while the rotating quasi2D turbulence is different from both the 3D rotating turbulence and from nonrotating 2D turbulence studied in other experiments.

The decay of homogeneous anisotropic turbulence
View Description Hide DescriptionWe present the results of a numerical investigation of threedimensional decaying turbulence with statistically homogeneous and anisotropic initial conditions. We show that at large times, in the inertial range of scales: (i) isotropic velocity fluctuations decay selfsimilarly at an algebraic rate which can be obtained by dimensional arguments; (ii) the ratio of anisotropic to isotropic fluctuations of a given intensity falls off in time as a power law, with an exponent approximately independent of the strength of the fluctuation; (iii) the decay of anisotropic fluctuations is not selfsimilar, their statistics becoming more and more intermittent as time elapses. We also investigate the early stages of the decay. The different shorttime behavior observed in two experiments differing by the phase organization of their initial conditions gives a new hunch on the degree of universality of smallscale turbulence statistics, i.e., its independence of the conditions at large scales.

Threedimensional instability of isolated vortices
View Description Hide DescriptionWe study the threedimensional stability of the family of vortices introduced by Carton and McWilliams [Mesoscale/Synoptic Coherent Structures in GeophysicalTurbulence, edited by Nikhoul and Jamart (Elsevier, New York, 1989)] describing isolated vortices. For these vortices, the circulation vanishes outside their core over a distance depending on a single parameter, the steepness α. We proceed to the direct numerical simulation of the linear impulse response to obtain both temporal and spatiotemporal instability results. In the temporal instability framework, growth rates are calculated as a function of the axial wavenumber k and the azimuthal wavenumber m. The stability analysis is performed at a Reynolds number of Re=667. It is shown that the most unstable mode is the axisymmetric mode regardless of the steepness parameter in the investigated range. When the steepness α is increased the band of unstable azimuthal modes widens, i.e., larger m are destabilized. The study of the spatiotemporal spreading of the wave packet shows that the mode is always the fastest traveling mode, for all studied values of the steepness parameter.

The temporally filtered Navier–Stokes equations: Properties of the residual stress
View Description Hide DescriptionRecent interest in the development of a unifying framework among direct numerical simulations, largeeddy simulations, and statistically averaged formulations of the Navier–Stokes equations, provides the motivation for the present paper. Toward that goal, the properties of the residual (subgridscale) stress of the temporally filtered Navier–Stokes equations are carefully examined. This includes the frameinvariance properties of the filtered equations and the resulting residual stress. Causal timedomain filters, parametrized by a temporal filter width 0<Δ<∞, are considered. For several reasons, the differential forms of such filters are preferred to their corresponding integral forms; among these, storage requirements for differential forms are typically much less than for integral forms and, for some filters, are independent of Δ. The behavior of the residual stress in the limits of both vanishing and infinite filter widths is examined. It is shown analytically that, in the limit Δ→0, the residual stress vanishes, in which case the Navier–Stokes equations are recovered from the temporally filtered equations. Alternately, in the limit Δ→∞, the residual stress is equivalent to the longtime averaged stress, and the Reynoldsaveraged Navier–Stokes equations are recovered from the temporally filtered equations. The predicted behavior at the asymptotic limits of filter width is further validated by numerical simulations of the temporally filtered forced, viscous Burger’s equation. Finally, finite filter widths are also considered, and both a priori and a posteriori analyses of temporal similarity and temporal approximate deconvolution models of the residual stress are conducted for the model problem.

Threedimensional linear stability analysis of liddriven magnetohydrodynamic cavity flow
View Description Hide DescriptionWe present numerical results of a linear threedimensional (3D) stability analysis of a square liddriven cavity flow under the influence of an external magnetic field which is directed parallel to the lid. The Lorentz force has a strong influence on the twodimensional (2D) flow structure, thereby changing number, shape and strength of the eddies. The resulting 3D stability behavior is rather complex since it depends on the 2D flow structure. Although increasing magnetic fields are able to damp 3D instability, in a parameter region around several branches of the neutral stability curve do exist. For a fixed Reynolds number in this range, an increase of the magnetic field strength may lead to a transition from a stable flow to an oscillatory unstable one.

Loworder dynamical model for lowPrandtl number fluid flow in a laterally heated cavity
View Description Hide DescriptionBy applying proper orthogonal decomposition (method of snapshots) to low Prandtl number fluid flow in a laterally heated cavity of dimensions in characteristic basic modes have been extracted. Using Galerkin projection of the governing equations on these basic modes, a lowdimensional dynamical model (set of ordinary differential equations) was constructed. Some results obtained from the loworder model are presented and compared with those calculated by direct numerical simulation (DNS). The factors influencing the reliability of the loworder model such as the length of the reference signal, the snapshot density, the number of modes chosen for Galerkin projection, the characteristic velocity, and the chosen expansions for velocity and temperature are discussed. It is found that the loworder model can exactly reproduce the results obtained by DNS at the design conditions (i.e., for the Grashof and Prandtl numbers at which the basic modes have been obtained). The model can also fairly well approach the DNS results in a domain around these conditions. Nevertheless, it seems that such models have to be used with care and that, in any case, they can qualitatively predict the DNS results only in a not very large range around the design conditions.

Feedback control of a flow past a cylinder via transverse motion
View Description Hide DescriptionThe instability giving rise to the Karman vortex street in a flow past a circular cylinder is responsible for the occurrence of large amplitude oscillations in the lift. In this work, we seek to control the instability via active feedback control by means of transverse displacements of the solid structure. Our investigation is based on Föppl’s fourdimensional potential flow model of point vortices. A feedback controller capable of manipulating the flow in order to maintain zero lift at all times is derived analytically by using perturbation methods and asymptotic expansions. We then apply the controller to the viscousflow by direct numerical simulation of the flow based on the twodimensional Navier–Stokes equations and show that our control algorithm is capable of keeping the lift close to zero in the impulsively started viscousflow and, therefore, controllingvortex shedding. Computations are carried out at the Reynolds numbers Re=100 and Re=200.

Coherent vortices and kinetic energy ribbons in asymptotic, quasi twodimensional fplane turbulence
View Description Hide DescriptionThis paper examines coherent vortices and spatial distributions of energy density in asymptotic states of numerically simulated, horizontally homogeneous, doubly periodic, quasi twodimensional fplane turbulence. With geophysical applications in mind, the paper progresses from freely decaying twodimensional flow to freely decaying equivalent barotropic flow, freely decaying twolayer quasigeostrophic (QG) flow, and, finally, statistically steady twolayer QG turbulence forced by a baroclinically unstable mean flow and damped by bottom Ekman friction. It is demonstrated here that, with suitable elaborations, a twovortex state having a sinhlike potential vorticity/streamfunction scatter plot arises in all of these systems. This extends, at least qualitatively, previous work in inviscid and freely decaying twodimensional flows to flows having stratification, forcing, and dissipation present simultaneously. Potential vorticity steps and ribbons of kinetic energy are shown to form in freely decaying equivalent barotropic flow and in the equivalent barotropic limit of baroclinically unstable flow, which occurs when Ekman damping is strong. Thus, contrary to expectations, strong friction can under some circumstances create rather than hinder the formation of sharp features. The ribbons are present, albeit less dramatically, in moderately damped baroclinically unstable turbulence, which is arguably a reasonable model for midocean mesoscale eddies.

Dynamics of twodimensional Rayleigh–Taylor bubbles for fluids with a finite density contrast
View Description Hide DescriptionWe study the motion of a twodimensional coherent structure of bubbles and spikes in the Rayleigh–Taylor instability for fluids with a finite density contrast in the case of a small amplitude initial perturbation. The theoretical and numerical solutions for the system of conservation laws are found, and the dynamics of the bubble shape and velocity in the nonlinear regime is described. Good agreement between theory and simulations is achieved. A comparison to earlier models is performed.

The influence of a uniform magnetic field on the Soret coefficient of magnetic nanoparticles
View Description Hide DescriptionInvestigations were made to determine the Soret coefficient of magnetic particles in a ferrofluid. Based on zero field measurements from which the Soret coefficient is quantitatively determined with a theoretical model, the influence of a magnetic field on this parameter will be shown. A clear dependence of the intensity of the thermodiffusive process on the magnetic field strength could be found. In addition it could be shown, that the direction of the field relative to the driving temperature gradient has a significant influence too. In particular a change of the sign of the Soret coefficient was observed if the magnetic field is orientated parallel to the temperature gradient.

Vortex breakdown in compressible flows in pipes
View Description Hide DescriptionThe effects of compressibility on vortexflows in pipes have been analyzed using both the axisymmetric Navier–Stokes (NS) equations and the quasicylindrical (QC) approximation. Numerical simulations of the full axisymmetric NS equations show that, for sufficiently large values of the Reynolds number,compressible flows present a multiplicity of steadystate solutions in a range of values of the swirl strength. The sensitivity of the vortexflow structure to the parameters of the problem: Mach number,Reynolds number, velocity profiles at the pipe entrance and pipe geometry has been also investigated. In particular, the critical swirl parameter necessary for the occurrence of vortex breakdown has been determined as a function of both the Mach number and the axial momentum of the flow at the pipe entrance. For large Reynolds number, the results of the QC approximation are found to be in good agreement with those of the full NS simulations. These results show that the upstream propagation of the sound waves seems to have a negligible influence on vortex breakdown and give support to the use of the QC approximation for the study of some aspects of the compressible swirling flows.

Integral space–time scales in turbulent wall flows
View Description Hide DescriptionA direct numerical simulation of the Navier–Stokes equations is used to compute the space–time correlations of velocity fluctuations in a turbulent channel flow. By examining the autocorrelation of the longitudinal wall shearstress as a function of the streamwise and temporal separations, the effects of the limited extent of the computational domain when (artificial) periodic boundary conditions are used can be described and quantified. A time scale similar to the conventional integral scale but statistically related to the life time of the turbulent structures is computed from spatiotemporal data. The convection velocity, defined as the direction in the ξ,τ plane where the autocorrelations have their maximum at vanishingly small time delay, is computed as a function of the distance from the wall, and compared with the data available in the literature. Based on autocorrelations, the accuracy within which Taylor’s hypothesis is verified is quantitatively assessed. Last, the effect of the spatial discretization on the statistical characterization of wall turbulence is discussed.

Dispersion of passive tracers in the direct enstrophy cascade: Experimental observations
View Description Hide DescriptionThe paper reports a statistical analysis of the separation of pairs in the enstrophy cascade, in a twodimensional flow. The flow is produced experimentally, using electromagnetic forcing. Two regimes of separation are found. At early times (i.e., within two integral times) the separation process is exponential, following Lin’s law [J. T. Lin, J. Atmos. Sci. 29, 394 (1972)]. In this range of time, the probability density functions(PDFs) of separations are selfsimilar in time, developing stretched exponential tails, and one may define a Lagrangiancorrelation time. Above two integral times, an algebraic regime takes place, with exponential tails for the PDFs of the separations, and selfsimilar Lagrangiancorrelation functions. The present work thus confirms the existence of two regimes, by analyzing a number of statistical quantities including the Lagrangian PDF and the temporal Lagrangiancorrelation functions which so far, were left undetermined for the Batchelor regime.

Protein labeling reactions in electrochemical microchannel flow: Numerical simulation and uncertainty propagation
View Description Hide DescriptionThis paper presents a model for twodimensional electrochemicalmicrochannel flow including the propagation of uncertainty from model parameters to the simulation results. For a detailed representation of electroosmotic and pressuredriven microchannel flow, the model considers the coupled momentum, species transport, and electrostatic field equations, including variable zeta potential. The chemistry model accounts for pHdependent protein labeling reactions as well as detailed buffer electrochemistry in a mixed finiterate/equilibrium formulation. Uncertainty from the model parameters and boundary conditions is propagated to the model predictions using a pseudospectral stochastic formulation with polynomial chaos (PC) representations for parameters and field quantities. Using a Galerkin approach, the governing equations are reformulated into equations for the coefficients in the PC expansion. The implementation of the physical model with the stochastic uncertainty propagation is applied to proteinlabeling in a homogeneous buffer, as well as in twodimensional electrochemicalmicrochannel flow. The results for the twodimensional channel show strong distortion of sample profiles due to ion movement and consequent buffer disturbances. The uncertainty in these results is dominated by the uncertainty in the applied voltage across the channel.

Closedloop Lagrangian separation control in a bluff body shear flow model
View Description Hide DescriptionWe show how the location of Lagrangian coherent structures, such as unstable manifolds of Lagrangian separation points, can be controlled via feedback control in twodimensional shear flows. Such control can be used, for instance, to guide fuel transport into designated regions of the flame in a combustor. Motivated by this example, we consider an unsteady vortex model for flow past a bluff body, and create unstable manifolds in this model at prescribed locations by applying control along the boundary. We find that oscillating the newly created unstable manifolds in 1:1 resonance with the von Kármán vortex shedding frequency enhances mixing in the wake significantly.

Lift forces on a cylindrical particle in plane Poiseuille flow of shear thinning fluids
View Description Hide DescriptionLift forces on a cylindrical particle in plane Poiseuille flow of shear thinningfluids are investigated by direct numerical simulation. Previous works on this topic for Newtonian fluids show that the twodimensional channel can be divided into alternating regions defined by the stability of the particle’s equilibrium. We observe stability regions with the same pattern in flows of shear thinningfluids and study the effects of shear thinningproperties on the distribution of the stability regions. Joseph and Ocando [J. Fluid Mech. 454, 263 (2002)] analyzed the role of the slip velocity and the angular slip velocity on migration and lift in plane Poiseuille flow of Newtonian fluids. They concluded that the discrepancy where is the angular slip velocity at equilibrium, changes sign across the equilibrium position. In this paper we verify that this conclusion holds in shear thinningfluids. Correlations for lift forces may be constructed by analogy with the classical lift formula of aerodynamics and the proper analogs of and Γ in the present context are and Using dimensionless parameters, the correlation is a power law near the wall and a linear relation (which can be taken as a power law with the power of one) near the centerline. The correlations are compared to analytical expressions for lift forces in the literature and we believe that the correlations capture the essence of the mechanism of the lift force. Our correlations for lift forces can be made completely explicit provided that the correlations relating and to prescribed parameters are obtained.

An explicit filtering method for large eddy simulation of compressible flows
View Description Hide DescriptionA method for large eddy simulation(LES) is presented in which the subgridscale modeling is achieved by filtering procedures alone. The procedure derives from a deconvolution model, and provides a mathematically consistent approximation of unresolved terms arising from any type of nonlinearity. The formal steps of primary filtering to obtain LES equations, approximate deconvolution to construct the subgrid model term and regularization are combined into an equivalent filter. This filter should be an almost perfect low pass filter below a cutoff wavenumber and then fall off smoothly. The procedure has been applied to a pressurevelocityentropy formulation of the Navier–Stokes equations for compressible flow to perform LES of two fully developed, turbulent, supersonic channel flows and has been assessed by comparison against direct numerical simulation (DNS) data. Mach numbers are 1.5 and 3.0, and Reynolds numbers are 3000 and 6000, respectively. Effects of filter cutoff location, choice of differentiation scheme (a fifthorder compact upwind formula and a symmetric sixthorder compact formula were used), and grid refinement are examined. The effects are consistent with, and are readily understood by reference to, filtering characteristics of the differentiation and the LES filter. All simulations demonstrate a uniform convergence towards their respective DNS solutions.
