Volume 16, Issue 1, January 2004
 LETTERS


Transient energy growth for the Lamb–Oseen vortex
View Description Hide DescriptionThe transient evolution of infinitesimal flow disturbances which optimally induce algebraic growth in the Lamb–Oseen (Gaussian) vortex is studied using a directadjoint technique. This optimal perturbation analysis reveals that the Lamb–Oseen vortex allows for intense amplification of kinetic energy for twodimensional and threedimensional perturbations of azimuthal wavenumber In both cases, the disturbances experiencing the most growth initially take the form of concentrated spirals at the outer periphery of the vortex which rapidly excite bending waves within the vortex core. In the limit of large wavelengths, the optimal perturbation leads to arbitrarily large growths via an original scenario combining the Orr mechanism with vortex induction.

A laboratory observation of the surface temperature and velocity distributions on a wavy and windy air–water interface
View Description Hide DescriptionTemperature and velocity distributions of the water surface are examined experimentally with infrared imaging techniques. The surface velocity is determined from the movement of the pattern of surface temperature cell. It is found that the mean wind drift is about much less than the widely cited measurements of Although many complicated thermal and dynamical processes control the surface temperature, we found that the probability distribution function (PDF) of the standardized water surface temperature does not vary significantly with wind speed. The increasing nonlinear effects of wave orbital motions and wave breaking on surfacemotion are shown by the similarity and trend of change in the PDFs of the water surface velocity normalized by the wave orbital velocity at different wind speeds. The standard deviation of the speed distribution increases with the wind speed while the basic skewed distribution shape remains.
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 ARTICLES


Size segregation in rapid, granular flows with continuous size distributions
View Description Hide DescriptionTwodimensional (dissipative) moleculardynamics simulations of particulate mixtures with Gaussian and lognormal particle size distributions are employed to gain insight on the segregation behavior of these mixtures when exposed to a granular temperature gradient. Simulations are performed for a collection of smooth, inelastic, hard disks (with constant material density and a constant coefficient of restitution) confined between two walls set to constant, though unequal, granular temperatures. As a result, a gradient in granular temperature develops across the domain. In general, particles of all sizes are found to move toward regions of low granular temperature (overall segregation). Species segregation is also observed. Specifically, large particles demonstrate a higher affinity for the lowtemperature regions, and thus accumulate in these cool regions to a greater extent than their smaller counterparts. Furthermore, the local particle size distribution remains of the same form (Gaussian or lognormal) as the overall (including all particles) size distribution. In addition, the behaviors of Gaussian size distributions and narrow lognormal distributions are found to be quite similar.

The effect of insoluble surfactant at dilute concentration on drop breakup under shear with inertia
View Description Hide DescriptionDirect numerical simulations are conducted with a volumeoffluid continuous surface stress algorithm. The linear equation of state is used to characterize the effects of an insoluble surfactant at low concentration on a drop in strong shear. The drop and the surrounding liquid have the same viscosity and density. Surfactant migration induces a Marangoni force that acts toward the drop center. For low inertia, viscous force opposes the Marangoni force, so that a stationary drop with surfactant is more elongated and less tilted than without. The addition of surfactant promotes breakup, lowering the critical capillary number. The first daughter drops are smaller than for the case of clean drops. For high inertia, the Marangoni force retracts the drop and retards breakup. The local values of surface tension are computed during drop evolution.

Fluid–body interaction in the presence of uniform vorticity and density gradient
View Description Hide DescriptionWe consider the case of a rigid or deformable body moving in a linear shear flow of an inviscid, incompressible and inhomogeneous fluid with a uniform density gradient. The body is impulsively introduced into the nonuniform ambient flow field possessing timedependent vorticity. In order to make the analysis amenable, it is further assumed that the size of the body is small with respect to the inhomogeneity of the ambient flow. By integrating the Euler equation it is shown that analytic expressions can be obtained for the hydrodynamical reactions (forces and moments) acting on the body which determine its trajectories. In addition to the traditional purely inertial quadratic terms, three new types of interaction modes are thus revealed: Vorticityinertia, density gradientinertia, and vorticitydensity gradient. The first two modes have been considered separately just recently but the third one is presented here for the first time. It is finally demonstrated that all three modes of interaction can be obtained from a relatively straightforward unified approach.

Instability of a rotating thread in a second immiscible liquid
View Description Hide DescriptionWe consider the surfacetensiondriven instability of a cylindrical liquid column surrounded by a second liquid when the entire system is rotating. Our calculations are in the limit that the flows in both the liquid thread and the outer fluid are viscously dominated, and include the centripetal and Coriolis forces; the effect of the Coriolis force has not previously been studied in the case that the flows in both liquids are viscous. We present numerical results of a linear temporal stability analysis, and an analytical result valid in the largeTaylornumber limit. We also use the boundaryintegral method to consider the evolution and instability of a finite cylindrical thread, which then relaxes when the rotation rate is reduced. These results are discussed in connection with recent experimental observations.

On the Faraday instability in a surfactantcovered liquid
View Description Hide DescriptionThe formation of standing waves at the surfactantcovered free surface of a verticallyvibrated liquid is analyzed in this work. Assuming that the surfactants are insoluble and the effects of lateral boundaries are negligible, linear stability analysis and Floquet theory are applied to the governing equations. A recursion relation involving the temporal modes of the freesurface deflection and surfactant concentration variation results, and is solved to determine the critical vibration amplitude needed to excite the standing waves and the corresponding critical wave number. It is found that the critical vibration amplitude shows a minimum with respect to the Marangoni number, meaning that surfactants can potentially lower the value of the critical amplitude relative to its value for an uncontaminated free surface. The critical wave number, however, is found to be an increasing function of the Marangoni number. Analysis of the phaseangle difference between the freesurface deflection and the surfactant concentration variation suggests that the minimum in the critical amplitude arises because the Marangoni flows help produce a velocity field near the free surface similar to that which would be present if the liquid were inviscid.

A nonlinear atomization model based on a boundary layer instability mechanism
View Description Hide DescriptionAn axisymmetric boundary element method has been used to simulate primary atomization of a liquid jet including the effects of the orifice passage geometry. A ring vortex is placed at the orifice exit plane; its strength and location are uniquely determined by the local boundary layer characteristics at this locale. Using this methodology, nonlinear simulations are performed that include hundreds of individual atomization events. A linear analysis due to Ponstein is used to estimate the number of droplets formed from individual rings of fluid which are pinched from the periphery of the jet. Numerous results have been obtained to assess the effects of fluid parameters and orifice design on droplet sizes and atomization characteristics. Predicted droplet sizes show agreement with some limited experimental data.

The hydrodynamics of an oscillating porous sphere
View Description Hide DescriptionWe determine the hydrodynamics of a rigid, weakly permeable sphere undergoing translational oscillations in an incompressible Newtonian fluid. We check using homogenization and scaling arguments that the flow inside the sphere may be modeled by Darcy’s law and that the Beavers–Joseph–Saffman (BJS) boundary condition still applies for oscillatory flows, provided the frequency of oscillation is not too high. The BJS boundary condition introduces a slip velocity and to leading order in where k is the particle permeability and a is the radius, the particle may be regarded as impermeable with a slip length independent of frequency. Under these circumstances we solve for the flow field, pressure distribution and drag explicitly and show their behavior for 0⩽ε⩽0.05 and frequencies relevant to electroacoustics (1–10 MHz). From the drag we find the leading order corrections due to particle permeability of the pseudosteady drag, Basset force and added mass.

The effects of quadratic drag on the inverse cascade of twodimensional turbulence
View Description Hide DescriptionWe explore the effects of a quadratic drag, similar to that used in bulk aerodynamic formulas, on the inverse cascade of homogeneous twodimensional turbulence. If a twodimensional fluid is forced at a relatively small scale, then an inverse cascade of energy will be generated that may then be arrested by such a drag at large scales. Both scaling arguments and numerical experiments support the idea that in a statistically steady state the length scale of energycontaining eddies will not then depend on the energy input to the system; rather, the only external parameter that defines this scale is the quadratic drag coefficient itself. A universal form of the spectrum is suggested, and numerical experiments are in good agreement. Further, the turbulent transfer of a passive tracer in the presence of a uniform gradient is well predicted by scaling arguments based solely on the energy cascade rate and the nonlinear drag coefficient.

Vapor flows condensing at incidence onto a plane condensed phase in the presence of a noncondensable gas. II. Supersonic condensation
View Description Hide DescriptionThis paper is the second part of the study of a steady flow of a vapor in a half space condensing onto a plane condensed phase of the vapor at incidence in the presence of a noncondensable gas near the condensed phase. The aim of the study is to clarify the behavior of the vapor and noncondensable gas on the basis of kinetic theory under the assumption that the molecules of the noncondensable gas are mechanically identical with those of the vapor. In the first part [S. Taguchi et al., Phys. Fluids 15, 689 (2003)], the case of subsonic condensation, where the Mach number corresponding to the flowvelocity component perpendicular to the condensed phase at infinity is less than unity, is considered. In the present second part, the case of supersonic condensation is investigated in detail on the same lines as the first part.

Effects of rotation on turbulent mixing: Nonpremixed passive scalars
View Description Hide DescriptionWe study by direct numerical simulations the effects of uniform solidbody rotation on passive scalar mixing in turbulent flow, with a focus on the unsteady problem of nonpremixed scalars in forced rotating turbulence with isotropic initial conditions in the velocity field. The expectation of reduced mixing as a result of reduced spectral transfer is readily verified in several aspects, including slower decay rates for the scalar variance, increased scalar mixing times, and slower relaxation of the probability density function from its initially bimodal form to a nearGaussian shape. Spectral transfer in the scalar field is shown to be dominated by very lowwavenumber velocity modes, and strongly suppressed at higher wavenumbers in the scalar field. Considerable departure from local isotropy is observed in the scalar gradient fluctuations, which are smaller in the direction along the axis of rotation where there is less mixing than in the orthogonal plane. A partial explanation is given in terms of the influence of a modified turbulence velocity structure on directional characteristics of spectral transfer, which leads to anisotropy in the scalar gradient spectra as well as onedimensional spectra of the scalar field. The observed anisotropy is stronger than that for the velocity field, especially for high rotation rates, and is more pronounced at Schmidt number 1 than at 1/8. A reduction in intermittency compared with nonrotating turbulence is also observed.

Gaseous slip models based on the Langmuir adsorption isotherm
View Description Hide DescriptionOn the basis of Langmuir’s theory of adsorption of gases on solids, a robust gaseous slip model is presented. The concept of accommodation coefficient and the difference of gas particles are explained within the new framework. It turned out that the Langmuir model recovers the Maxwellmodel in the firstorder approximation in the case of the microchannel gas flow. In order to validate the new approach, the model is applied to problems of technical interests: pressuredriven microchannel gas flow and low Reynolds number gas flow past a sphere. With the help of previous theoretical and experimental results it is shown that with an adjustable parameter the model in lowspeed creeping regime with moderate Knudsen numbers yields a prediction in qualitative agreement with the data.

Compressibility effects on the Rayleigh–Taylor instability growth between immiscible fluids
View Description Hide DescriptionThe linearized Navier–Stokes equations for a system of superposed immiscible compressible ideal fluids are analyzed. The results of the analysis reconcile the stabilizing and destabilizing effects of compressibility reported in the literature. It is shown that the growth rate n obtained for an inviscid, compressible flow in an infinite domain is bounded by the growth rates obtained for the corresponding incompressible flows with uniform and exponentially varying density. As the equilibrium pressure at the interface increases (less compressible flow),n increases towards the uniform density result, while as the ratio of specific heats γ increases (less compressible fluid), n decreases towards the exponentially varying density incompressible flow result. This remains valid in the presence of surface tension or for viscous fluids and the validity of the results is also discussed for finite size domains. The critical wavenumber imposed by the presence of surface tension is unaffected by compressibility. However, the results show that the surface tension modifies the sensitivity of the growth rate to a differential change in γ for the lower and upper fluids. For the viscous case, the linearized equations are solved numerically for different values of and γ. It is found that the largest differences compared with the incompressible cases are obtained at small Atwood numbers. The most unstable mode for the compressible case is also bounded by the most unstable modes corresponding to the two limiting incompressible cases.

Twophase Couette–Taylor flow: Arrangement of the dispersed phase and effects on the flow structures
View Description Hide DescriptionThis study investigates the mutual interactions between a continuous and a dispersed phase (noncondensable or condensable) in the wellknown Couette–Taylor flow between two concentric cylinders at low Reynolds numbers, where the outer cylinder is immobilized. In this experiment, the turbulent structures take place progressively. The noncondensable dispersed phase (air) is introduced either by ventilation, generated by agitation of a free surface situated at the top of the gap between the two cylinders. The condensable dispersed phase is generated by cavitation due to a drop in pressure. Comparisons are made between the single phase flow patterns and those observed in ventilated or cavitating flow. Two particular arrangements of the dispersed phase are experimentally evident, according to the Reynolds number of the flow. For low Reynolds numbers, bubbles are trapped in the core of the Taylor cells, whereas they migrate to the outflow regions near the inner cylinder for higher Reynolds numbers. Assessment of the forces applied to the bubbles and computation of their equilibrium position can act as a base in describing the bubble capture. When bubbles are located near the wall in the outflow region, it is found that the three first instabilities are strongly influenced by the dispersed phase. The cavitating flow is also characterized by an earlier appearance of the third instability.

A note on powerlaw scaling in a Taylor–Couette flow
View Description Hide DescriptionRecent studies [Lathrop et al., Phys. Rev. A 46, 6390 (1992); Lewis et al., Phys. Rev. E 59, 5457 (1999)] on Taylor–Couette flow, where the inner cylinder is rotating and the outer one is at rest, show that, despite earlier predictions [Wendt, Ing. Arch. 4, 557 (1933); Tong et al., Phys. Rev. Lett. 65, 2780 (1990)], the nondimensional torque does not follow a fixed powerlaw scaling (i.e., where α is a constant value) for Here, we perform simultaneous flow visualization and high precision torque measurements of the same flow configuration using a Haake RS75 Rheometer to establish if this is also true in the lower Reynolds number range Results show that, although α varies with the Reynolds number, it can be approximated reasonably well with a constant value for and for The latter finding is in good agreement with that of Wendt [Ing. Arch. 4, 557 (1933)]. A possible explanation for the differences with the results of earlier studies is provided in this paper.

Phaseresolved flow field produced by a vibrating cantilever plate between two endplates
View Description Hide DescriptionThe flow field created by a vibrating cantilever plate was studied using phaseresolved particle imagevelocimetrymeasurements as well as a smoke visualization technique. The cantilever is 38 mm wide, 31 mm long, and is actuated by a piezoelectric material. It is immersed in initially quiescent air, i.e., no free stream velocity is imposed on the system. The cantilever’s vibration frequency in these experiments is set to 180 Hz—the fundamental natural frequency of cantilever. The flow is quite complicated in nature. During each vibration cycle a pair of counterrotating vortices is generated. A high velocity region is formed between these two counterrotating vortices in which the maximum velocity is nearly four times the maximum speed of the free end of the plate. Front and rear walls are installed at the lateral edges of the cantilever initially with the thought of making the flow quasitwodimensional. While a twodimensional flow field is indeed formed near the cantilever tip, the flow downstream of the tip is complex and threedimensional. Phaseresolved velocity fields for five different amplitudes are acquired in detail. The corresponding Reynolds numbers based on the cantilever tip vibration amplitude and the tip speed are 146, 126, 101, 72, and 43, respectively. The nondimensionalized velocity fields are almost identical and symmetric near the tip, but asymmetric flows are formed and the nondimensionalized velocity fields are no longer identical further downstream of the tip. The time dependent circulation of each vortex is calculated by applying the general theory of oscillating, deformable airfoils and compared to the experimental circulation.

Miscible density fingering of chemical fronts in porous media: Nonlinear simulations
View Description Hide DescriptionNonlinear interactions between chemical reactions and Rayleigh–Taylor type density fingering are studied in porous media or thin HeleShaw cells by direct numerical simulations of Darcy’s law coupled to the evolution equation for the concentration of a chemically reacting solute controlling the density of misciblesolutions. In absence of flow, the reactiondiffusion system features stable planar fronts traveling with a given constant speed and width When the reactant and product solutions have different densities, such fronts are buoyantly unstable if the heavier solution lies on top of the lighter one in the gravity field. Density fingering is then observed. We study the nonlinear dynamics of such fingering for a given model chemical system, the iodatearsenious acidreaction.Chemical reactions profoundly affect the density fingering leading to changes in the characteristic wavelength of the pattern at early time and more rapid coarsening in the nonlinear regime. The nonlinear dynamics of the system is studied as a function of the three relevant parameters of the model, i.e., the dimensionless width of the system expressed as a Rayleigh number the Damköhler number and a chemical parameter which is a function of kinetic constants and chemical concentration, these two last parameters controlling the speed and width of the stable planar front. For small the asymptotic nonlinear dynamics of the fingering in the presence of chemical reactions is one single finger of stationary shape traveling with constant nonlinear speed and mixing zone This is drastically different from pure density fingering for which fingers elongate monotonically in time. The asymptotic finger has axial and transverse averaged profiles that are selfsimilar in unit lengths scaled by Moreover, we find that scales as For larger tip splittings are observed.

Equivalence of two different integral representations of droplet distribution moments in condensing flow
View Description Hide DescriptionIt is proved that two different and independently derived integral representations of droplet size distribution moments encountered in the literature are equivalent and, moreover, consistent with the general dynamic equation that governs the droplet size distribution function. One of these representations consists of an integral over the droplet radius while the other representation consists of an integral over time. The proof is based on analytical solution of the general dynamic equation in the absence of coagulation but in the presence of both growth and nucleation. The solution derived is explicit in the droplet radius, which is in contrast with the literature where solutions are presented along characteristics. This difference is essential for the equivalence proof. Both the case of nonconvected vapor as well as the case of convected vapor are presented.

Double diffusion natural convection in a rectangular enclosure filled with binary fluid saturated porous media: The effect of lateral aspect ratio
View Description Hide DescriptionThreedimensional, double diffusion,natural convection in a rectangular enclosure filled with binary fluid saturating porous media is investigated numerically. The effect of lateral aspect ratio on the heat, mass, and momentum transfer is systematically studied. For certain range of parameters, it is interesting to find that the flow patterns may duplicate themselves as the lateral aspect ratio increases by integer factors, which is similar to longitudinal roll formation in a Rayleigh–Bénard problem. For the mentioned range of parameters the change in the lateral aspect ratio has no influence on the rates of heat and mass transfer. However, for other ranges of parameters, the flow exhibits completely different patterns and the rates of heat and mass transfer are influenced drastically compared with that of cubic cavity. In general, the flow of three and twodimensional results are difficult to justify, especially if interest is on the flow structure.
