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Volume 12, Issue 5, May 2000
 LETTERS


Geometry and scale relationships in high Reynolds number turbulence determined from threedimensional holographic velocimetry
View Description Hide DescriptionHolographic particle imagevelocimetrymeasurements of a fully developed turbulent flow in a square duct are used for examining the relative alignment between filtered vorticity, strainrate and subgridscale stress tensors. Similar to DNS and previous measurements, the filtered vorticity has a preferred alignment with the intermediate strainrate eigendirection. Contrary to typical eddy viscosity models, the most compressive strainrate and most extensive subgridscale stress eigendirections have a strongly preferred relative orientation of The orientations of the other eigendirections are less deterministic and more complex.

The kinetic energy spectrum of the twodimensional enstrophy turbulence cascade
View Description Hide DescriptionA direct numerical simulation of forced twodimensional turbulence with hyperviscosity is performed at resolution A stage is reached at which the flux of enstrophy from large to small scales is approximately constant in time. The cubic and quintic relations for the thirdorder velocity structure function derived by Lindborg [J. Fluid Mech. 388, 259 (1999)] are verified. The calculated kinetic energy spectrum in the constant enstrophy flux range has the form where is the enstrophy dissipation. This is in accordance with the prediction of Kraichnan [Phys. Fluids 10, 1417 (1970)] and Batchelor [Phys. Fluids 12, II233 (1969)]. The logarithmic correction, suggested by Kraichnan [J. Fluid Mech. 47, 525 (1970)], is not present in the calculated spectrum.

 ARTICLES


Transient response of a capsule subjected to varying flow conditions: Effect of internal fluid viscosity and membrane elasticity
View Description Hide DescriptionThe transient deformation of an axisymmetric capsule freely suspended in a pure straining flow is studied, for sudden or periodic variations of the intensity of the rate of strain. The particle Reynolds number is supposed to be very small and the problem is solved numerically by means of the boundary integral method. In the case of a sudden start of flow, the time response of the capsule can be approximated by an exponential function, and is thus characterized by only two parameters: the equilibrium deformation and the characteristic response time The respective influence of viscosity ratio, membrane elasticity, and initial particle geometry is analyzed. The dynamic response of the capsule subjected to periodic variations of the rate of strain is also studied. The response time appears to be an appropriate parameter to estimate the capsule adaptability to changing flow conditions.

Structure, density, and velocity fluctuations in quasitwodimensional nonBrownian suspensions of spheres
View Description Hide DescriptionNonBrownian sedimenting suspensions exhibit density and velocityfluctuations. We have performed experiments on a quasitwodimensional counterflow stabilized suspension of 2000 spherical particles, namely a liquid–solid fluidized bed in a Hele–Shaw cell. This twodimensional suspension displays a uniform concentration but the particle radial distribution function and the fluctuations of the particle number in a subvolume of the suspension suggest that the microstructure is far from being random. We have also measured the velocityfluctuations of a test particle and the fluctuations of the mean particle velocity in a subvolume. It happens that the relation between velocity and concentration fluctuations in a subvolume can be deduced from a balance between buoyancy and parietal friction forces.

Particle clustering due to hydrodynamic interactions
View Description Hide DescriptionDynamic simulations of an isotropic suspension of particles in a viscous gas are performed. The energy in the suspension decays with time as a result of viscous dissipation in the gas. The rate of viscous dissipation in sufficiently energetic suspensions, those with a high Stokes number, is consistent with the theory of Sangani et al. [J. Fluid Mech. 313, 309–341 (1996)] for homogeneous hardsphere suspensions. As the suspension loses energy, the dissipation rate decreases dramatically and the particles cluster as indicated by the presence of many more near neighbors than would be found in a hard sphere distribution.

Asymptotic estimates for twodimensional sloshing modes
View Description Hide DescriptionEstimates for the natural frequencies of linear twodimensional sloshing modes in channels composed of two planar walls, either opening or closing at the bottom, are derived using conformal transformation techniques. The results are asymptotic in the sense that the wavelength of surface waves are assumed small in comparison to the horizontal extent of the quiescent free surface. An experiment was constructed to test the asymptotic theory for odd sloshing modes in two symmetric and three asymmetric containers. Good corroboration between measurement and theory is obtained when the increase in frequency due to surface tension, not accounted for in the theoretical analysis, is estimated and removed from the experimental data.

On the stability limits of long nonaxisymmetric cylindrical liquid bridges
View Description Hide DescriptionThere is a selfsimilar solution for the stability limits of long, almost cylindrical liquid bridges between equal disks subjected to both axial and lateral accelerations. The stability limits depend on only two variables; the socalled reduced axial, and lateral Bond numbers. A novel experimental setup that involved rotating a horizontal cylindrical liquid bridge about a vertical axis of rotation was designed to test the stability limits predicted by the selfsimilar solution. Analytical predictions compared well with both numerical and experimental results.

Stabilization of electrically conducting capillary bridges using feedback control of radial electrostatic stresses and the shapes of extended bridges
View Description Hide DescriptionElectrically conducting, cylindrical liquid bridges in a densitymatched, electrically insulating bath were stabilized beyond the Rayleigh–Plateau (RP) limit using electrostatic stresses applied by concentric ring electrodes. A circular liquid cylinder of length L and radius R in real or simulated zero gravity becomes unstable when the slenderness exceeds The initial instability involves the growth of the socalled (2, 0) mode of the bridge in which one side becomes thin and the other side rotund. A modesensing optical system detects the growth of the (2, 0) mode and an analog feedback system applies the appropriate voltages to a pair of concentric ring electrodes positioned near the ends of the bridge in order to counter the growth of the (2, 0) mode and prevent breakup of the bridge. The conducting bridge is formed between metal disks which are grounded. Three feedback algorithms were tested and each found capable of stabilizing a bridge well beyond the RP limit. All three algorithms stabilized bridges having S as great as 4.3 and the extended bridges broke immediately when feedback was terminated. One algorithm was suitable for stabilization approaching where the (3, 0) mode is predicted to become unstable for cylindrical bridges. For that algorithm the equilibrium shapes of bridges that were slightly under or over inflated corresponded to solutions of the Young–Laplace equation with negligible electrostatic stresses. The electrical conductivity of the bridge liquid need not be large. The conductivity was associated with salt added to the aqueous bridge liquid.

The doublehelical branch structure of fixed contact line liquid bridge equilibria
View Description Hide DescriptionAttempts to stabilize the fixed contact line cylindrical liquid bridge have generally implicitly assumed that it was related to stable equilibria in a continuous manner. An examination of the branch structure of equilibria demonstrates that for longer liquid bridges, the cylinder becomes separate from normally stable equilibria and hence likely cannot be stabilized by a continuous perturbation. All axisymmetric equilibria for a fixed contact line liquid bridge of fixed moderate length in the absence of applied forces (zero gravity, no spin) are found to lie on a single semiinfinite bridged double helix. This helix breaks repeatedly as the length of the liquid bridge is increased, separating the stable truncated sphere state from the generally desirable cylindrical state. This structural change appears to explain why several approaches to stabilization of long cylindrical liquid bridges beyond the classical Plateau–Rayleigh limit have been largely unsuccessful over the past few decades. The first breakage of the helix, when liquid bridge length equals 9.0973 times radius, corresponds roughly to the maximum length of cylindrical liquid bridge achieved experimentally via a perturbative applied force (using acoustic radiation pressure). An examination of the deformations of the helix under gravity reveals that for moderate length liquid bridges at small Bond number, all axisymmetric equilibria lie on a single unbroken branch which forms a single (unbridged) semiinfinite double helix. Combined effects of gravity and length are investigated as well, resulting in multiple disconnected loops of equilibria.

Fixed boundary dual liquid bridges in zero gravity
View Description Hide DescriptionThe equilibria and stability of fixed contact line dual liquid bridges are considered. The dual liquid bridges considered consist of two fixed length single bridges joined by an open channel so that both bridges are in pressure equilibrium. The system is simplified by requiring all bounds to be of equal radius, and also by neglecting gravity or other applied forces. The dual liquid bridge is found to be generally more stable than a single bridge of equal length in the fixed pressure case, but less stable in the fixed volume case. The maximum length of dual liquid bridge in the fixed pressure case is double that for a single bridge, 7.4547 times the radius. In the fixed volume case, a rupture of the stability envelope leads to ranges of boundary conditions for which there are no stable dual liquid bridges of any volume. One exception to fixed volume destabilization is the cylindrical dual bridge. The maximum length attainable for a cylinder is 8.9868 times the radius, which not coincidentally is also the secondary stability limit for a single fixed volume cylinder (beyond the classical limit of times the radius). The results suggest that any application which pumps fluid through a series of cylindrical liquid bridges would be most favorable using a dual liquid bridge with pressureconstrained pumping.

Direct numerical simulations of the elliptic instability of a vortex pair
View Description Hide DescriptionThe objective of this study is to perform direct numerical simulations (DNS) of the threedimensional shortwavelength elliptic instability developing in a counterrotating vortex pair, and to reproduce numerically a watertank experiment. The main features of the elliptic instability are recovered by the simulations. In particular, the spatial structure and the temporal evolution of the most amplified perturbation mode during the linear regime correspond to both experimental measurements and theoretical predictions. The longterm evolution is also simulated, and the stages leading to transition to turbulence are described. Some elements resulting from simulations related to the interaction between the shortwavelength elliptic instability and the longwavelength Crow instability are provided.

The nonlinear development of threedimensional disturbances at hyperbolic stagnation points: A model of the braid region in mixing layers
View Description Hide DescriptionThe properties of steady, twodimensional flows with spatially uniform strain rates and rotation rates where and hence open, hyperbolic, streamlines are investigated. By comparison with a high resolution numerical simulation of a free shear layer, such a quadratic flow is an idealized local model of the “braid” region which develops between neighboring saturated Kelvin–Helmholtz billows in an unstable free shear layer. A class of exact threedimensional nonlinear solutions for spatially periodic perturbations is derived. These solutions satisfy the condition that the amplitude of the timevarying wave number of the perturbation remains bounded in time, and hence that pressure plays an asymptotically small role in their dynamics. In the limit of long time, the energy of such perturbations in an inviscid flow grows exponentially, with growth rate and the perturbation pressure plays no significant role in the dynamic evolution. This asymptotic growth rate is not the maximal growth rate accessible to general perturbations, which may grow transiently at rate independently of However, almost all initial conditions lead to, at most, transient growth and hence finite asymptotic perturbation energy in an inviscid flow as time increases, due to the finite amplitude effects of pressure perturbations.Perturbations which do undergo significant transient growth take the form of streamwisealigned perturbationvorticity which varies periodically in the spanwise direction. By comparison of this local model with a numerically simulated mixing layer, appropriately initialized “hyperbolic instabilities” appear to have significantly larger transient growth rates than an “elliptical instability” of the primary billow core. These hyperbolic instabilities appear to be a simple model for the spanwise periodic perturbations which are known to lead to the nucleation of secondary rib vortices in the braid region between adjacent billow cores.

Instabilities in a laterally heated liquid layer
View Description Hide DescriptionWe study a convection problem in a freesurface container with lateral walls heated at different temperatures. The effects of buoyancy and thermocapillarity are taken into account. A basic convective state appears as soon as a temperature gradient with nonzero horizontal component is applied. This state bifurcates to new convective solutions for further values on the imposed temperature gradient. Our main contribution is to consider this situation in a container finite not only in the vertical coordinate, but also in the direction of the gradient. The third dimension is kept infinite. We determine the basic state, compare it with the usual one of parallel flow approach, and study its stability. When the lateral heating walls are considered new results are found. The boundary conditions on the top surface are no longer restricted to those that allow analytical solutions for the basic state, and we have considered for the heat interchange with the atmosphere the Newton law with constant ambient temperature. Due to this boundary condition, two control parameters related to the temperature field appear. One is the temperature difference between lateral walls as in previous research, and the new one is the temperature difference between the atmosphere and the cold wall. After a stationary bifurcation a threedimensional structure which along the infinite direction consists of longitudinal rolls grows. On the vertical plane along the gradient direction this structure is nonhomogeneous but located near the hot side. These features coincide with observations of recent experiments.

Numerical study of thermoacoustic waves in an enclosure
View Description Hide DescriptionThe behavior of thermoacoustic waves in a nitrogenfilled twodimensional cavity is numerically studied in order to investigate how these waves may be used as an effective heat removal mechanism. The compressible, unsteady Navier–Stokes equations were solved for a series of initial conditions by combining a fluxcorrected transport algorithm for convection with models for temperaturedependent viscosity and thermal conduction. By considering a onedimensional test problem and comparing the results to existing data, the accuracy of the present numerical method is verified. In the problems considered, the vertical walls of a cavity were heated or cooled to generate the thermoacoustic waves. Both impulsive and gradual changes of the wall temperatures were considered. When the vertical wall was heated impulsively and nonuniformly, the waves induced twodimensional flows within the enclosure. The observed thermoacoustic waves oscillate and eventually decay due to viscous and heat dissipation.

Absolute and convective instability character of slender viscous vortices
View Description Hide DescriptionMotivated by the need for effective vortex control, the character of absolute and convective instabilities (AI/CI) of incompressible and highMach number slender vortices with axialvelocity deficit is studied. Attention is focused on the disturbance modes which lead to the maximum absolute growth rate, and their dependence on flow conditions such as axialflow profile, Reynolds number, and Mach number. A significant difference between the AI/CI and temporalinstability characters of the vortices occurs as the axial velocity deficit reduces. These theoretical results are applied to the flow region where vortex breakdown happens. It is found that the breakdown region is absolutely unstable, where waves are dominated by the spiral disturbance with lowest azimuthal wave number, in reasonable agreement with measurement.

Leewave breaking over obstacles in stratified flow
View Description Hide DescriptionExperimental results are presented on the leewave breaking process which occurs at low Froude numbers when uniform and strongly stratified flow approaches twodimensional and quasi twodimensional Gaussianshaped obstacles. It was found that the leewave breaking process is essentially independent of the twodimensional and the quasi twodimensional shape of the obstacles. The attainment of the critical condition where the steepening wave becomes statically unstable does not mark a threshold to breakdown. Instead, the wave remains dynamically stable for several buoyancy periods, overturning into an “S”shape with maximum overturning reaching about 55° past the vertical. It is observed that the primary instability forms a quasi twodimensional spanwise vortex over the central portion of the obstacles and is mainly shear driven. The quasi twodimensional spanwise vortex persists for a few buoyancy periods before undergoing a threedimensional convective instability, similar to a Rayleigh–Taylor instability. As a result, an array of toroidal vortex structures aligned parallel to the obstacle crest forms. These vortex structures of size are inclined into the flow yielding three strong components of vorticity.

Nonlinear geostrophic adjustment, cyclone/anticyclone asymmetry, and potential vorticity rearrangement
View Description Hide DescriptionWithin the context of the rotating shallow water equations, it is shown how initially unbalanced states possessing certain symmetries dynamically evolve to lose those symmetries during nonlinear geostrophic adjustment. Using conservation law methods, it is demonstrated that the adjustment of equal and opposite (circular) mass imbalances results in a balanced end state where cyclones are stronger than anticyclones; the reverse holds true for momentum imbalances. In both cases, the degree of this asymmetry is shown to be directly proportional to the amount of initial imbalance (a measure of the nonlinearity occurring during timedependent adjustment). On the other hand, the degree of asymmetry is maximal for imbalances of Rossby deformation scale. As for the potential vorticity, it is shown that its final profile can be noticeably different from its initial one; from an Eulerian perspective, this rearrangement is not confined to uniform shifts of potential vorticity fronts. Direct 2D numerical initial value problems confirm the asymmetry in the predicted final states and establish a relatively fast time scale for adjustment to complete. The robustness of these results is confirmed by studying, in addition, the adjustment of elliptical mass imbalances. The numerical integrations reveal that, during geostrophic adjustment, potential vorticity rearrangement occurs irreversibly on a fast wave time scale.

Oscillatory shear layers in source driven flows in an unbounded rotating fluid
View Description Hide DescriptionThe internal structure of oscillatory shear layers occurring in rapidly rotating fluids is investigated. An analytical treatment is possible for flows driven by a distribution of sources in an unbounded fluid. “Shear layers” are shown to be envelopes of wave packets of inertial waves. The modification of these layers by a magnetic field and a stable stratification are also studied.

Local pressuretransport structure in a convective atmospheric boundary layer
View Description Hide DescriptionLocal pressuretransport structure in a convective atmospheric boundary layer is studied through largeeddy simulation and a conditional sampling technique. Two cases are simulated: A freeconvection boundary layer and a sheared convective boundary layer with where is the boundary layer height and L is the Monin–Obukhov length. Results show that pressuretransport flux tends to increase turbulent kinetic energy in the lower part of the sheared convective boundary layer. Furthermore, the rootmeansquare resolved pressure fluctuation and the resolved negative pressure fluctuation due to become much stronger in the sheared case. Flow visualization demonstrates that strong pressure transport is physically correlated with vortical structure embedded within largescale updrafts. A conditional sampling technique is applied to study statistical characteristics of resolved fields surrounding strong pressure transport events. The conditional field reveals a boundarylayerscale roll circulation with a largescale thermal located at its center and characterized by a negative pressure minimum. Conditional pressure transport is a gain in the lower part of the pressure minimum and a loss in the upper part. The conditional vorticity lines converge to four distinct regions relative to the thermal: Largescale horseshoeshaped vorticity lines are wrapped around the thermal; smallscale archshaped vorticity lines drag behind the thermal; helical vorticity lines originate in the thermal core; and converging vorticity lines are found above the neck of the largescale horseshoeshaped vorticity lines. These regions roughly coincide with conditional negative momentum fluxes. We thus conclude that local pressuretransport structures are spatially associated with localized low pressure regions and strong vertical vorticity fluctuations, being embedded within thermals and advected along with largescale convective rolls.

Anticonvection in systems with heat release on the interface
View Description Hide DescriptionThe generation of anticonvection in the presence of heat sources (or sinks) homogeneously distributed on the interface in layers with finite thickness, is studied in the framework of linear theory. The general transformation formula, which predicts the existence of anticonvection in any fluid system, is derived. This formula is applied to a system of real fluids.
