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May 2000

Volume 12, Issue 5, pp. 941-1261

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Geometry and scale relationships in high Reynolds number turbulence determined from three-dimensional holographic velocimetry

Bo Tao, Joseph Katz, and Charles Meneveau

Phys. Fluids 12, 941 (2000); http://dx.doi.org/10.1063/1.870348 (4 pages) | Cited 27 times

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Holographic particle image velocimetry measurements of a fully developed turbulent flow in a square duct (ReH = mathcH/ν = 1.2×105, η = 100 μm, Reλ = 310) are used for examining the relative alignment between filtered vorticity, strain-rate and subgrid-scale stress tensors. Similar to DNS and previous measurements, the filtered vorticity has a preferred alignment with the intermediate strain-rate eigendirection. Contrary to typical eddy viscosity models, the most compressive strain-rate and most extensive subgrid-scale stress eigendirections have a strongly preferred relative orientation of 34°. The orientations of the other eigendirections are less deterministic and more complex. © 2000 American Institute of Physics.
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47.27.-i Turbulent flows
42.40.-i Holography
47.80.-v Instrumentation and measurement methods in fluid dynamics
47.32.C- Vortex dynamics

The kinetic energy spectrum of the two-dimensional enstrophy turbulence cascade

Erik Lindborg and Krister Alvelius

Phys. Fluids 12, 945 (2000); http://dx.doi.org/10.1063/1.870379 (3 pages) | Cited 25 times

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A direct numerical simulation of forced two-dimensional turbulence with hyperviscosity is performed at resolution 40962. 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 third-order 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 E(k) = Kϵω2/3k−3, where ϵω 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. © 2000 American Institute of Physics.  
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47.27.-i Turbulent flows
47.32.C- Vortex dynamics
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Transient response of a capsule subjected to varying flow conditions: Effect of internal fluid viscosity and membrane elasticity

A. Diaz, N. Pelekasis, and D. Barthès-Biesel

Phys. Fluids 12, 948 (2000); http://dx.doi.org/10.1063/1.870349 (10 pages) | Cited 16 times

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The 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 D∞ and the characteristic response time τs. 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 τs appears to be an appropriate parameter to estimate the capsule adaptability to changing flow conditions. © 2000 American Institute of Physics.
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47.55.Kf Particle-laden flows

Structure, density, and velocity fluctuations in quasi-two-dimensional non-Brownian suspensions of spheres

F. Rouyer, D. Lhuillier, J. Martin, and D. Salin

Phys. Fluids 12, 958 (2000); http://dx.doi.org/10.1063/1.870350 (6 pages) | Cited 9 times

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Non-Brownian sedimenting suspensions exhibit density and velocity fluctuations. We have performed experiments on a quasi-two-dimensional counter-flow stabilized suspension of 2000 spherical particles, namely a liquid–solid fluidized bed in a Hele–Shaw cell. This two-dimensional 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 velocity fluctuations 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. © 2000 American Institute of Physics.
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47.55.Kf Particle-laden flows
47.15.-x Laminar flows
82.70.Kj Emulsions and suspensions

Particle clustering due to hydrodynamic interactions

Jonathan J. Wylie and Donald L. Koch

Phys. Fluids 12, 964 (2000); http://dx.doi.org/10.1063/1.870351 (7 pages) | Cited 12 times

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Dynamic 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 hard-sphere 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. © 2000 American Institute of Physics.
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82.70.Kj Emulsions and suspensions
64.75.-g Phase equilibria

Asymptotic estimates for two-dimensional sloshing modes

Anthony M. J. Davis and Patrick D. Weidman

Phys. Fluids 12, 971 (2000); http://dx.doi.org/10.1063/1.870352 (8 pages) | Cited 1 time

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Estimates for the natural frequencies of linear two-dimensional 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. © 2000 American Institute of Physics.
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47.35.-i Hydrodynamic waves
47.60.-i Flow phenomena in quasi-one-dimensional systems

On the stability limits of long nonaxisymmetric cylindrical liquid bridges

F. Zayas, J. I. D. Alexander, J. Meseguer, and J.-F. Ramus

Phys. Fluids 12, 979 (2000); http://dx.doi.org/10.1063/1.870353 (7 pages) | Cited 8 times

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There is a self-similar 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 so-called 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 self-similar solution. Analytical predictions compared well with both numerical and experimental results. © 2000 American Institute of Physics.
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68.03.Cd Surface tension and related phenomena
47.20.Dr Surface-tension-driven instability

Stabilization of electrically conducting capillary bridges using feedback control of radial electrostatic stresses and the shapes of extended bridges

Mark J. Marr-Lyon, David B. Thiessen, Florian J. Blonigen, and Philip L. Marston

Phys. Fluids 12, 986 (2000); http://dx.doi.org/10.1063/1.870354 (10 pages) | Cited 16 times

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Electrically conducting, cylindrical liquid bridges in a density-matched, 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 S = L/2R exceeds π. The initial instability involves the growth of the so-called (2, 0) mode of the bridge in which one side becomes thin and the other side rotund. A mode-sensing 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 S = 4.493… 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. © 2000 American Institute of Physics.
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47.20.Dr Surface-tension-driven instability
47.65.-d Magnetohydrodynamics and electrohydrodynamics

The double-helical branch structure of fixed contact line liquid bridge equilibria

Brian J. Lowry

Phys. Fluids 12, 996 (2000); http://dx.doi.org/10.1063/1.870355 (9 pages) | Cited 5 times

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Attempts 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 semi-infinite 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) semi-infinite double helix. Combined effects of gravity and length are investigated as well, resulting in multiple disconnected loops of equilibria. © 2000 American Institute of Physics.
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47.20.-k Flow instabilities
68.03.-g Gas-liquid and vacuum-liquid interfaces
68.05.-n Liquid-liquid interfaces

Fixed boundary dual liquid bridges in zero gravity

Brian J. Lowry

Phys. Fluids 12, 1005 (2000); http://dx.doi.org/10.1063/1.870356 (11 pages) | Cited 5 times

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The 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 2π 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 pressure-constrained pumping. © 2000 American Institute of Physics.
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47.20.-k Flow instabilities

Direct numerical simulations of the elliptic instability of a vortex pair

F. Laporte and A. Corjon

Phys. Fluids 12, 1016 (2000); http://dx.doi.org/10.1063/1.870357 (16 pages) | Cited 23 times

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The objective of this study is to perform direct numerical simulations (DNS) of the three-dimensional short-wavelength elliptic instability developing in a counter-rotating vortex pair, and to reproduce numerically a water-tank 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 long-term 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 short-wavelength elliptic instability and the long-wavelength Crow instability are provided. © 2000 American Institute of Physics.
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47.32.C- Vortex dynamics
47.15.Fe Stability of laminar flows
47.11.-j Computational methods in fluid dynamics
47.20.-k Flow instabilities
47.27.-i Turbulent flows
47.27.Cn Transition to turbulence

The nonlinear development of three-dimensional disturbances at hyperbolic stagnation points: A model of the braid region in mixing layers

C. P. Caulfield and R. R. Kerswell

Phys. Fluids 12, 1032 (2000); http://dx.doi.org/10.1063/1.870358 (12 pages) | Cited 9 times

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The properties of steady, two-dimensional flows with spatially uniform strain rates ϵ and rotation rates γ where ϵ2 ≥ γ2, 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 three-dimensional nonlinear solutions for spatially periodic perturbations is derived. These solutions satisfy the condition that the amplitude of the time-varying 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 2math, 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 2ϵ, independently of γ. 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 streamwise-aligned perturbation vorticity 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. © 2000 American Institute of Physics.
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47.20.-k Flow instabilities
47.11.-j Computational methods in fluid dynamics
47.32.C- Vortex dynamics

Instabilities in a laterally heated liquid layer

A. M. Mancho and H. Herrero

Phys. Fluids 12, 1044 (2000); http://dx.doi.org/10.1063/1.870359 (8 pages) | Cited 12 times

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We study a convection problem in a free-surface 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 three-dimensional 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. © 2000 American Institute of Physics.
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47.27.T- Turbulent transport processes
47.20.-k Flow instabilities
47.60.-i Flow phenomena in quasi-one-dimensional systems

Numerical study of thermoacoustic waves in an enclosure

Bakhtier Farouk, Elaine S. Oran, and Toru Fusegi

Phys. Fluids 12, 1052 (2000); http://dx.doi.org/10.1063/1.870360 (10 pages) | Cited 12 times

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The behavior of thermoacoustic waves in a nitrogen-filled two-dimensional 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 flux-corrected transport algorithm for convection with models for temperature-dependent viscosity and thermal conduction. By considering a one-dimensional 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 two-dimensional flows within the enclosure. The observed thermoacoustic waves oscillate and eventually decay due to viscous and heat dissipation. © 2000 American Institute of Physics.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
47.40.-x Compressible flows; shock waves
47.27.T- Turbulent transport processes
43.35.Ud Thermoacoustics, high temperature acoustics, photoacoustic effect
44.10.+i Heat conduction
47.10.-g General theory in fluid dynamics

Absolute and convective instability character of slender viscous vortices

Xie-Yuan Yin, De-Jun Sun, Ming-Jun Wei, and Jie-Zhi Wu

Phys. Fluids 12, 1062 (2000); http://dx.doi.org/10.1063/1.870361 (11 pages) | Cited 16 times

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Motivated by the need for effective vortex control, the character of absolute and convective instabilities (AI/CI) of incompressible and high-Mach number slender vortices with axial-velocity 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 axial-flow profile, Reynolds number, and Mach number. A significant difference between the AI/CI and temporal-instability 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. © 2000 American Institute of Physics.
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47.20.-k Flow instabilities
47.32.C- Vortex dynamics
47.27.T- Turbulent transport processes
47.40.-x Compressible flows; shock waves

Lee-wave breaking over obstacles in stratified flow

Olivier S. Eiff and Philippe Bonneton

Phys. Fluids 12, 1073 (2000); http://dx.doi.org/10.1063/1.870362 (14 pages) | Cited 8 times

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Experimental results are presented on the lee-wave breaking process which occurs at low Froude numbers when uniform and strongly stratified flow approaches two-dimensional and quasi two-dimensional Gaussian-shaped obstacles. It was found that the lee-wave breaking process is essentially independent of the two-dimensional and the quasi two-dimensional 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 two-dimensional spanwise vortex over the central portion of the obstacles and is mainly shear driven. The quasi two-dimensional spanwise vortex persists for a few buoyancy periods before undergoing a three-dimensional 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 ∼ 3H are inclined into the flow yielding three strong components of vorticity. © 2000 American Institute of Physics.
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47.55.Hd Stratified flows
47.20.-k Flow instabilities
47.27.T- Turbulent transport processes

Nonlinear geostrophic adjustment, cyclone/anticyclone asymmetry, and potential vorticity rearrangement

Allen C. Kuo and Lorenzo M. Polvani

Phys. Fluids 12, 1087 (2000); http://dx.doi.org/10.1063/1.870363 (14 pages) | Cited 7 times

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Within 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 time-dependent 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. © 2000 American Institute of Physics.
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47.32.C- Vortex dynamics

Oscillatory shear layers in source driven flows in an unbounded rotating fluid

A. Tilgner

Phys. Fluids 12, 1101 (2000); http://dx.doi.org/10.1063/1.870364 (11 pages) | Cited 2 times

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The 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. © 2000 American Institute of Physics.
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47.35.-i Hydrodynamic waves
47.32.-y Vortex dynamics; rotating fluids
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.55.Hd Stratified flows

Local pressure-transport structure in a convective atmospheric boundary layer

Ching-Long Lin

Phys. Fluids 12, 1112 (2000); http://dx.doi.org/10.1063/1.870365 (17 pages) | Cited 8 times

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Local pressure-transport structure in a convective atmospheric boundary layer is studied through large-eddy simulation and a conditional sampling technique. Two cases are simulated: A free-convection boundary layer and a sheared convective boundary layer with −zi/L ≈ 17, where zi is the boundary layer height and L is the Monin–Obukhov length. Results show that pressure-transport flux tends to increase turbulent kinetic energy in the lower part of the sheared convective boundary layer. Furthermore, the root-mean-square resolved pressure fluctuation and the resolved negative pressure fluctuation due to −u1,2ru2,1r become much stronger in the sheared case. Flow visualization demonstrates that strong pressure transport is physically correlated with vortical structure embedded within large-scale updrafts. A conditional sampling technique is applied to study statistical characteristics of resolved fields surrounding strong pressure transport events. The conditional field reveals a boundary-layer-scale roll circulation with a large-scale 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: Large-scale horseshoe-shaped vorticity lines are wrapped around the thermal; small-scale arch-shaped 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 large-scale horseshoe-shaped vorticity lines. These regions roughly coincide with conditional negative momentum fluxes. We thus conclude that local pressure-transport structures are spatially associated with localized low pressure regions and strong vertical vorticity fluctuations, being embedded within thermals and advected along with large-scale convective rolls. © 2000 American Institute of Physics.
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92.60.hk Convection, turbulence, and diffusion
92.60.Fm Boundary layer structure and processes
47.27.T- Turbulent transport processes
47.11.-j Computational methods in fluid dynamics

Anticonvection in systems with heat release on the interface

A. A. Nepomnyashchy, I. B. Simanovskii, and L. M. Braverman

Phys. Fluids 12, 1129 (2000); http://dx.doi.org/10.1063/1.870366 (4 pages) | Cited 3 times

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The 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. © 2000 American Institute of Physics.
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47.27.T- Turbulent transport processes
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.54.-r Pattern selection; pattern formation

A priori analyses of three subgrid-scale models for one-parameter families of filters

C. David Pruett and Nikolaus A. Adams

Phys. Fluids 12, 1133 (2000); http://dx.doi.org/10.1063/1.870367 (10 pages) | Cited 8 times

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The decay of isotropic turbulence in a compressible flow is examined by direct numerical simulation (DNS). A priori analyses of the DNS data are then performed to evaluate three subgrid-scale (SGS) models for large-eddy simulation (LES): an eddy-diffusivity model (M1) [J. Fluid Mech. 238, 1 (1992)], a stress-similarity model (M2) [J. Fluid Mech. 275, 83 (1994)], and a gradient model (M3) [Theor. Comput. Fluid Dyn. 8, 309 (1996)]. The models exploit one-parameter second- or fourth-order filters of the Pade type, which permit the cutoff wave number kc to be tuned independently of the grid increment Δx. The modeled (M) and exact (E) SGS-stresses are compared component-wise by correlation coefficients of the form C(E,M) computed over the entire three-dimensional fields. In general, M1 correlates poorly against exact stresses (C<0.2), M3 correlates moderately well (C ≈ 0.6), and M2 correlates remarkably well (0.8<C<1.0). Specifically, correlations C(E,M2) are high provided the grid and test filters are of the same order. Moreover, the highest correlations (C ≈ 1.0) result whenever the grid and test filters are identical (in both order and cutoff). Finally, present results reveal the exact SGS stresses obtained by grid filters of differing orders to be only moderately well correlated. This implies for LES that the model cannot be specified independently of the filter. © 2000 American Institute of Physics.
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47.27.-i Turbulent flows
47.40.-x Compressible flows; shock waves
47.11.-j Computational methods in fluid dynamics

Statistics of filtered velocity in grid and wake turbulence

Stefano Cerutti and Charles Meneveau

Phys. Fluids 12, 1143 (2000); http://dx.doi.org/10.1063/1.870368 (23 pages) | Cited 25 times

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Data on spatially filtered turbulence are commonly needed for a priori sub-grid model studies and for a posteriori testing of large eddy simulation (LES) codes. In this paper, hot-wire anemometry is used to record very long records of such data, required for good convergence of high-order statistics. An array consisting of four X-wire probes placed transversal to the flow direction is built. Unlike previous single-probe hot-wire measurements, which only allowed stream-wise filtering using Taylor’s hypothesis, the array permits cross-stream filtering as well. Measurements which are spatially filtered at a length-scale Δ pertaining to the inertial-range of turbulence are performed in grid and wake turbulence. The data can be used directly to compare with results from LES. From the data, fundamental differences between filtered and unfiltered velocity fields are examined through probability density functions and the scaling behavior of high-order structure functions. A comparative study of probability density functions of filtered and unfiltered velocity increments shows that the tails of the distributions are affected by the filtering even at scales much larger than the filter scale. Significant differences are also observed in regard to the scaling of structure functions. It is shown that extended self-similarity, a recent technique for measuring inertial range scaling exponents, yields questionable results when applied to structure functions of filtered velocity. © 2000 American Institute of Physics.
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47.27.wb Turbulent wakes
02.50.-r Probability theory, stochastic processes, and statistics

Interaction of vorticity, rate-of-strain, and scalar gradient in stratified homogeneous sheared turbulence

P. J. Diamessis and K. K. Nomura

Phys. Fluids 12, 1166 (2000); http://dx.doi.org/10.1063/1.870369 (23 pages) | Cited 18 times

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The structure and dynamics of stably stratified homogeneous sheared turbulence is investigated in terms of the triadic interaction of vorticity ω, rate-of-strain S, and scalar (density fluctuation) gradient G ≡ ∇ρ′. Results of direct numerical simulations are presented. Due to the presence of the mean velocity and scalar gradients, distinct directional preferences develop which affect the dynamics of the flow. The triadic interaction is described in terms of the direct coupling of primary mechanism pairs and influential secondary effects. Interaction of ω and S is characterized by the coupling of vortex stretching and locally-induced rotation of the S axes. Due to the intrinsic directionality of baroclinic torque, the generated ω acts to impede S axes rotation. Interaction of ω and G involves an inherent negative feedback between baroclinic torque and reorientation of G by ω. This causes baroclinic torque to act as a sink which promotes decay of ω2. Interaction of S and G is characterized by a positive feedback between differential acceleration and gradient amplification by compressive straining which promotes persistence in vertical G. In high-amplitude, rotation-dominated regions of the flow, differential acceleration effects enhance the attenuation of vertical ω while shear and baroclinic torque tend to maintain horizontal ω. This leads to a predominance of horizontal ω in these regions which manifests itself as collapsed vortex structures. As the flow develops, the third invariant of the velocity gradient tensor tends towards zero indicating locally two-dimensional flow. © 2000 American Institute of Physics.
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47.27.nb Boundary layer turbulence
47.27.Gs Isotropic turbulence; homogeneous turbulence
47.55.Hd Stratified flows
47.32.C- Vortex dynamics

Characteristics of chemically reacting compressible homogeneous turbulence

F. A. Jaberi, D. Livescu, and C. K. Madnia

Phys. Fluids 12, 1189 (2000); http://dx.doi.org/10.1063/1.870370 (21 pages) | Cited 13 times

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Direct numerical simulations (DNS) are conducted to study the turbulence-chemical reaction interactions in homogeneous decaying compressible fluid flows. The reaction is of a single-step irreversible Arrhenius type. The results indicate that the heat of reaction has a noticeable influence on the solenoidal and the dilatational turbulent motions. The effect of reaction on the solenoidal velocity field is primarily due to variation of the molecular diffusivity coefficients with temperature and appears at small scales. However, the dilatational motions are affected more than the solenoidal motions and are intensified at all length scales. The decay rate of the turbulent kinetic energy is dependent on the molecular dissipation and the pressure-dilation correlation. In isothermal reacting cases, the net contribution of the pressure-dilatation is small and the turbulent energy decays continuously due to viscous dissipation. In the exothermic reacting cases, the pressure-dilatation tends to increase the turbulent kinetic energy when the reaction is significant. Analysis of the flow structure indicates that the flow is dominated by strain in the reaction zones. Also, consistent with previous studies, the scalar gradient tends to align with the most compressive strain eigenvector and the vorticity vector tends to align with the intermediate strain eigenvector. The heat of reaction weakens this preferential alignment, primarily due to variation in molecular transport coefficients. The spatial and the compositional structure of the flame are also affected by the modification of the turbulence and the molecular coefficients. © 2000 American Institute of Physics.
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47.70.Fw Chemically reactive flows
47.27.Gs Isotropic turbulence; homogeneous turbulence
47.40.-x Compressible flows; shock waves
82.40.-g Chemical kinetics and reactions: special regimes and techniques
82.60.Cx Enthalpies of combustion, reaction, and formation

Shock-induced mixing of nonhomogeneous density turbulent jets

J. C. Hermanson and B. M. Cetegen

Phys. Fluids 12, 1210 (2000); http://dx.doi.org/10.1063/1.870371 (16 pages) | Cited 1 time

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An experimental study of the mixing enhancement and changes in flow structure arising from the interaction of weak normal shock waves with turbulent jets was conducted. The experimental configuration was an axisymmetric jet processed by weak normal shock waves propagating in a shock tube along the jet axis. Experiments involved three different jet gases: helium, air, and carbon dioxide, each in a coflowing air stream, with nominal jet fluid to ambient density ratios of 0.14, 1.00, and 1.52, respectively. The jet local Reynolds number was Reδ ≈ 25 000 and the nominal oncoming shock Mach numbers were 1.23 and 1.45. Planar laser Mie light scattering from mineral oil smoke was utilized for flow visualization and for obtaining jet fluid concentration distributions across diametric planes of jets. Analysis of the spatial probability density function (pdf) of jet fluid concentration indicates that the average helium jet fluid concentration levels decrease and become more uniform in the regions processed by the shock waves. The degree of mixing enhancement increases with increasing shock strength, and amounts to nearly 30% for the stronger shock (M = 1.45). The passage of a shock through low-density (helium) jets induces the formation of a flow structure that resembles a large-scale, toroidal vortex. The air and carbon dioxide jets exhibit neither a vortex-like structure or a significant change in mixing upon shock passage, unlike the helium jets. A comparison of the results for the helium and carbon dioxide jets indicates that the reversal of the density ratio between the jet and the surroundings, and the consequent change in the sign of baroclinic vorticity does not yield similar effects in terms of flow structure or mixing enhancement. The average concentration behind the shock wave decreases for both air and helium jets with increasing distance behind the shock. These features are explained qualitatively in terms of a simple characteristic time scale argument. The spatially averaged scalar dissipation calculated from the concentration data decreases for both the air and helium jets due to shock passage. The change is less marked for the air jet than for the helium jet for a given shock strength. © 2000 American Institute of Physics.
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47.27.wg Turbulent jets
47.27.-i Turbulent flows
47.40.Ki Supersonic and hypersonic flows
47.40.Nm Shock wave interactions and shock effects
47.80.-v Instrumentation and measurement methods in fluid dynamics
47.32.C- Vortex dynamics
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