bluuebunny/crossref_metadata_2025 huggingface dataset:
Limits on the cross-field propagation of streams of cold plasma
Authors: Borovsky Joseph E.
Published: July 2002

When injected across an ambient magnetic field, a stream of collisionless plasma polarizes, and the resulting polarization electric field may allow the stream to penetrate the magnetic field. The polarization charge spreads from the stream sides along the magnetic-field lines and any ambient plasma that is magnetically connected to the stream will be picked up to form Alfvén wings of co-moving plasma. As the stream and wing plasmas move across the magnetic field, their outer edges are continually stripped off. Because of these processes, the stream must expend charge, momentum, and kinetic energy in order to continue its cross-field motion. These expenditures derive from five requirements of charge from the stream: charge is required (1) to polarize the stream plasma, (2) to replace the charge stripped from the stream’s edges as it propagates, (3) to set up the Alfvén wings on the stream, (4) to replace the charge stripped from the sides of the wings as they propagate, and (5) to supply any conduction currents in the ambient plasma. By using idealized stream configurations, approximate limits on the propagation distance are obtained.
Numerical study of a many-particle adiabatic invariant
Authors: Hjorth P. G. , O’Neil T. M.
Published: July 2002

For a pure electron plasma in a sufficiently strong magnetic field, an unusual many-electron adiabatic invariant is predicted to constrain the collisional dynamics. To the extent that this invariant is preserved, no exchange of energy is possible between the parallel and perpendicular degrees of freedom; the system can acquire and maintain two different temperatures, T∥ and T⊥. However, since an adiabatic invariant is not an exact constant of the motion, equilibration eventually takes place, but on an exponentially long time scale. This Letter presents the results of a molecular dynamics simulation, which verifies the existence of this unusual invariant and verifies the theoretically predicted equilibration rate.
Effect of trapped electrons on current drive
Authors: Cohen Ronald H.
Published: July 2002

Trapped-particle effects on electron–cyclotron resonance heating (ECRH) and lower-hybrid current drive are studied using the adjoint formalism. A square-well model for the collision operator is used to obtain an analytic form for the Green’s function that is shown to be quite accurate. In constructing the current, the wave-heated distribution function is allowed to have an effective temperature along the velocity-space resonance curve that is different from the bulk temperature of the scattering electrons. These calculations are used to illustrate the deleterious effect of heating on the outside of a flux surface. Relativity and strong heating are each shown to increase current-drive efficiency for heating on the inside of the flux surface with Y≡harmonic number×cyclotron frequency/wave frequency less than 1, and decrease or reverse the driven current in the opposite limits. A significant limit on ECRH current drive in a mildly relativistic plasma, resulting from an upper bound on the minimum resonant energy, is demonstrated.
Chapman–Enskog solution for diffusion: Pidduck’s equation for arbitrary mass ratio
Authors: Tompson R. V. , Loyalka S. K.
Published: July 2002

In several studies of rarefied gas dynamics and particle transport, not only the diffusion coefficient, but also a detailed description of the Chapman–Enskog solution for diffusion is required. The case of diffusion of a trace species in a background gas is considered for arbitrary molecular mass ratio, and accurate results are reported for the Chapman–Enskog solution obtained by solving numerically an integral equation of Pidduck.
Magnetohydrodynamic unsteady flow in a tube of variable cross section in an axial magnetic field
Authors: Deshikachar K. S. , Rao A. Ramachandra
Published: July 2002

Oscillatory flow in a tube of slowly varying cross section is investigated in the presence of a uniform magnetic field in the axial direction. A perturbation solution including steady streaming is presented. The pressure and shear stress on the wall for various parameters governing the flow are discussed.
The influence of end-plate potential control on magnetohydrodynamic normal modes and stability in mirror machines
Authors: Kaiser Thomas B. , Cohen Bruce I.
Published: July 2002

By adjusting the electrostatic potential on the end plates of a mirror plasma, the plasma’s magnetohydrodynamic (MHD) stability can be altered. Furthermore, the plasma’s MHD response to low-frequency modulation of the end plates can be used to pump unwanted ions that collect in a thermal barrier. Here, precise boundary conditions are derived for the MHD equations of motion to model an end plate separated from the plasma by a sheath.
Focusing effects on waves propagating in a nonuniform plasma
Authors: Glasser Alan H. , Bravo-Ortega Armando
Published: July 2002

The effects of ray focusing on the propagation of waves in a nonuniform plasma are considered. The treatment is based on two complementary approaches. First Bernstein’s wave energy equation is integrated numerically and studied analytically in order to gain an understanding of the singularities to which it can give rise. Second, a bundle of rays is also studied numerically and found to cross at exactly the same point in space where the energy equation produces a singularity. The particular numerical examples are done for lower hybrid waves in a tokamak.
Low Reynolds number flow resulting from an array of rotlets
Authors: Smith S. H.
Published: July 2002

Simple analytical solutions are presented for the two-dimensional Stokes’ flow resulting from symmetric arrays of rotlets inside a circular cylinder. From these expressions, streamline patterns are easily drawn which show different varieties of free and attached eddies within the fluid; they bear many comparisons with the recent experiments of Munson and Sturges [Phys. Fluids 26, 1173 (1983)].
Evolution of some isolated disturbances to Jeffery–Hamel flow
Authors: Eagles P. M. , Georgiou G. A.
Published: July 2002

The stability of Jeffery–Hamel flow in a divergent wedge is considered by means of some initially localized disturbances, whose evolution downstream with time is studied by an integral of fixed frequency modes with respect to the frequency parameter. It is found, typically, that even in regions of parameter space that are nominally ‘‘unstable,’’ the original localized disturbance grows very little before decaying downstream.
Electron acceleration by plasma waves in a nonuniform plasma
Authors: Brooks R. D. , Pietrzyk Z. A.
Published: July 2002

High-energy electrons in plasmas have been attributed to various causes including trapping by electron plasma waves created by stimulated Raman scattering. A theory based on the acceleration of trapped electrons by such electron plasma waves as they propagate in the presence of a density gradient away from the region where they are created is presented. Results of a simple model and a wave–particle simulation consistent with experimental results are included.
Congruent reduction in geometric optics and mode conversion
Authors: Friedland Lazar , Kaufman Allan N.
Published: July 2002

Standard eikonal theory reduces, to N=1, the order of the system of equations underlying wave propagation in inhomogeneous plasmas. The condition for this remarkable reducibility is that only one eigenvalue of the unreduced N×N dispersion matrix D(k,x) vanishes at a time. If, in contrast, two or more eigenvalues of D become simultaneously small, the geometric optics reduction scheme becomes singular. These regions are associated with linear mode conversion and are described by higher-order systems. A new reduction scheme is developed based on congruent transformations of D, and it is shown that, in degenerate regions, a partial reduction of order is still possible. The method comprises a constructive step-by-step procedure, which, in the most frequent (doubly degenerate) case, yields a second-order system, describing the pairwise mode conversion problem in four-dimensional plasmas. This N=2 case is considered in detail, and dimensionality arguments are used in studying the characteristic ordering of the elements of the reduced dispersion tensor in mode conversion regions. The congruent reduction procedure is illustrated by classifying pairwise degeneracies in cold multispecies magnetized plasmas.
An integral method for two-temperature ionizing laminar boundary layers
Authors: Subramaniam V. V. , Lawless J. L.
Published: July 2002

An integral method is developed in order to solve approximately the governing equations for a multitemperature, nonequilibrium ionizing, compressible boundary layer. This method is based on classical momentum and energy integral methods which are used in conjunction with the Howarth–Dorodnitsyn transformation. A novel feature of this method is the separate treatment of the translational or sensible energy equations for each species. As an illustrative example, this method is applied to the problem of a shock-generated ionizing argon boundary layer on a flat surface at a uniform temperature. Reasonable agreement for this case is found between this approximate theory and existing experimental and numerical results.
Free-streamline analysis of deformation and dislodging by wind force of drops on a surface
Authors: Durbin P. A.
Published: July 2002

Free-streamline theory is used to analyze the deformation and dislodging by wind pressure of drops of liquid adhered by surface tension to a solid surface. The critical Weber number for droplets to be dislodged is determined as a function of advancing and receding contact angle. Graphical results for drop shape are in good agreement with observation.
The calculation of some Batchelor flows: The Sadovskii vortex and rotational corner flow
Authors: Moore D. W. , Saffman P. G. , Tanveer S.
Published: July 2002

Steady, inviscid, incompressible, two-dimensional flows with vortex patches bounded by vortex sheets (Batchelor flows) are calculated numerically. Two particular cases are considered: the vortex on a plane wall (Sadovskii vortex) and the vortex in a right-angled corner. Nonlinear integral equations are derived for the shape of the bounding vortex sheet which are solved numerically. Two different formulations are employed to check the results. Previous results by Sadovskii [Appl. Math. Mech. 35, 773 (1971)] and Chernyshenko (Royal Aircraft Establishment library translations Report No. 2133, 1983) for specific values of the parameters are confirmed. Only symmetrical solutions are found to exist.
Nonlinear resonance of two-dimensional ion layers
Authors: Prasad S. A. , Morales G. J.
Published: July 2002

A nonlinear theory of wave resonances in a two-dimensional ion layer confined under the surface of liquid helium is presented. The ion layer is modeled as a two-dimensional cold plasma fluid. In addition to the usual nonlinearities present in the continuity equation and the equation of motion, the theory considers a nonlinear dependence of the mass of a plasma particle on its velocity, as suggested by indirect experimental evidence. Secular perturbation theory is used to find the plasma response when the damped, nonlinear system is driven externally. For typical experimental parameters, the mass nonlinearity is found to be the dominant nonlinear effect, giving rise to a backbending of the resonance curve.
Magnetic flux compression by dynamic plasmas. II. Supersonic self-similar solutions for magnetic cumulation
Authors: Felber F. S. , Liberman M. A. , Velikovich A. L.
Published: July 2002

Supersonic cumulative compressions of axial magnetic fields in cylindrically symmetric plasmas are studied. New self-similar solutions of the ideal magnetohydrodynamic (MHD) equations are presented. The solutions describe cumulative compressions of radially imploding plasma with entrained magnetic fields, subsequent reflections of MHD shock waves from the axis, compressions of hollow plasma liners, and implosions of fast magnetosonic waves.
Strong resonance in two-dimensional non-Boussinesq convection
Authors: Manogg G. , Metzener P.
Published: July 2002

Two-dimensional convection is described and analyzed in the case of strong 2:1 resonance. The density variation due to the temperature to linear order and the viscous heating as perturbations to the usual Boussinesq approximation are introduced. In addition the temperature dependence of the viscosity is taken into account. In this special setting one is able to quantify the influence of these effects on the dynamics. They break the symmetry with respect to reflections at the horizontal midplane that is artificially induced when adopting the Boussinesq approximation, and give rise to an O(2) symmetric bifurcation problem. Time-dependent solutions appear and become stable when the Prandtl number lies between two critical values, between zero and one. In this case there also exists a structurally stable heteroclinic orbit very close to the onset of motion in a small amplitude limit. A similar orbit exists outside this limit if Pr is sufficiently small and the viscosity ratio is relatively large. This behavior is in contrast to previous results obtained by adopting the Boussinesq approximation where only stationary convection patterns persist. Finally a brief survey over real fluids is given and the resulting dynamics is described.
Focusing of weak shock waves and the von Neumann paradox of oblique shock reflection
Authors: Tabak Esteban G. , Rosales Rodolfo R.
Published: July 2002

Some phenomena involving intersection of weak shock waves at small angles are considered: the focusing of curved fronts at arêtes, the transition between regular and irregular reflection of oblique shock waves on rigid walls and the diffraction patterns arising behind obstacles. The intersection of three shock waves plays a central role in most of these phenomena, giving rise to the von Neumann paradox of oblique shock reflection and to the curious transition between linear and fully nonlinear focusing investigated experimentally by Sturtevant and Kulkarny [J. Fluid Mech. 73, 651 (1976)]. This ‘‘triple-point paradox’’ is studied in the context of an asymptotic model, and a solution is proposed that involves an unusual kind of singularity.
Liquid-metal buoyant convection in a vertical cylinder with a strong vertical magnetic field and with a nonaxisymmetric temperature
Authors: Ma Nancy , Walker John S.
Published: July 2002

In this paper the buoyant convection of a liquid metal in a circular cylinder with a vertical axis and with electrically insulating walls is treated. There is an externally applied, uniform, vertical magnetic field. A nonaxisymmetric heat flux at the vertical wall of the cylinder produces a nonaxisymmetric temperature, which drives a nonaxisymmetric liquid motion. The magnetic field is sufficiently strong that inertial effects and convective heat transfer can be neglected. For large values of the Hartmann number Ha, the liquid region is divided into an inviscid core, Hartmann layers with an O(Ha−1) dimensionless thickness adjacent to the horizontal top and bottom walls, and a side layer with an O(Ha−1/2) dimensionless thickness adjacent to the vertical wall. The characteristic velocity is chosen as the magnitude of the core velocity for an axisymmetric temperature. For an axisymmetric temperature, the core velocity is O(1), and the flow circuit is completed by an O(Ha1/2) vertical velocity inside the side layer. A nonaxisymmetric temperature drives much larger, O(Ha) azimuthal and vertical velocities inside the side layer. This high-velocity side layer produces an O(Ha1/2) velocity across the core. Perfect axisymmetry is a special case for which a vertical magnetic field strongly suppresses buoyant convection. With a deviation from axisymmetry, electromagnetic suppression of buoyant convection is weaker: there are strong jets adjacent to the vertical wall and a strong flow across the core.
Study of tracer dispersion in self-affine fractures using lattice–gas automata
Authors: Gutfraind Ricardo , Ippolito Irene , Hansen Alex
Published: July 2002

This paper studies the problem of hydrodynamic dispersion of a tracer in a fluid flowing through a two-dimensional rough channel bounded by self-affine surfaces. Changing the surface roughness exponent H, rough walls having different microstructure are obtained. In order to simulate hydrodynamics, a lattice–gas automata modified to introduce two different species of particles is used. In the studied range of Péclet numbers (20–50), the concentration profiles along the channel are well described by Gaussian-type dispersion. A clear enhancement of the dispersion due to roughness is observed. For the studied regime of Péclet numbers, a simple approach is proposed which allows us to interpret the dispersion enhancement in terms of surface roughness. It is shown that the dispersion enhancement in the rough channel is due to the presence of two characteristic lengths, the hydraulic diameter δH which determines the velocity in the channel and the average aperture δav which determines the transverse diffusion length; next shown is that the dispersion in the rough channel varies as D∥∼(δav/δH)2. The values of δH obtained from the dispersion results are compared with those obtained from permeability measures and a good agreement is observed. In the studied domain of Péclet numbers, the roughness exponent H has only a weak influence on the dispersion.
The equilibrium states and the stability analysis of Reynolds stress equations for homogeneous turbulent shear flows
Authors: Lee Won Geun , Chung Myung Kyoon
Published: July 2002

An analysis is performed to examine the equilibrium states and the stability of modeled Reynolds stress equations for homogeneous turbulent shear flows. The system of the governing equations consists of four coupled ordinary differential equations for b11, b22, b12, and ε/Sk. Depending on the model constants adopted, the solution of this system may converge, diverge, oscillate, or the equilibrium solution may not exist. It is shown that the rapid part of the pressure–strain correlation is most responsible for such different behaviors. Constraints for the model constants in various Reynolds stress models are obtained by stability conditions for the equilibrium states as well as by their physically realizable bounds. It is observed that most models for the pressure–strain correlation that are linear in the anisotropy tensor are stable and produce reasonable equilibrium solutions. Whereas quadratic or cubic models often oscillate and converge onto unrealistic states, especially under high shear conditions.
Steady creeping flow down a slope
Authors: Higuera F. J.
Published: July 2002

An accurate numerical solution of the Reynolds equation for a steady liquid layer flowing down a slightly inclined plate from a point source is presented. The boundary condition determining the perimeter of the layer, which is a steady free boundary, is different from that corresponding to an advancing boundary, and is handled using a specially devised pseudo-transient method and curvilinear coordinates fitted to this boundary. The results are compared with previous numerical simulations.
Unsteady swirling flow in an enclosed cylinder with reflectional symmetry
Authors: Lopez J. M.
Published: July 2002

A numerical investigation of the multiple stable solutions found in confined swirling flows is presented. The flows consist of fluid in a completely filled cylinder driven by the constant corotation of the two end walls. When reflectional symmetry at the cylinder half-plane is imposed, the flow corresponds to that in a cylinder of half the height driven by the bottom end wall, with the top surface being flat and stress-free. Comparisons with available experiments in this case are made and the observed toroidal recirculation zones attached to the free surface are described in terms of secondary motions induced by the bending of vortex lines. Calculations are also presented where the reflectional symmetry is not imposed and the possibility of the flow breaking this symmetry is discussed.
A three-dimensional instability in mixed convection with streamwise periodic heating
Authors: Tangborn Andrew V. , Zhang Sara Q. , Lakshminarayanan Venkatesan
Published: July 2002

Three-dimensional numerical simulations of flow through a channel with spatially periodic temperature boundary conditions in the streamwise direction have been carried out. A spectral method employing Fourier series expansion in the streamwise and spanwise directions and Chebyshev expansion in the vertical direction is used. A supercritical bifurcation to three-dimensional flow is found to occur before the onset of unsteadiness. The bifurcation to unsteady three-dimensional flow is also found to be supercritical. The unsteady three-dimensional flow oscillates at a slightly lower frequency than the two-dimensional flow, and introduces a slightly higher incommensurate frequency causing quasiperiodic flow and a slow spanwise wave motion.
Internal capillary-gravity waves of a two-layer fluid with free surface over an obstruction—Forced extended KdV equation
Authors: Choi J. W. , Sun S. M. , Shen M. C.
Published: July 2002

In this paper we study steady capillary-gravity waves in a two-layer fluid bounded above by a free surface and below by a horizontal rigid boundary with a small obstruction. Two critical speeds for the waves are obtained. Near the smaller critical speed, the derivation of the usual forced KdV equation (FKdV) fails when the coefficient of the nonlinear term in the FKdV vanishes. To overcome this difficulty, a new equation, called a forced extended KdV equation (FEKdV) governing interfacial wave forms, is obtained by a refined asymptotic method. Various solutions and numerical results of this equation are presented.
Effect of density gradients in confined supersonic shear layers. I. Two-dimensional disturbances
Authors: Peroomian Oshin , Kelly R. E.
Published: July 2002

The effect of density gradients on two-dimensional (2-D) supersonic wall modes (acoustic modes) of a 2-D confined compressible shear layer are investigated using linear analysis. Due to the inadequacies of the hyperbolic tangent velocity profile, the boundary layer basic flow profiles are used. First, a test case is taken with the same parameters as in a previous analysis by Tam and Hu [J. Fluid Mech. 203, 51 (1989)], who used a hyperbolic tangent profile. For the boundary layer profiles, three generalized inflection points are found giving rise to three modes. The first two show similar properties to those found by Tam and Hu, whereas the third is a new mode that can have a higher growth rate than the others. As the density ratio is increased above that of the test case, the smallest of the three neutral phase speeds tends toward the speed of the lower-velocity stream, and the other two eventually coalesce and then disappear. These two effects lead to a linear resonance between some of the modes that increases the cutoff frequency and growth rate of the lowest mode. In fact, growth rates of two to four times the test case were found as the density ratio was increased to 7. A similar trend (linear resonance) is observed as the density ratio is decreased from the test case, but the growth rate is only slightly changed from the test case.
Effect of density gradients in confined supersonic shear layers. II. Three-dimensional modes
Authors: Peroomian Oshin
Published: July 2002

The effect of density gradients on three-dimensional (3-D) supersonic acoustic modes and 3-D subsonic modes in a compressible confined shear layer were investigated using linear analysis. The compressible Rayleigh equation with the solution of the steady compressible boundary layer equations as its basic profiles was solved for two different density ratios, 1.398 and 3.0, and several spanwise wave numbers. For a density ratio of 1.398, the 2-D C01 mode had the highest growth rate for a fixed aspect ratio B/H=2. At the higher-density ratio, the 3-D mode had a slightly higher maximum growth rate than the two-dimensional (2-D) mode, and the maximum growth rate was at a location where the phase speed was supersonic with respect to the fast stream.
Geometrical effect on detonation initiation by a nonuniform hot pocket of reactive gas
Authors: He L. , Law C. K.
Published: July 2002

The coupling between combustion processes and gasdynamic effects in reactive mixtures with nonuniform temperature or concentration distributions may lead to the formation of detonations, producing very large-pressure waves. This type of large-pressure wave generation is one of the main mechanisms responsible for the knocking phenomenon in internal combustion engines and for the transition from deflagation to detonation in accidental explosions. In this paper, both theoretical analysis and one-dimensional numerical simulation are carried out to determine the critical conditions for the large overpressure generations by a nonuniform hot pocket. The analysis based on the square wave model shows that due to the curvature effect, a self-sustained quasi-CJ spherical detonation may not exist when the radius of the detonation front is smaller than a critical radius. It is found that the critical conditions for the self-sustained propagation of detonations control the formation of detonations: it occurs only when the position of the formation determined by Zeldovich’s condition is larger than this critical value. The order of magnitude of the so-determined critical size of the hot pocket for successful initiation is much larger than the critical size estimated from Zeldovich’s condition. This point is confirmed by our direct numerical simulations. The magnitude of the critical size is also in good agreement with the experimental results.
The bifurcation of circular jets in crossflow
Authors: Huq Pablo , Dhanak M. R.
Published: July 2002

An experimental study of an incompressible circular jet in a crossflow and theoretical analysis based on inviscid flow models are described. The jet exits from a rigidly mounted pipe projecting distant from the floor of a tunnel carrying a steady stream of water; density of the jet and the stream are the same. The results of scalar and velocity measurements and visualizations showed that the jet bifurcated into two separated, counterrotating arms for values of ε=U∞/UJET, the ratio of the mean crossflow velocity U∞ to the mean jet discharge velocity UJET, less than or equal to 0.25. The angle of separation between the two arms of the bifurcated jet was found to vary inversely with ε. For higher values of ε the jet does not bifurcate but is dominated by a different mode of instability. The structure of the flow field, which is different for bifurcated and nonbifurcated jets, comprised a variety of vortical structures which survived for very long distances x beyond x/2a≳400, where a is the radius of the jet exit and x is distance downstream from the jet axis. The location of the point of bifurcation is predicted from consideration of potential flow models and the characteristics of bifurcating elliptical jets. The location of the point of bifurcation is more distant from the jet exit for smaller values of ε, and experimental results were in good agreement with the theoretical predictions. The initial jet trajectory is shown to be associated with the presence in the wake of vorticity shed from the pipe. The near-field geometry and centerline trajectory of the jet are also found to be in accord with predictions in that it is observed that z∼x1/2 and z∼ε−1. Dilutions of bifurcated jets are found to be greater than for nonbifurcated jets.
Statistical mechanics of bubbly liquids
Authors: Yurkovetsky Yevgeny , Brady John F.
Published: July 2002

The dynamics of bubbles at high Reynolds numbers is studied from the viewpoint of statistical mechanics. Individual bubbles are treated as dipoles in potential flow. A virtual mass matrix of the system of bubbles is introduced, which depends on the instantaneous positions of the bubbles, and is used to calculate the energy of the bubbly flow as a quadratic form of the bubbles’ velocities. The energy is shown to be the system’s Hamiltonian and is used to construct a canonical ensemble partition function, which explicitly includes the total impulse of the suspension along with its energy. The Hamiltonian is decomposed into an effective potential due to the bubbles’ collective motion and a kinetic term due to the random motion about the mean. An effective bubble temperature—a measure of the relative importance of the bubbles’ relative to collective motion—is derived with the help of the impulse-dependent partition function. Two effective potentials are shown to operate: one due to the mean motion of the bubbles, dominates at low bubble temperatures, where it leads to their grouping in flat clusters normal to the direction of the collective motion, while the other, temperature-invariant, is due to the bubbles’ position-dependent virtual mass and results in their mutual repulsion. Numerical evidence is presented for the existence of the effective potentials, the condensed and dispersed phases, and a phase transition.
Scaling of the fingering pattern of an impacting drop
Authors: Marmanis H. , Thoroddsen S. T.
Published: July 2002

We have studied experimentally the fingered splatter left behind after a liquid drop impacts a solid surface at high values of the Reynolds and Weber numbers. The viscosity and surface tension of the liquid was varied by using several different fluid mixtures. The surface chosen was a thick paper sheet, on which the drop left a clear signature of the impact pattern. The maximum spreading of the fluid and the number of fingers seem to scale with an Impact Reynolds number, U(π2ρD3/16σ)1/4/ν1/2, where U is the impact velocity, ν the kinematic viscosity of the fluid, ρ the fluid density, σ the surface tension and D the drop diameter. The number of fingers is weakly dependent on the surface tension and depends primarily on the inertial-viscous interaction.
Experimental study of rotating disk flow instability. II. Forced flow
Authors: Jarre S. , Le Gal P. , Chauve M. P.
Published: July 2002

The destabilization of the rotating disk flow subject to a forcing is experimentally investigated. An isolated roughness element of size of order δ (the constant boundary layer thickness) is placed under the linear threshold of the cross-flow instability in order to create a hydrodynamic pattern of finite amplitude and localized in space. The experimental neutral stability curve is first established. The resulting double parabolic curve exhibits two minima: one of which is due to the amplification of fundamental modes, the other one is linked to the emergence of superharmonic modes. Dispersion curves determined by means of two-point measurements appear to be shifted away from those measured in the natural case (without forcing). We show that this discrepancy is due to the presence of weak nonlinear effects which can be described by a Ginzburg–Landau amplitude equation. Lastly, we present an original method that enables to determine both components of the group velocity vector using the measured dispersion relations and wave packet propagation angle.
Surface and internal signatures of organized vortex motions in stratified fluids
Authors: Fung Y. T. , Chang Simon W.
Published: July 2002

Internal vortex patterns and the corresponding free surface signatures generated in the late wakes by a submerged sphere moving in a stratified fluid are numerically simulated by a three-dimensional time-dependent model. The flow is assumed to be incompressible and hydrostatic with the Boussinesq approximation. A free surface is included to admit barotropic modes and to investigate the surface signature of internal vortices. The turbulent mixing is modeled using the Smagorinsky formula for horizontal fluxes and a Richardson number closure for vertical fluxes. The numerical techniques include a second-order finite difference scheme with a staggered and stretched grid system. A split-explicit method is used to separately integrate the fast barotropic modes and the slow baroclinic modes in time. This method allows us to economically simulate the time history of the slowly evolving vortices. Preliminary results for the velocity field, the flow pattern, the density distribution, and the induced surface signature are presented. They consistently reveal the existence of coherent structures in the stratified flow field. Sensitivity studies are performed to examine how the depth of submerged objects, the depth of channel floors, and the size of moving objects affect the evolution of the horizontal vortices. A mechanism based on the interaction of the wake vorticity and the buoyancy induced oscillation is proposed for the generation and growth of the horizontal vortices in stratified fluids. The vorticity stretching thus produced in the direction of stratification is responsible for the generation and evolution of concentrated vortices in stratified fluids. This mechanism explains why the horizontal vortices appear long after the initial disturbances generated by a submerged moving body have dissipated, and why they exist only in stratified fluids but not in homogeneous media. In view of the proposed mechanism, the horizontal vortices are buoyancy-induced and a model with the stratification properly represented is required to adequately describe the organized vortex motion in stratified wakes.
Pressure–velocity–velocity statistics in isotropic turbulence
Authors: Hill Reginald J.
Published: July 2002

Relationships are derived between pressure–velocity–velocity (PVV) statistics, fourth-order velocity structure functions, and the pressure structure function. The PVV statistics are related to the correlation of pressure at one point with the product of two velocity components at another point. The Navier–Stokes equation, isotropy, and incompressibility are used; no other assumption is used. Thus the relationships apply for all Reynolds numbers and can be used as a benchmark to determine how well turbulence models mimic pressure fluctuations in Navier–Stokes turbulence. A necessary condition limiting compressibility is given. The inertial-range and viscous-range formulas of the PVV statistics are obtained. The results are compared with previous theories that used the joint Gaussian approximation. Data from grid turbulence are used to evaluate the statistics.
The behavior of a gas in the continuum limit in the light of kinetic theory: The case of cylindrical Couette flows with evaporation and condensation
Authors: Sone Yoshio , Takata Shigeru , Sugimoto Hiroshi
Published: July 2002

Cylindrical Couette flows of a rarefied gas between two concentric circular cylinders consisting of the condensed phase of the gas, where evaporation or condensation occurs, are considered on the basis of kinetic theory, with interest in the behavior of the gas in the continuum limit. The limiting solution is obtained by asymptotic analysis of the Boltzmann equation. In some range of the parameters of the problem, neither evaporation nor condensation occurs. The limiting solution in this case is different from the continuum solution (the conventional Couette flow without evaporation and condensation on the cylinders) and is subject to the effect of the flow that is induced if the effect of gas rarefaction is taken into account. This paradoxical result is confirmed by investigating the behavior of the numerical solution of the kinetic equation as the Knudsen number approaches zero.
A subgrid-scale model based on the estimation of unresolved scales of turbulence
Authors: Domaradzki J. Andrzej , Saiki Eileen M.
Published: July 2002

A new method for large eddy simulations is described and evaluated. In the proposed method the primary modeled quantity is the unfiltered velocity field appearing in the definition of the subgrid-scale stress tensor. An estimate of the unfiltered velocity is obtained by expanding the resolved large-scale velocity field to subgrid-scales two times smaller than the grid scale. The estimation procedure consists of two steps. The first step utilizes properties of a filtering operation and the representation of quantities in terms of basis functions such as Fourier polynomials. In the second step, the phases associated with the newly computed smaller scales are adjusted in order to correspond to the small-scale phases generated by nonlinear interactions of the large-scale field. The estimated velocity field is expressed entirely in terms of the known, resolved velocity field without any adjustable constants. The modeling procedure is evaluated in a priori analyses using direct numerical simulation results of channel flow at low Reynolds number and in actual large eddy simulations of channel flow at two different Reynolds numbers. In all cases, the new model performs better than or comparable to classical eddy viscosity models for the majority of physical quantities. In particular, all components of the subgrid-scale stress tensor are predicted accurately and the procedure naturally accounts for backscatter without any adverse effects on the numerical stability.
Cavity flows of elastic liquids: Two-dimensional flows
Authors: Pakdel Peyman , Spiegelberg Stephen H. , McKinley Gareth H.
Published: July 2002

There is a wealth of experimental and computational results available for the motion of Newtonian fluids in the lid-driven cavity geometry, however little is known about the corresponding motion of viscoelastic fluids. We use laser Doppler velocimetry (LDV) and digital particle image velocimetry (DPIV) to probe the dynamics of viscoelastic fluid motion in the classic “lid-driven cavity” problem for a range of industrially important aspect ratios (0.25⩽Λ⩽4) using an ideal elastic fluid as the test material. The magnitude of non-Newtonian effects in the cavity are characterized by the dimensionless Deborah number and the experiments span the range 0⩽De⩽0.35. Elastic effects break the symmetry observed in the velocity field of cavity flows of viscous Newtonian fluids at zero Reynolds number. At low De, the flow remains two-dimensional but increasing the imposed velocity causes the center of the primary recirculating vortex in the cavity to shift progressively upstream. At larger Deborah numbers, the fluid motion becomes unstable and a three-dimensional flow develops. Upon cessation of the forcing boundary motion, a pronounced elastic recoil is observed which leads to a rapid reversal in the direction of the recirculating vortex. This transient motion subsequently decays through viscous dissipative effects on the elastic time scale of the fluid. The kinematics of the localized corner flow near the downstream corner are studied in detail and the distinguishing features of the viscoelastic corner flow with respect to the classic knife-edge problem of Taylor are reported.
Inverse modeling for large-eddy simulation
Authors: Geurts Bernard J.
Published: July 2002

Approximate higher order polynomial inversion of the top-hat filter is developed with which the turbulent stress tensor in large-eddy simulation can be consistently represented using the filtered field. Generalized (mixed) similarity models are proposed which improved the agreement with the kinetic energy transfer to small scales. These similarity models are analyzed for random periodic signals and the ensemble averaged spectra of the turbulent stress tensor and the corresponding models are compared.
On the gravity-driven draining of a rivulet of viscous fluid down a slowly varying substrate with variation transverse to the direction of flow
Authors: Wilson S. K. , Duffy B. R.
Published: July 2002

In this paper we use a lubrication approximation to investigate the locally unidirectional gravity-driven draining of a thin rivulet of Newtonian fluid down a slowly varying substrate. The work generalizes the recent study by Duffy and Moffatt [Chem. Eng. J. 60, 141 (1995)] of gravity-driven draining down a locally planar substrate to include the effects of substrate variation transverse to the direction of flow. Asymptotic and numerical results are obtained for several simple convex and concave transverse substrate profiles. In all the cases investigated these results show a number of common features. In particular, they show that a single stable slowly varying rivulet running continuously from the top to the bottom of a large horizontal circular cylinder is possible only if the transverse substrate profile is a sufficiently shallow trough. If the profile is a deeper trough then no such rivulet is possible near the bottom of the cylinder, while if the profile is a ridge then no such rivulet is possible near the top of the cylinder.
Chloride transport models for wick action in concrete at large Peclet number
Authors: Puyate Y. T. , Lawrence C. J. , Buenfeld N. R. , McLoughlin I. M.
Published: July 2002

Wick action is the transport of water and any species it may contain through a concrete element from a face in contact with water to a drying face. Analytical models are presented for chloride transport in concrete due to wick action. Two cases are considered for convection-controlled systems: (1) No precipitation of chloride salt at a wet-dry interface, and (2) precipitation of chloride salt at the interface. For both cases, a constant concentration of chloride salt is assumed for the face of the concrete in contact with salt solution, while at the interface continuity of fluxes is assumed for Case 1, and a constant chloride saturation level for Case 2. Perturbation techniques are used to solve the transient problems for the two cases investigated. The perturbation solution is compared with experimental and numerical results and good agreement is found when chloride binding is accounted for.
Shock waves in a uniform bubbly flow
Authors: Kameda Masaharu , Shimaura Naoto , Higashino Fumio , Matsumoto Yoichiro
Published: July 2002

An experimental and numerical study of transient shock wave phenomena in a liquid containing noncondensable gas bubbles is presented. Experiments are done in a shock tube with an upwardly directed bubbly flow to obtain a uniform spatial distribution of bubbles. The bubbly flow has an initial gas volume fraction of 0.2%. The bubbles have a radius of 0.6 mm. The liquid used is a silicone oil whose kinematic viscosity is 50×10−6 m2/s. Nitrogen and SF6 gas bubbles are tested to bring out the thermal effects of the bubble interior. The numerical calculation is performed using a modified mathematical model based on Kameda and Matsumoto [Phys. Fluids 8, 322 (1996)]. The transient pressure profiles determined in the experiment for the upwardly bubbly flow agree well quantitatively with those obtained by the numerical calculation using a uniform spatial distribution of bubbles. The SF6 experiment shows that the radial motion of the bubbles should be estimated by solving an equation in which the liquid compressibility is taken into account.
Particle segregation in monodisperse sheared suspensions
Authors: Tirumkudulu Mahesh , Tripathi Anubhav , Acrivos Andreas
Published: July 2002

It has been known for a long time that many mixtures of granular materials tend to segregate when tumbled in a rotating horizontal cylinder, with the different components separating into bands of relatively pure single concentration along the rotational axis [Mixing of Solids, Advances in Chemical Eng., edited by T. B. Drew and J. W. Hoopes (Academic Press, New York, 1952), Vol. 2, p. 211]. Here we report a phenomenon that seems to be analogous, but in suspensions of monodisperse neutrally buoyant spherical particles in a Newtonian liquid medium being sheared in a partially filled horizontal Couette device in which the suspension separates itself into alternating regions of high and low particle concentration along the length of the tube. The experiment is mostly qualitative, the aim at this stage being primarily to provide photographic evidence of a curious and as yet unexplained phenomenon.
Scaling laws in granular flows down rough inclined planes
Authors: Pouliquen O.
Published: July 2002

In this paper, new scaling properties for granular flows down rough inclined planes are presented. In the dense steady uniform flow regime, we have systematically measured the mean velocity of the flow as a function of the inclination of the surface θ and of the thickness h of the layer. The results obtained for different systems of beads corresponding to different surface roughness conditions are shown to collapse into a single curve when properly scaled. The scaling is based on the measurement of the minimum thickness hstop(θ) necessary to observe a steady uniform flow at inclination θ. From this experimental observation an empirical description for granular flows down inclined planes is proposed in terms of a dynamic friction coefficient.
Onset of convection in a fluid-saturated rectangular box, bottom heated by constant flux
Authors: Wang C. Y.
Published: July 2002

Thermoconvective instability of a rectangular box containing a fluid-saturated porous media is studied. The box top is maintained at constant temperature and the bottom is heated by constant flux.
Coupled Korteweg–de Vries equations describing, to high-order, resonant flow of a fluid over topography
Authors: Marchant T. R.
Published: July 2002

The near-resonant flow of a fluid over a localized topography is examined. The flow is considered in the weakly nonlinear long-wave limit and is governed by the forced Korteweg–de Vries (fKdV) equation at first order. It is shown that the unidirectional assumption, of right-moving waves only, is incompatible with mass conservation at second order. To resolve this incompatibility, a forced coupled KdV system, which allows left-moving waves, is derived to third order (two orders beyond the fKdV approximation). The second-order fKdV equation is reformulated as an asymptotically equivalent forced Benjamin–Bona–Mahony (fBBM) equation, as its numerical scheme has superior stability. First- and second-order predictions for the resonant flow of surface water waves are compared and the mass flux between the right- and left-moving waves is found. An analytical estimate for the mass flux between the right- and left-moving waves is also derived and good agreement with the numerical solution is obtained.
Against the wind
Authors: Chomaz J.-M. , Couairon A.
Published: July 2002

The linear and the nonlinear dynamics of open unstable flow in a finite domain of size L is studied on a modified supercritical Ginzburg–Landau equation. When the advection term is nonzero, the bifurcation to a finite-amplitude state occurs when the instability is absolute, even for large L. The standard weakly nonlinear theory is limited to a control parameter domain of size varying as L−5 due to the nonnormality of the linear evolution operator. The fully nonlinear solution is given and two generic cases are discussed: a supercritical case in which the instability is absolute and a subcritical case in which the instability is solely convective. The subcritical case gives a mathematical example of a bypass transition due to transient growth. The supercritical case allows a fully quantitative comparison, including the effect of the domain size, with results obtained by Büchel et al. for the size of the bifurcated solutions in the Taylor–Couette problem with throughflow.