bluuebunny/crossref_metadata_2025 huggingface dataset:
Lyapunov stability of relativistic fluids and plasmas
Authors: Holm Darryl D. , Kupershmidt Boris A.
Published: July 2002

Lyapunov stability of relativistic ideal fluid and plasma equilibria is studied analytically using the energy-Casimir method. Two- and three-dimensional relativistic equilibria in a fixed bounded domain are investigated within the framework of the macroscopic multifluid plasma model. Linearized Lyapunov stability conditions and stability norms are given, accounting for warm-plasma effects as well as relativistic and electromagnetic effects. The resulting Lyapunov stability conditions are compared to spectral stability analyses for relativistic cold plasmas in various examples and special cases, including (1) non-neutral electron flow in a planar diode and (2) circularly symmetric plasma flow enclosed in a coaxial waveguide. These linearized stability results can be extended readily to nonlinear Lyapunov stability conditions for finite-amplitude perturbations by employing standard convexity arguments for the Lyapunov functions given here. The relativistic stability conditions are shown to reduce either to their nonrelativistic counterparts or to trivial identities in the nonrelativistic limit.
The symmetry properties of the effective diffusivity tensor in anisotropic porous media
Authors: Koch Donald L. , Brady John F.
Published: July 2002

The effect of anisotropic grain structures on the average transport properties resulting from flow through porous media is derived using methods that involve ensemble averaging the basic conservation equations and a multiple-scale analysis. The Lagrangian or ‘‘moments’’ effective diffusivity tensor, defined as the long-time limit of the time rate of change of the mean-squared displacement of a tracer particle, is equivalent to the symmetric part of the Eulerian diffusivity, defined as the mass flux induced by a linear concentration gradient in the limit of long times. In an anisotropic medium there may be a component of the mass flux perpendicular to the imposed concentration gradient, resulting in an effective diffusivity tensor that is not symmetric. Such an effect is not detected by the moments or Lagrangian approach.
The transition from free molecule to collisional flow during vaporization into vacuum by the test-particle method
Authors: Tsai Chuen-Horng , Olander Donald R.
Published: July 2002

A test-particle method was developed to estimate the conditions that lead to collision-dominated evaporation during pulse heating of a solid surface in vacuum. The method consists of calculating the number density of evaporated molecules above the surface neglecting collisions and then sending a test particle through this cloud. The probability that the test particle escapes from the cloud without making a collision is the measure of the importance of intermolecular collisions during the blow off. The method is applied to heating of a ∼1 cm diam spot on the surface with a heat pulse of ∼1 msec duration. These conditions characterize laboratory laser vaporization experiments intended to measure the vapor pressures of refractory solids at very high temperatures. The principal variable which determines the escape probability is the maximum surface temperature during the transient. When applied to laser heating of uranium dioxide, collisional effects in the vapor are predicted to begin at a maximum surface temperature between 2600 and 2800 K.
A turbulent dynamo model for the reversed field pinches of plasma
Authors: Yoshizawa Akira , Hamba Fujihiro
Published: July 2002

A dynamo model for reversed field pinches (RFP’s) is proposed from the viewpoint of magnetohydrodynamic (MHD) turbulence. This model aims at investigating the sustainment phase of RFP’s, and consists of the mean magnetic induction equation and three equations for the bulk properties of MHD fluctuations, namely, the MHD turbulent energy, its dissipation rate, and the MHD helicity. In particular, the alpha dynamo effect is composed of the familiar alpha term and a new alpha term closely related to inhomogeneity of the field. This model paves the way for explaining the generation and sustainment of alpha and beta effects. Moreover, it can treat finite plasma pressure gradients and fulfill the vanishing of plasma currents at the plasma edge. This model can also be extended to the Earth’s magnetic dynamo model where the mean motion of a fluid plays an important role.
Direct interaction approximation of turbulence in the wave packet representation
Authors: Nakano Tohru
Published: July 2002

The wave packet representation of the Navier–Stokes equations is developed. In order to show its feasibility, it is applied to turbulence in the framework of the direct interaction approximation (DIA). The theory is free from a spurious divergence encountered in the usual DIA theory. The effect of convection due to large eddies is successfully eliminated without relying on any ad hoc approximation, but the contribution from their velocity gradient is included. The Kolmogorov spectrum with the Kolmogorov constant 1.67 is predicted if the shell width is set equal to 2. The passive scalar field in turbulence can be treated similarly, yielding the counterpart of the Kolmogorov constant 0.84. Both the constants agree with experiment fairly well, implying that the present wave packet representation is reliable.
Experiments on dielectric liquid bridges subjected to axial electric fields
Authors: Ramos Antonio , González Heliodoro , Castellanos Antonio
Published: July 2002

Experimental determination of the critical axial electric field needed to hold a nonconducting liquid bridge of given slenderness is presented. The Plateau tank technique is used to minimize gravity forces on earth. Improvement of previous data is achieved by determining the gravitational Bond number. The results are compared to numerical calculations of the stability limits, showing a good agreement.
Boundary layer receptivity to free-stream vorticity
Authors: Buter T. A. , Reed H. L.
Published: July 2002

The receptivity to free-stream vorticity of the boundary layer over a flat plate with an elliptic leading edge is investigated numerically by solving the incompressible Navier–Stokes system in general curvilinear coordinates with the vorticity and streamfunction as dependent variables. A small-amplitude vortical disturbance is introduced at the upstream boundary and the governing equations solved time accurately to evaluate the spatial and temporal growth of the perturbations leading to instability waves [Tollmien–Schlichting (TS) waves] in the boundary layer. The effect of disturbance amplitude, orientation, and the effect of the leading edge and of surface curvature are investigated for the case of spanwise vorticity. Simulations reveal, for the conditions considered, a linear variation in the TS response with forcing amplitude for perturbations of free-stream velocity that are either symmetrical or asymmetrical with respect to the basic-state stagnation streamline. The presence near the leading edge of a large, oscillating component of velocity normal to the airfoil axis for the case of asymmetrical forcing results, for the same strength of input disturbance, in an increase in the TS response aft of the juncture and in the appearance of a superharmonic component of the disturbance motion near the tip of the nose. This superharmonic decays rapidly in the streamwise direction. In all cases considered, the first clear appearance of the TS mode occurs aft of the surface pressure-gradient maximum. Changes to the geometry that increase the maximum in steady surface pressure gradient are found to increase receptivity.
A modified restricted Euler equation for turbulent flows with mean velocity gradients
Authors: Girimaji Sharath S. , Speziale Charles G.
Published: July 2002

The restricted Euler equation captures many important features of the behavior of the velocity gradient tensor observed in direct numerical simulations (DNS) of isotropic turbulence. However, in slightly more complex flows the agreement is not good, especially in regions of low dissipation. In this paper, it is demonstrated that the Reynolds-averaged restricted Euler equation violates the balance of mean momentum for most homogeneous turbulent flows with only two major exceptions: isotropic and homogeneously sheared turbulence. A new model equation which overcomes this shortcoming and is more widely applicable is suggested. This model is derived from the Navier–Stokes equation with a restricted Euler-type approximation made on the fluctuating velocity gradient field. Analytical solutions of the proposed modified restricted Euler equation appear, at this point, to be difficult to obtain. Hence, a strategy for numerically calculating the velocity gradient tensor is developed. Preliminary calculations tend to indicate that the modified restricted Euler equation captures many important aspects of the behavior of the fluctuating velocity gradients in anisotropic homogeneous turbulence.
A numerical Eulerian approach to mixing by chaotic advection
Authors: Toussaint Valérie , Carrière Philippe , Raynal Florence
Published: July 2002

Results of numerical simulation of the advection-diffusion equation at large Péclet number are reported, describing the mixing of a scalar field under the action of diffusion and of a class of steady, bounded, three-dimensional flows, which can have chaotic streamlines. The time evolution of the variance of scalar field is calculated for different flow parameters and shown to undergo modulated exponential decay, with a decay rate which is a maximum for certain values of the flow parameters, corresponding to cases in which the streamlines are chaotic everywhere. If such global chaos is present, the decay rate tends to oscillate, whereas the presence of regular regions produces a more constant decay rate. Significantly different decay rates are obtained depending on the detailed properties of the chaotic streamlines. The relationship between the decay rate and the characteristic Lyapunov exponents of the flow is also investigated.
Analytical (perturbation) solution to the problem of free-molecule gas flows in two-body systems: Results for flows over two unequal-size cylinders
Authors: Peters Michael H.
Published: July 2002

In this study, the grand (translational) friction tensor for free-molecule (large Knudsen number) flows over two, unequal-size cylinders is obtained analytically considering both ‘‘shielding’’ effects and multiple collisions off cylinder surfaces, as well as including both diffuse and specular molecule-surface boundary conditions. A perturbation solution is used where the leading-order term accounts for molecular collisions from the free-streaming gas including all shielding effects. The first-order correction term is also obtained here and accounts for collisions by molecules reflected off neighboring surfaces from the free-stream gas. It is shown that the grand friction tensor is symmetric under the conditions of small ratios of the free-stream gas velocity to the thermal gas velocity, the same type of molecular reflection boundary condition on both cylinders, and constant temperature. It is also shown that the two-term expansion formula is accurate under isothermal conditions in the so-called ‘‘far-field’’ limit where the surface to surface cylinder separation distance is greater than approximately one to two cylinder diameters for equal-size cylinders. The accuracy of the two-term expansion is also shown to diminish as the two cylinders approach one another (‘‘near field’’ behavior). It is also demonstrated how the far-field results given here can be extended to more than two cylinders and to cylinders moving relative to the free-stream gas. This study compliments an earlier study [R. Ying and M. H. Peters, J. Fluid Mech. 207, 353 (1989)] for small Knudsen numbers, or the ‘‘slightly rarefied gas’’ case.
A new class of instabilities of rotating fluids
Authors: Lifschitz Alexander , Fabijonas Bruce
Published: July 2002

Standing waves in a rotating ideal fluid are considered. It is shown that all of them are unstable with respect to short-wavelength perturbations. Moreover, it is demonstrated that the growth rate of the corresponding instabilities tends to infinity when either the amplitude of the standing wave increases or its spatial scale decreases without bound. It is suggested that the observed instabilities are akin to the Hadamard instabilities.
Stability of an isorotating liquid bridge between equal disks under zero-gravity conditions
Authors: Slobozhanin Lev A. , Perales José M.
Published: July 2002

The stability of the relative equilibrium of an isorotating axisymmetric liquid bridge between two equal-radius coaxial disks under zero-gravity conditions has been investigated in detail. The free surface is assumed to be pinned to the edges of the disks and in equilibrium and only perturbations compatible with this pinning are considered. In the plane of the dimensionless variables characterizing the liquid bridge length and the liquid bridge volume, the stability regions for a set of values of the Weber number have been calculated. The stability region structure and the nature of critical perturbations change when the Weber number, W, passes through the values W0 (2.05<W0<2.06) and W1 (2.44<W1<2.45). It has been found that, for W<W0, the stability region is connected, and the neutral stability may take place with respect to nonaxisymmetric perturbations as well as to axisymmetric ones. In the latter case, it has been established whether the critical axisymmetric perturbations are reflectively symmetric or reflectively antisymmetric about the equatorial plane. When the increasing Weber number passes through the value W0, the stability region breaks into two disconnected parts. The first exists for all Weber numbers larger than W0. For the states belonging to the boundary of this part, only nonaxisymmetric perturbations are critical. The second part exists only for Weber numbers between W0 and W1. Its boundary is determined by the states that may be neutrally stable to nonaxisymmetric perturbations or to axisymmetric ones. The characteristics of the shape of the neutrally stable surfaces have been calculated for a wide range of the Weber number.
Linear stability analysis of salt fingers with surface evaporation or warming
Authors: Renardy Yuriko Yamamuro , Schmitt Raymond W.
Published: July 2002

Oceanic observations [Atmos. Ocean 29, 340 (1991)] have revealed small-scale thermohaline plumes near the surface of a calm sea under warming conditions. The stratification was favorable for the double-diffusive salt finger instability, though a previously unreported up–down asymmetry was found in which narrow downward cells are balanced by a broader, weaker upwelling. The scales of the thermal structures are consistent with asymmetric hexagonal salt-finger modes [J. Phys. Oceanogr. 24, 855 (1994)], but no selection mechanism for the asymmetry has previously been identified. This paper explores the influence of nonlinear profiles of temperature and salinity, as might arise due to surface evaporation or warming, on the linear stability problem in a salt-fingering regime. Three models are considered. In the first, a sharp, nonlinear solute-concentration gradient is applied at the upper boundary, as might arise by surface evaporation. A Bénard mode appears, driven by the destabilizing density gradient in the thin boundary layer and influencing motion only within the boundary-layer thickness. In the second model, a weak salinity gradient is introduced below the boundary layer; double-diffusive bulk modes influence the motion across the entire fluid. Nonlinear interaction of the boundary layer and bulk modes provides a mechanism for maintaining salt fingers with up–down asymmetry. The third model contains a large temperature gradient at the surface, as might arise from warming by solar radiation, overlying a quasi-isothermal region above a region of moderate gradient. The largest-growth modes are found to be salt fingers that extend throughout the middle region and disappear in the top and bottom regions. This vertical structure is close to that of the asymmetric salt fingers described in Osborn [Atmos. Ocean 29, 340 (1991)]. The differing length scales of the regions impress an up–down asymmetry on plumes; this is expected to yield a hexagonal pattern at the onset.
The dynamics of a concentration interface in a dilute suspension of solid heavy particles
Authors: Druzhinin O. A.
Published: July 2002

Gravitational settling of solid heavy particles in a dilute suspension is studied analytically and numerically. The particle Reynolds number is assumed to be less than unity, for which the viscous drag force on the particle is well approximated by the linear Stokes law. The particulate volume fraction (or concentration) c is assumed to be small enough for the effects of particle–particle interactions to be negligible. The ratio δ=ρp/ρf of the particle and fluid densities is considered large enough however, so that the momentum exchange between the two phases caused by the viscous drag forces (which is of the order of the particulate mass loading factor cδ) is significant. The particulate base concentration, c0(y), is assumed to be a smooth function of the vertical coordinate y (hence, a stratified suspension) and a perturbation of the initially stationary settling regime is considered in the form of a horizontally propagating monochromatic wave with wavenumber k and frequency ω(k). Analytical solutions for the perturbations in the limit of small particle inertia (such that ωτp≪1, where τp is the particle response time) are found to be similar to those for internal waves propagating in a stratified fluid with effective density ρeff=ρf(1+c0(y)δ). On the other hand, it is found that in the opposite limit of large particle inertia (ωτp≫1) the perturbations are damped. As an example, we consider a suspension consisting of two layers with uniform concentrations of particles c1 (for y>+h/2) and c2 (for y<−h/2) separated by the interface layer of thickness h, where the concentration gradient is substantial. The solutions obtained in the long-wave limit kh≪1 show that if the concentration in the lower layer exceeds that in the upper layer (c2>c1), the disturbance of the interface brings about wavy motions analogous to internal waves in a two-layer fluid. In the case of inverse stratification (c2<c1) the disturbance grows exponentially and generates plume-like “bubbles,’’ similar to those produced due to the Rayleigh–Taylor instability in a two-layer fluid. The results of the numerical simulations show that, as expected, the waves are damped and the instability growth rate is reduced for particles having larger inertia.
Burgers’ equation with high Reynolds number
Authors: Zhang D. S. , Wei G. W. , Kouri D. J. , Hoffman D. K.
Published: July 2002

Burgers’ equation, involving very high Reynolds numbers, is numerically solved by using a new approach based on the distributed approximating functional for representing spatial derivatives of the velocity field. For moderately large Reynolds numbers, this simple approach can provide very high accuracy while using a small number of grid points. In the case where the Reynolds number ⩾105, the exact solution is not available and a discrepancy exists in the literature. Our results clarify the behavior of the solution under these conditions.
Hamiltonian moment reduction for describing vortices in shear
Authors: Meacham S. P. , Morrison P. J. , Flierl G. R.
Published: July 2002

This paper discusses a general method for approximating two-dimensional and quasigeostrophic three-dimensional fluid flows that are dominated by coherent lumps of vorticity. The method is based upon the noncanonical Hamiltonian structure of the ideal fluid and uses special functionals of the vorticity as dynamical variables. It permits the extraction of exact or approximate finite degree-of-freedom Hamiltonian systems from the partial differential equations that describe vortex dynamics. We give examples in which the functionals are chosen to be spatial moments of the vorticity. The method gives rise to constants of motion known as Casimir invariants and provides a classification scheme for the global phase space structure of the reduced finite systems, based upon Lie algebra theory. The method is illustrated by application to the Kida vortex [S. Kida, J. Phys. Soc. Jpn. 50, 3517 (1981)] and to the problem of the quasigeostrophic evolution of an ellipsoid of uniform vorticity, embedded in a background flow containing horizontal and vertical shear [Meacham et al., Dyn. Atmos. Oceans 14, 333 (1994)]. The approach provides a simple way of visualizing the structure of the phase space of the Kida problem that allows one to easily classify the types of physical behavior that the vortex may undergo. The dynamics of the ellipsoidal vortex in shear are shown to be Hamiltonian and are represented, without further approximation beyond the assumption of quasigeostrophy, by a finite degree-of-freedom system in canonical variables. The derivation presented here is simpler and more complete than the previous derivation which led to a finite degree-of-freedom system that governs the semi-axes and orientation of the ellipsoid. Using the reduced Hamiltonian description, it is shown that one of the possible modes of evolution of the ellipsoidal vortex is chaotic. These chaotic solutions are noteworthy in that they are exact chaotic solutions of a continuum fluid governing equation, the quasigeostrophic potential vorticity equation.
Flame–vortex interaction in a reacting vortex ring
Authors: Hewett J. S. , Madnia C. K.
Published: July 2002

Direct numerical simulations are used to study the flame–vortex interaction in a laminar reacting vortex ring. The chemical reaction occurs by a one-step, Arrhenius-type reaction that mimics the combustion of typical hydrocarbon and air. The ring is generated by an axisymmetric jet that is impulsed to emit a cold fuel through a nozzle. The fuel enters a quiescent ambient at a much higher temperature. By adjusting the ratio of the ambient and fuel temperatures, the ignition either occurs during the formation or post-formation phase of the ring. When ignition occurs during the formation phase of the ring, the bulk of combustion is by a flame at the front of the vortex bubble. When ignition is delayed until after the formation phase, most of the reaction occurs inside the vortex ring. It is found that premixing the fuel and the oxidizer enhances the amount of product formation. The heat released from the reaction significantly affects production, redistribution, and diffusion of the vorticity throughout the field. The results of the simulations also reveal that the heat of reaction affects the strain rate fields differently depending on when the ignition of the ring occurs.
Motion stability of a deformable body in an ideal fluid with applications to the N spheres problem
Authors: Galper A. R. , Miloh T.
Published: July 2002

The Liapunov stability problem of the translation or spiraling motion of an arbitrary deformable body (the deformation of which is governed by the corresponding Hamiltonian) is treated here using the modified Energy–Casimir approach. The appropriate stability criteria are derived. It is shown that some unstable translational motions can be stabilized by a deformational or rotational motion. This formalism is further applied to the stability problem related to the motion of N (generally unequal) rigid spheres embedded in a potential flow field. The assembly of N-spheres is treated as an entire N-connected single deformable body. The Liapunov stability of the motion of two spheres in the direction orthogonal to their lines of centers and that of three spheres in the direction orthogonal to their plane of centers, is demonstrated and proven as a special case. Some existing conditions of clustering for a bubble cloud are also rederived and extended.
Numerical study of the collapse of an axisymmetric mixed region in a pycnocline
Authors: Terez Dmitry , Knio Omar M.
Published: July 2002

The collapse of an axisymmetric mixed region in a continuously stratified pycnocline is analyzed using direct simulation of the Navier–Stokes equations in the Boussinesq limit. Attention is focused on cylindrical mixed regions of size comparable to the thickness of the pycnocline, which lies between two deep layers of different densities. Computed results show that the collapse leads to the formation of a cylindrical internal gravity wave that encloses a concentrated toroidal vortex. The vortex roll-up is related to the strain-induced intensification of vorticity and is found to be most pronounced for “tall” and horizontally compact mixed regions. The wave and vortex gradually decay as they spread radially in the pycnocline. After significant decay has occurred, the vortex disintegrates but the wave continues to propagate away from the mixed region. A sharp-nosed intrusion is left in the wake of the wave, which is no longer able to transport fluid. A Lagrangian particle scheme is used to visualize and quantify the wave structure. Analysis of particle distributions shows that the toroidal vortices entrain ambient stratified fluid into their cores. It is found that the speed of the cylindrical solitary wave is lower than the two-dimensional (2D) weakly-nonlinear prediction. In addition, unlike the 2D case, the wave speed does not appear to be a simple function of the wave amplitude. The vortex decay is finally analyzed in terms of a simplified model on the viscous cancellation of the two strained vortices of opposite sign. An approximate qualitative agreement between model predictions and computations is found. The comparison highlights the role of viscous diffusion of vorticity as well as the contributions of entrainment and baroclinic vorticity generation to the vortex decay.
Direct numerical simulation of particle deposition onto a free-slip and no-slip surface
Authors: van Haarlem Bas , Boersma Bendiks J. , Nieuwstadt Frans T. M.
Published: July 2002

We consider here the direct numerical simulation (DNS) of channel flow with two different surfaces: a no-slip, fixed wall and on the opposite side a free-slip, free surface. The simulated velocity field agrees well with the experimental data for a free-surface flow obtained by Komori et al. [Int. J. Heat Mass Transf. 25, 513 (1982)]. The DNS is used to simulate particle trajectories, which are computed with a dynamic particle equation in which only the drag force given by the Stokes law is taken into account. For the particle time scale, nondimensionalized in terms of the fixed-wall friction velocity and the kinematic viscosity, we use the values τ+=5 and τ+=15. A statistically stationary condition is studied that is obtained by the introduction of a uniform distribution of particles at the beginning of the channel and by continuous removal through deposition at the two walls. The steady-state concentration distribution is nonuniform across the channel width, primarily due to the process whereby particles are trapped close to the surface. Moreover, we find that the wall–normal concentration profiles are self-similar. The deposition on both the no-slip and the free-slip wall can be described by a constant deposition coefficient, with for τ+=5 the larger value on the free-slip wall and for τ+=15 the opposite, i.e., the larger value over the no-slip wall. To study the deposition process in more detail we consider the cross channel particle fluxes and velocity statistics that are conditioned on deposition events. By means of instantaneous near-wall particle distributions we also consider the patterns of particles and their accumulation in certain areas of the flow. For a no-slip surface the well-known result that particles tend to collect in the low-speed streaks is confirmed. The patterns of particles near the free-slip surface are completely different, which can be explained in terms of the different types of coherent structures that are present near this surface.
Influence of gravity on nonlinear transport in the planar Couette flow
Authors: Tij Mohamed , Garzó Vicente , Santos Andrés
Published: July 2002

The effect of gravity on a dilute gas subjected to the steady planar Couette flow with arbitrarily large velocity and temperature gradients is analyzed. The results are obtained from the Bhatnagar–Gross–Krook kinetic model by means of a perturbation expansion in powers of the external field. The reference state corresponds to the pure (nonlinear) Couette flow solution, which retains all the hydrodynamic orders in the shear rate and the thermal gradient. To first order in the gravity field, we explicitly obtain the hydrodynamic profiles and the five relevant nonlinear transport coefficients; the shear viscosity η, the two viscometric functions Ψ1,2, and the two nonzero elements, κxy and κyy, of the thermal conductivity tensor. The results show that, in general, the influence of gravity on the rheological properties η and Ψ1,2 tend to decrease as the shear rate increases, while this influence is especially important in the case of the thermal conductivity coefficient, κyy, which measures the heat flux parallel to the temperature gradient.
Coexisting acoustic-rotational flow in a cylinder with axisymmetric sidewall mass addition
Authors: Staab P. L. , Zhao Q. , Kassoy D. R. , Kirkkopru K.
Published: July 2002

Time-dependent flow dynamics within a cylinder with sidewall mass injection are investigated. A time-dependent injection velocity, prescribed along the sidewall boundary of a long, narrow, half-open cylinder, induces a low Mach number, high Reynolds number flow. The injection is the source of planar acoustic disturbances which interact with the injected fluid to produce vorticity on the sidewall in an inviscid manner. The analysis of these flow processes is based on the Navier–Stokes equations, which are reduced to simpler forms using a multiple-scale asymptotic analysis. The equations that arise from the analysis describe the leading-order vorticity dynamics. These nonlinear equations possess both wave and diffusion properties and are solved in an initial value sense. The results show that the vorticity produced at the sidewall convects toward the center of the cylinder, diffuses radially, and convects downstream.
Characteristics of subgrid-resolved-scale dynamics in anisotropic turbulence, with application to rough-wall boundary layers
Authors: Juneja Anurag , Brasseur James G.
Published: July 2002

Large-eddy simulation (LES) of the atmospheric boundary layer (ABL) using eddy viscosity subgrid-scale (SGS) models is known to poorly predict mean shear at the first few grid cells near the ground, a rough surface with no viscous sublayer. It has recently been shown that convective motions carry this localized error vertically to infect the entire ABL, and that the error is more a consequence of the SGS model than grid resolution in the near-surface inertial layer. Our goal was to determine what first-order errors in the predicted SGS terms lead to spurious expectation values, and what basic dynamics in the filtered equation for resolved scale (RS) velocity must be captured by SGS models to correct the deficiencies. Our analysis is of general relevance to LES of rough-wall high Reynolds number boundary layers, where the essential difficulty in the closure is the importance of the SGS acceleration terms, a consequence of necessary under-resolution of relevant energy-containing motions at the first few grid levels, leading to potentially strong couplings between the anisotropies in resolved velocity and predicted SGS dynamics. We analyze these two issues (under-resolution and anisotropy) in the absence of a wall using two direct numerical simulation datasets of homogeneous turbulence with very different anisotropic structure characteristic of the near-surface ABL: shear- and buoyancy-generated turbulence. We uncover three important issues which should be addressed in the design of SGS closures near rough walls and we provide a priori tests for the SGS model. First, we identify a strong spurious coupling between the anisotropic structure of the resolved velocity field and predicted SGS dynamics which can create a feedback loop to incorrectly enhance certain components of the predicted velocity field. Second, we find that eddy viscosity and “similarity” SGS models do not contain enough degrees of freedom to capture, at a sufficient level of accuracy, both RS-SGS energy flux and SGS-RS dynamics. Third, to correctly capture pressure transport near a wall, closures must be made more flexible to accommodate proper partitioning between SGS stress divergence and SGS pressure gradient.
On stability of flow in an annular channel
Authors: Shapiro I. , Shtilman L. , Tumin A.
Published: July 2002

Linear and nonlinear stability of a flow between the walls of two coaxial cylinders has been investigated. The linear analysis has been carried out within the framework of the temporal linear stability theory. The eigenvalue map has been obtained using the collocation method based on Chebyshev polynomials. The nonlinear analysis is based on a novel parallel code for DNS (direct numerical simulations) of a coaxial pipe flow with periodic boundary conditions in the streamwise direction. It is shown that the major source of finite amplitude instability is associated with the interaction of three-dimensional disturbances and streamwise rolls.
Equilibria of corotating nonuniform vortices
Authors: Ehrenstein U. , Rossi M.
Published: July 2002

Inviscid equilibria for a pair of two-dimensional vortices of different size and circulation are numerically computed. Previous analyses studied the case of vorticity patches. In the present investigation, we introduce vortex profiles ranging from patches to Lamb-type profiles, and analyze how classical results are altered when the vorticity distribution is not piecewise constant. Furthermore we study how nonuniformity of the vorticity distribution affects the instability threshold which has been previously interpreted as a sign of the merging process. It is shown as well how this instability point is modified when one of the vortices is replaced by a point vortex of identical circulation. For this purpose, a numerical solution procedure has been developed capable of computing the perturbed streamlines, using Green’s function integrals.
Direct simulation Monte Carlo study of quantum effects on the spherical expansion of 4He
Authors: Koura Katsuhisa
Published: July 2002

Quantum effects on the translational nonequilibrium at low temperatures in a spherical expansion of 4He from room temperature are studied using the direct simulation Monte Carlo method to make a comparison with the experimental measurements along the axis of a helium free jet expansion. The quantum-mechanical scattering cross sections are obtained by a quantum phase-shift calculation for the Lennard-Jones and more elaborate Hartree–Fock dispersion potentials. It is shown that the parallel and perpendicular kinetic temperatures are higher and lower, respectively, for the quantum-mechanical scattering than for the classical-mechanical scattering. A comparison with the parallel temperature determined by fitting the ellipsoidal velocity distribution function to the measured spectral profiles indicates that the parallel kinetic temperature for the quantum-mechanical scattering is higher than the measured temperature, with which the parallel kinetic temperature for the classical-mechanical scattering is fortuitously in better agreement. Because both the parallel and perpendicular velocity distribution functions appreciably deviate from Maxwellians and the Maxwellian (half-width) fit temperatures are lower than the kinetic temperatures, the discrepancy between the quantum-mechanical and measured parallel temperatures may partly be resolved by the difference between the kinetic and fitting temperatures.
Resonant coupling of oscillating gas or vapor bubbles in water: An experimental study
Authors: Ohsaka K. , Trinh E. H.
Published: July 2002

Resonant coupling of oscillating gas or vapor bubbles in water is experimentally studied using a two-frequency acoustic apparatus. First, the threshold amplitude of resonant coupling between the volume and axisymmetric shape oscillations is measured for gas bubbles in the shape modes, n=3–6, and for vapor bubbles in the modes, n=4 and 5, where n is the mode number. The result qualitatively agrees with a theoretical prediction based on a phase-space analysis. Secondly, the efficiency of two coupling conditions, two–one (2:1) and one–one (1:1) resonant conditions is compared for the n=4 and 5 modes. The result of the comparison can be generalized as follows: When n is an even number, the (1:1) coupling condition has better energy transfer efficiency than (2:1). The relationship reverses when n is an odd number, i.e., the (2:1) coupling condition has better energy transfer efficiency than (1:1).
Addendum to ‘‘Collective transport of alpha particles due to Alfvén wave instability’’ [Phys. Fluids B 5, 3217 (1993)]
Authors: Breizman B. N. , Berk H. L. , Ye H.
Published: July 2002

Ya. I. Kolesnichenko and his cowerkers observed that the alpha particle energy losses due to Alfvén wave excitation in an ignited plasma did not exceed 25% of the total alpha particle energy. (AIP)
Stimulated Raman scattering from symmetrically illuminated two-layered spherical targets with 527 nm laser light
Authors: Tsukamoto M. , Tanaka K. A. , Mima K. , Kado M. , Miyamoto S. , Nakai M. , Norimatsu T. , Takagi M. , Nishihara K. , Yamanaka T. , Nakai S. , Nishiguchi A.
Published: July 2002

Spectrally shifted Raman light with time was observed from two-layered spherical targets irradiated with 527 nm random phased laser light. The target was composed of a foam shell and an outer thin plastic layer. The Raman spectrum shifted rapidly to the short-wavelength side during the laser pulse. The start timing was earlier than that of the usually observed Raman light at an experiment with a single-layered plastic shell target. It was inferred that a plasma shoulder with a long scale length moved outward on the expanding plasma, consistent with the observed Raman light.
Comment on ‘‘An analytic treatment of the bounded and free presheaths with arbitrary viscosity in magnetized flowing plasmas’’ [Phys. Plasmas 1, 2864 (1994)]
Authors: Hutchinson I. H.
Published: July 2002

It is contended that Chung’s (Ref. 1) approximation of equations describing one-dimensional of presheaths does not take into consideration the viscosity. It includes only the convective momentum transport. ALso the mathematical treatment of the free-presheath is faulty in its choice of the boundary conditions at infinity. (AIP)
Effects of energetic ions on kinetic Alfvén wave in a tokamak plasma
Authors: Ding N. , Huang L. , Qiu X. M. , Long Y. X.
Published: July 2002

The effects of energetic ions on the electric field structure and the energy deposition of kinetic Alfvén wave (KAW) in a tokamak plasma are considered. A cylindrical geometry is adopted and a linearized kinetic model including the bulk plasma and the energetic ions is established. These effects of fusion alpha particles (abbreviated, alphas) in deuterium–tritium (D–T) tokamak plasmas are numerically analyzed. The energetic ions tend to alter the wave structure and the energy deposition. The absorption of the kinetic Alfvén wave by the bulk plasma depends sensitively on both the velocity distribution of alphas and the spatial profile of the alpha particle density, as well as on the frequency of the injected wave. Numerical results of the wave structure and the power absorption are given for the parameters of D–T plasmas. The present studies lead to the following discoveries: (1) The slowing-down alpha particle distribution reduces the KAWs energy deposition and the Maxwellian alphas have hardly any influence over it; (2) the more the (slowing-down) alphas near the resonant layer, the more heavily they prevent the KAWs power absorption by the bulk plasma; (3) the lower frequency of the injected wave within the range of KAWs continuum, the more heavily the KAWs structure and power absorption by the bulk plasma are affected by alpha particles; and (4) the energy deposition decreases rapidly as the total number of alphas increases.
Nonlocal diffusivity: Impact on transient transport studies
Authors: Jacchia A. , Mantica P. , De Luca F. , Galli P. , Gorini G.
Published: July 2002

Nonlocal effects are observed in a number of transient transport studies in tokamaks and stellarators. In this paper some consequences of nonlocality are discussed on the basis of a heuristic model for the electron heat diffusivity (χe). The main consequence is the presence of an additional (‘‘missing’’) heating power term (p̃χ) in the heat transport equation. Suitable combinations of p̃χ and modulated power profiles should give rise to detectable effects in modulated heating experiments such as those planned on the Frascati Tokamak Upgrade (FTU) [R. Andreani et al., in Fusion Technology, Proceedings of the 16th Symposium, London, 1990, edited by B. E. Keen, M. Huguet, and R. Hemsworth (Elsevier Science, Amsterdam, 1991), Vol. 1, p. 218]. Failure to properly include p̃χ effects (if present) can lead to an overestimate of χe from heat wave propagation analysis.
The relativistic drift Hamiltonian
Authors: Boozer Allen H.
Published: July 2002

The relativistic Hamiltonian for the guiding center motion of particles in electric and magnetic fields is given in its canonical form. This drift Hamiltonian is valid if the particle gyroradius is sufficiently small compared to the spatial scale, and the cyclotron frequency is sufficiently large compared to the temporal scale, of the magnetic and electric fields. A method for determining the required magnetic coordinates for an earth-like magnetic field is also given.
Stimulated Brillouin scattering in the strong coupling regime
Authors: Guzdar P. N. , Liu C. S. , Lehmberg R. H.
Published: July 2002

Stimulated Brillouin scattering (SBS) has been reexamined in the strong coupling limit. The three-wave interaction in the strong coupling regime, which gives rise to a purely growing mode for wave numbers k≳2k0, where k0 is the wave vector of the pump wave, has been studied. This regime was first found by Cohen and Max [Phys. Fluids 22, 1121 (1979)]. In this regime, for a flowing plasma, a significant portion of the unstable spectrum is found to be blueshifted even for the Mach number equal to unity. For the inhomogeneous case, the convective gain in the strong coupling limit turns out to be identical to the gain in the SBS in the weak coupling limit regime.
Outflow boundary conditions for the moments of a particle distribution function
Authors: Weitzner Harold
Published: July 2002

The constraints on the moments of a distribution function satisfying an outflow condition are given. When a kinetic equation is approximated by a finite system of equations for the moments, the appropriate number of boundary conditions is found by analysis of the characteristics of the system.
Characteristics of a weakly ionized non-neutral plasma
Authors: Peurrung A. J. , Barlow S. E.
Published: July 2002

A scheme that allows stable confinement of a weakly ionized non-neutral plasma is discussed. The method requires the forced rotation of the neutral gas within the trap about an axis that roughly coincides with the trap’s magnetic and mechanical axes. A number of the basic equilibrium and nonequilibrium properties of such a trapped plasma are calculated.
Effects of the ion-beam density and velocity on the excitation of multimode soliton
Authors: Nagasawa T. , Honzawa T.
Published: July 2002

Multimode solitons are observed to be excited in an ion-beam–plasma system. But, the excitation of some mode solitons of these is found to be suppressed under a certain condition depending on the density and velocity of a low-energy ion beam, produced by the applied negative pulse. Furthermore, weak interaction between the slow-beam soliton and ion-acoustic soliton is also observed to cause small time lags in their trajectories on the distance–time plane.
Comment on ‘‘Bifurcations from periodic solution in a simplified model of two-dimensional magnetoconvection,’’ by N. Bekki and T. Karakisawa [Phys. Plasmas 2, 2945 (1995)]
Authors: Knobloch E. , Proctor M. R. E. , Rucklidge A. M. , Weiss N. O.
Published: July 2002

In a recent paper, N. Bekki and T. Karakisawa (Ref. 1) considered two-dimensional Boussinesq convection in an imposed vertical magnetic field. We would like to point out that a number of their results and claims are incorrect. These can be seen by comparing their work with ours. (AIP).
Analytic expressions for polarimetry in plasma with large Cotton–Mouton or Faraday effects
Authors: Segre S. E.
Published: July 2002

Analytic expressions for plasma polarimetry are derived for the case when either the Cotton–Mouton effect or the Faraday effect is large while the other effect is small.
Very high- and high-confinement mode limited discharges in DIII-D
Authors: Jackson G. L. , Taylor T. S. , Lasnier C. J. , Leonard A. W. , Burrell K. H. , Greenfield C. M. , Hill D. N. , Hyatt A. W. , Kim J. , Osborne T. H. , Strait E. J. , Whyte D. , Wood R. D.
Published: July 2002

The first observations of marginally limited very high confinement mode (VH-mode) discharges have been achieved in DIII-D [Nucl. Fusion Special Supplement: World Survey of Activities in Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1990)] with significant reductions in peak heat flux conducted to plasma facing surfaces. In addition, quasistationary well limited high confinement-mode (H-mode) discharges have been obtained in DIII-D, also with reduced peak heat flux. This demonstration of reduced peak heat flux while maintaining high performance, i.e., high energy confinement time, can be important for the design of fusion ignition devices. Energy confinement enhancements in these high triangularity discharges are comparable to diverted discharges with similar parameters: τE/τITER-89P=2.9 for VH-mode and τE/τITER-89P=1.8 for quasistationary high confinement mode (H mode), where τITER-89P is the empirically derived low confinement mode (L-mode) energy confinement scaling relation [Nucl. Fusion 30, 1999 (1990)]. Comparisons of the conducted heat flux, particle flux, and radiated power profiles show a shift toward the inner wall as the discharge configuration becomes more limited. In addition to the advantage of reduced peak heat flux in these limiter discharges, such configurations also allow more effective use of the internal vessel volume, providing the potential for higher performance, i.e., higher plasma current at a fixed safety factor, q95.
Stationary turbulent spectra of toroidal ηi mode
Authors: Pakyari Alireza , Pavlenko Vladimir P.
Published: July 2002

Toroidal ion temperature gradient (ITG) driven drift mode turbulence has been analyzed analyti- cally and numerically. By using weak nonlinearity arguments and random phase approxima- tion, dynamic and wave kinetic equations are derived. Three different nonlinearities, namely E×B, convective, and diamagnetic nonlinearities, play important roles in the turbulent spectral transfer. The power spectra of the weak ITG-mode turbulence are obtained analytically for |k|≫1 and |k|<1 ranges in the wave number space. Forward energy cascading due to convective and diamagnetic nonlinearities will balance the inverse energy cascading due to E×B nonlinearity at |k|≊1/ρs (k is the wave number, ρs=cs/ωci, where cs is the sound velocity and ωci is the ion cyclotron frequency) and results in energy condensation at |k|≊1/ρs.