bluuebunny/crossref_metadata_2025 huggingface dataset:
Modeling of dynamic bipolar plasma sheaths
Authors: Grossmann J. M. , Swanekamp S. B. , Ottinger P. F.
Published: July 2002

The behavior of a one-dimensional plasma sheath is described in regimes where the sheath is not in equilibrium because it carries current densities that are either time dependent, or larger than the bipolar Child–Langmuir level determined from the injected ion flux. Earlier models of dynamic bipolar sheaths assumed that ions and electrons evolve in a series of quasiequilibria. In addition, sheath growth was described by the equation Zen0ẋs=‖ ji‖−Zen0u0, where ẋs is the velocity of the sheath edge, ji is the ion current density, n0u0 is the injected ion flux density, and Ze is the ion charge. In this paper, a generalization of the bipolar electron-to-ion current density ratio formula is derived to study regimes where ions are not in equilibrium. A generalization of the above sheath growth equation is also developed, which is consistent with the ion continuity equation and which reveals new physics of sheath behavior associated with the emitted electrons and their evolution. Based on these findings, two new models of dynamic bipolar sheaths are developed. Larger sheath sizes and potentials than those of earlier models are found. In certain regimes, explosive sheath growth is predicted.
Sheath dynamics of electrodes stepped to large negative potentials
Authors: Calder A. C. , Hulbert G. W. , Laframboise J. G.
Published: July 2002

Results are presented of particle simulations of the time-dependent behavior of the plasma sheath surrounding an electrode whose potential is abruptly changed from 0 to some negative value. The surrounding plasma is assumed isotropic and collisionless, and the electrode is a sphere or infinite cylinder. Potential steps up to −1000kTe/e are considered. The time histories and frequency spectra of sheath and plasma oscillations initiated by the potential step are studied. The energy in sheath oscillations (frequency <ωp) escapes by nonlinear coupling to plasma oscillations (frequency ωp). The time scale for sheath–plasma coupling depends strongly on the ion-to-electron mass ratio. Both linear and nonlinear ion acoustic waves are excited by the response to the potential step. Near a small (radius 1λD) cylindrical electrode, trapped ions are shown to make an important contribution to the sheath ion density. The height of the transient peak in collected current for a cylindrical electrode displays strong dependence on the ion-to-electron temperature ratio, for sufficiently large potential steps.
Wave breaking and absorption efficiency for short pulse p-polarized laser light in a very steep density gradient
Authors: Kato S. , Bhattacharyya B. , Nishiguchi A. , Mima K.
Published: July 2002

The nonlinear interaction of an ultrashort-pulse laser with a solid target is investigated by using a newly developed particle simulation code, which enables the analysis of laser–plasma interaction in the very steep density gradient in which the laser light penetrates into an overdense plasma. For an ultrashort laser pulse, the plasma density scale length Ld satisfies Ld≤r0 for an electron excursion length r0. Laser absorption and electron acceleration processes are proposed for the above situation. It is found that the wave breaking is the main mechanism of the electron acceleration and laser absorption, as is discussed in Brunel’s paper [Phys. Rev. Lett. 59, 52 (1987)].
Equilibrium and dynamics of uniform density ellipsoidal non-neutral plasmas
Authors: Dubin D. H. E.
Published: July 2002

When a single-species plasma is confined in a harmonic Penning trap at cryogenic temperature, the thermal equilibrium is approximately a uniform density spheroid (ellipsoid of revolution). Normal modes corresponding to quadrupole excitations of this plasma have recently been measured. In this paper, nonlinear equations of motion are derived for these quadrupole oscillations. For large amplitudes, the oscillations deform a spheroidal plasma into a triaxial ellipsoid with time-dependent shape and orientation. The integrals of the motion are found and the cylindrically symmetric finite-amplitude oscillations of a spheroid are studied. An analysis of all possible ellipsoidal equilibria is also carried out. New equilibria are discovered which correspond to finite-amplitude versions of the noncylindrically symmetric linear quadrupole oscillations. The equilibria are shown to fall into two classes in which the ellipsoids are either tilted or aligned with respect to the magnetic field. Some of these equilibria have densities well above the Brillouin limit.
Long-time diffusion in plasma turbulence with broad uniform spectrum
Authors: Ishiharaa O. , Ha H. , Watanabe S.
Published: July 2002

The long-time behavior of charged particles in plasma turbulence with uniform broad wave spectrum is studied numerically. The diffusivity of the particle velocity distribution is characterized by the quasilinear nature for extended time, while a transient diffusion precedes with the enhanced nonquasilinear diffusion rate when resonance overlapping is relatively weak. The observed long-time quasilinear diffusion coefficient eventually decreases due to the finiteness of the resonance region. The transient-type diffusion is revealed only by the higher-order numerical calculation.
Non-Markovian diffusion in plasma turbulence
Authors: Xia H. , Ishihara O. , Hirose A.
Published: July 2002

Motion of charged particles in electrostatic plasma turbulence is studied analytically and numerically. Analytical study is based on a stochastic differential equation, the generalized Langevin equation, which is derived by the projection operator method with the assumption that the random fluctuation field is a Gaussian and wide sense stationary process. The equation describes the particle velocity as a stochastic process driven by field fluctuations, and is applied to evaluate the velocity diffusion coefficient. The non-Markovian velocity diffusivity is characterized by the retarded turbulent collision term which contributes to the memory effect of the wave–particle interaction. Test-particle numerical experiments are carried out by following trajectories of charged particles in Langmuir turbulence. The observed diffusion coefficient in a relatively strong turbulence deviates from predicted values of the quasilinear and the extended resonance broadening theories. The present non-Markovian formulation explains well such a departure of the diffusion rate.
Lower-hybrid waves in a plasma with negative ions
Authors: An T. , Merlino R. L. , D’Angelo N.
Published: July 2002

The low-frequency lower-hybrid (LH), ion–ion mode was investigated experimentally in a plasma consisting of K+ positive ions, SF6− negative ions, and electrons. The frequency of this mode was found to increase with increasing ε, the relative negative ion concentration. The observations are compared with fluid calculations.
Observation of radio-frequency ion heating in a double plasma device
Authors: Schott L.
Published: July 2002

When a sinusoidal voltage with an angular frequency in the range ωpi≤ω0≤10ωpi and an amplitude of 0≤A (Vrms)<1.6Te (eV) is applied to the separating mesh of a double plasma device, the temperature of the ions passing through the mesh increases approaching that of the plasma electrons (Te≂Ti≂1 eV). The effective ion temperatures inferred from energy analyzer data are in good agreement with those obtained from the phase velocity of a small amplitude ion-acoustic test wave. The heating effect is largest at ω0≂1.5ωpi.
Effect of a poloidal shear flow on the probability of accessing the multiple saturated states in the resistive interchange instability
Authors: Carreras B. A. , Lynch V. E. , Garcia L.
Published: July 2002

A systematic study based on 400 nonlinear single-helicity calculations with random initial perturbations shows that multiple nonlinear states exist at saturation. They are characterized by different values of the poloidal wave number of the dominant mode in the spectrum. As a consequence, the saturated states have different levels of fluctuations and different self-consistent poloidal flow profiles. The presence of an external shear poloidal flow does not always directly change the saturation level of the fluctuations. For low shear flows, it can increase the probability of accessing the high saturated levels. For very high values of the flow shear, however, there is suppression of the fluctuations. A curvature poloidal flow reduces the saturation level of each state and increases the probability of accessing the low fluctuation levels. Transitions between saturated states accompanied by sudden changes in flow profile have been observed. Most of the observed transitions are from a low to a high level of fluctuations.
Fluid simulations of conducting-wall-driven turbulence in boundary plasmas
Authors: Xu X. Q.
Published: July 2002

It is clear that the edge plasma plays a crucial role in global tokamak confinement. This paper is a report on simulations of a new drift wave type instability driven by conducting wall (also originally named as a ∇Te instability) [Phys. Fluids B 3, 1364 (1991)]. A 2d(x,y) fluid code has been developed in order to explore the anomalous transport in the boundary plasmas. The simulation consists of a set of fluid equations (in the electrostatic limit) for the vorticity ∇⊥2φ, and the temperature Te in a shearless plasma slab confined by a uniform, straight magnetic field Bz with two divertor (or limiter) plates intercepting the magnetic field. The model has two regions separated by a magnetic separatrix: In the edge region inside the separatrix, the model is periodic along the magnetic field while in the scrapeoff layer (SOL) region outside the separatrix, the magnetic field is taken to be of finite length with model (logical sheath) boundary conditions at diverter (or limiter) plates. The simulation results show that the observed linear instability agrees well with theory, and that a saturated state of turbulence is reached. In saturated turbulence, clear evidence of the expected long-wavelength mode penetration into the edge is seen, an inverse cascade of wave energy (toward both long wavelengths and low frequencies) is observed. The simulation results also show that amplitudes of potential and the electron temperature fluctuations are somewhat above and the heat flux are somewhat below those of the simplest mixing-length estimates. A full inverse cascade of the turbulence indicates that the cross-field transport is not diffusive. A self-consistent simulation to determine the microturbulent SOL electron temperature profile has been done, the results of which reasonably agree with the experimental measurements.
The electron distribution function in a bumpy torus
Authors: Swain D. W. , Cobble J. A. , Hillis D. L. , Richards R. K. , Uckan T.
Published: July 2002

New and improved diagnostic techniques and increased theoretical understanding of electron-cyclotron heating (ECH) have led to a new picture of the electron distribution function in the ELMO Bumpy Torus (EBT). For electron energies ≤2 keV, the distribution function can be approximated as consisting of two components: a cold isotropic bulk component and a warm anisotropic tail. For typical steady-state EBT-Scale (EBT-S) operation (microwave power input of 100 to 150 kW) in the T-mode (the operating mode of interest for fusion experiments), bulk densities and temperatures of ne =0.5–0.7×1012 cm−3 and Te ≤100 eV are observed, while the warm tail component has Te =200–800 eV, and densities ≤0.4 that of the cold component. The non-Maxwellian nature of the distribution function is caused by ECH.
Optimized Fourier representations for three-dimensional magnetic surfaces
Authors: Hirshman S. P. , Meier H. K.
Published: July 2002

The selection of an optimal parametric angle θ describing a closed magnetic flux surface is considered with regard to accelerating the convergence rate of the Fourier series for the Cartesian coordinates x(θ,φ)≡R−R0 and y(θ,φ)≡Z−Z0. A system of algebraic equations, which are quadratic in the Fourier amplitudes of x and y, is derived by minimizing the width of the surface power spectrum. The solution of these nonlinear equations, together with the prescribed surface geometry, determines a unique optimal angle. A variational principle is used to solve these constraint equations numerically. Application to the representation of three-dimensional magnetic flux surfaces is considered.
Conditional Reynolds stress in a strongly heated turbulent boundary layer with premixed combustion
Authors: Cheng R. K. , Ng T. T.
Published: July 2002

A two-color laser Doppler anemometry technique has been used to measure velocity statistics and Reynolds stress in a turbulent boundary layer over a strongly heated wall (Tw=1100 K) with premixed ethylene–air combustion. Measurements in the isothermal and nonreacting heated wall turbulent boundary layers were also made for comparison. Conditional velocity covariance −∼(uv) are deduced using the quadrant and ‘‘hole’’ analysis methods. The conditional data obtained in the isothermal layer are in exellent agreement with those deduced by others based on hot-wire data. The results obtained in the heated and reacting layers indicate that the decrease in mean Reynolds stress can be attributed to a reduction in the −∼(uv) contributions associated with a burst of low momentum fluid form the wall. The reduction is much more significant in the reacting layer than in the heated layer. Comparison with previous density shows that the changes in conditional −∼(uv) contributions occur mostly within the constant density sublayer of combustion products adjacent to the wall. In the region where combustion reaction takes place, no significant change in the turbulence intensities or Reynolds stress is found.
Error magnetic fields in a cylindrical plasma: Stability with zero pressure
Authors: Miller Guthrie
Published: July 2002

The importance of error magnetic fields is that, if large enough, they cause the destruction of magnetic surfaces. In this paper error fields in a cylindrical plasma are described by nonlinear tearing mode theory, which deals with plasma equilibria having concentrated currents flowing along closed magnetic field lines. Because of the small spatial scale of the current distribution, resistive diffusion is significant even for small resistivity and, in certain cases, causes instability. An energy principle exists and is discussed. This conceptual framework is used in a study of the stability of zero pressure equilibria toward spontaneous generation of error fields, relevant for the reversed field pinch program. Cylindrical Ohmic states are shown to be extremely unstable. Relaxed states (having flattened current profiles) have much better stability. Both completely relaxed states of the Taylor type and partially relaxed Robinson-type states are studied. A new class of metal–liner stabilized profiles is found, which offers one explanation for the apparent stability observed in experiments with distant conducting shells. The possibility that relaxed states have weakly stochastic magnetic field lines is discussed.
Kinetic theory of the electromagnetic drift modes driven by pressure gradients
Authors: Horton W. , Sedlak J. E. , Choi Duk-In , Hong B. G.
Published: July 2002

Kinetic equations for the electromagnetic drift modes are derived and analyzed for the stability of tokamaks in the local approximation. In the dissipationless, hydrodynamic limit, the fifth-order polynomial dispersion relation previously studied is recovered. The kinetic velocity space integrals in the ion dynamics are shown to modify the five principal modes of oscillation and their polarizations. It is shown that in kinetic stability theory the critical plasma pressure defined in magnetohydrodynamic theory determines a transition from microinstability to macroinstability.
The ponderomotive force in a magnetized plasma: The effect of radio-frequency-induced magnetization
Authors: Vaclavik J. , Sawley M. L. , Anderegg F.
Published: July 2002

The ponderomotive force acting on a magnetized plasma resulting from a radio-frequency (rf) electric field is studied both theoretically and experimentally. The fundamental difference between the predictions of the single-particle and fluid approaches is emphasized and its origin elucidated. An experiment is described that illustrates the collective interaction of a fluid with an rf field. This collective behavior manifests itself in the perpendicular ponderomotive force by the interaction of the rf-induced magnetization current with the magnetic field.
Asymmetric magnetic flux generation, m=1 activity, and edge phenomena on a reversed-field pinch
Authors: Howell R. B. , Ingraham J. C. , Wurden G. A. , Weber P. G. , Buchenauer C. J.
Published: July 2002

The ZT-40M [Fusion Tech. 8, 1571 (1985)] reversed-field pinch has been used to study magnetic flux perturbations during high-θ [θ=Bθ(a)/〈Bφ〉>1.6] discharges. Asymmetric toroidal magnetic flux perturbations are found to be associated with magnetic flux emerging through the toroidal shell gap and with m=0 magnetic disturbances moving toroidally. Ramping current discharges, which are a special case of high-θ operation, show the most robust self-generation of toroidal flux. The electron density fluctuations on the inside major radius and associated m=1 and m=0 fluctuations seen on edge magnetic field probes provide a clearer picture of activity during a soft x-ray sawtooth crash. During the sawtooth crash, significant magnetic energy is apparently converted into kinetic energy of the particles.
Cyclotron resonance phenomena in a non-neutral plasma
Authors: Prasad S. A. , Morales G. J. , Fried B. D.
Published: July 2002

A kinetic theory of electrostatic cyclotron waves in a single component plasma slab of density n0(x) immersed in a uniform magnetic field B0ẑ is presented. The space charge electric field E0(x)x̂ in such a plasma modifies the single particle gyrofrequency from Ω=qB0/mc to Ω1(x)=[Ω2−ω2p(x)]1/2 in the limit rc/L ≪1 (where rc is the orbit size and L−1=d ln E0/dx), causing the upper hybrid frequency to have the value (Ω21+ω2p)1/2 =Ω. Finite Larmor radius effects introduce a velocity dependence into the single particle gyrofrequency Ω1, leading to energy transfer to the particles located at the resonant layers where ω−kyvE(x) =Ω1(x) [vE(x)ŷ being the E×B drift velocity]. This energy transfer mechanism is operative even when kz =0. Another nonzero Larmor radius effect is the appearance of thermal modes that are the analogs of Bernstein modes of neutral plasmas. When driven by an external capacitor plate antenna, these modes exhibit behavior similar to Tonks–Dattner resonances.
Renormalization of the diffusion tensor for high-frequency, electromagnetic modes
Authors: Litwin C. , Sudan R. N.
Published: July 2002

The resonance broadening theory is used to derive the diffusion tensor for resonant particles in a spectrum of electromagnetic modes propagating parallel to the magnetic field. The magnetic trapping limit for saturation of wave amplitudes is discussed.
Two-dimensional focusing of a supersonic free jet by a rectangular orifice
Authors: Teshima Koji
Published: July 2002

Supersonic free jets issuing from rectangular orifices have been observed by using a laser-induced fluorescence technique. Anisotropy of expansion in two directions, the orifice length (z) and width (y), apparently occurs in the jet structure at a large pressure ratio (between reservoir and vacuum chambers); the jet spreads in the y direction whereas it converges in the z direction. This effect is enhanced by interaction of lateral shocks from both ends of the orifice when a small aspect ratio orifice is used. Under a flow condition whereby the shocks reflect normally on the axis, the jet becomes very thin in the z direction.
Oscillating field current drive experiments in a reversed field pinch
Authors: Schoenberg K. F. , Ingraham J. C. , Munson C. P. , Weber P. G. , Baker D. A. , Gribble R. F. , Howell R. B. , Miller G. , Reass W. A. , Schofield A. E. , Shinohara S. , Wurden G. A.
Published: July 2002

Steady-state current sustainment by oscillating field current drive (OFCD) utilizes a technique in which the toroidal and poloidal magnetic fields at the plasma surface are modulated at audio frequencies in quadrature. Experiments on the ZT-40M reversed field pinch [Fusion Technol. 8, 1571 (1985)] have examined OFCD over a range of modulation amplitude, frequency, and phase. For all cases examined, the magnitude of the plasma current is dependent on the phase of the modulations as predicted by theory. However, evidence of current drive has only been observed at relatively low levels of injected power. For larger modulation amplitudes, the data suggest that substantial current drive is offset by increased plasma resistance as a result of modulation enhanced plasma–wall interactions. The initial experimental results and supporting theoretical interpretations of OFCD are discussed.
Streaming tearing instability in the current sheet with a super-Alfvénic flow
Authors: Wang S. , Lee L. C. , Wei C. Q.
Published: July 2002

The tearing instability in a current sheet, which has a sub-Alfvénic or super-Alfvénic plasma flow in the current layer, is investigated based on the linearized compressible magnetohydrodynamic (MHD) equations. An initial-value method is employed to obtain the linear growth rate and eigenmode profiles of the fastest growing mode. The results show that for a sub-Alfvénic plasma flow parallel to the neutral sheet, the growth rate of the tearing instability is only slightly larger than that of the pure tearing mode without the flow. On the other hand, a large increase in the growth rate of the most unstable mode is observed, when the streaming speed V0m in the central region of the current sheet increases above a critical speed VC≂1.2VA∞. Here VA∞ is the Alfvén speed far away from the current layer. This study shows that when the electric resistivity η is zero, the sausage mode is excited because of a super-Alfvénic plasma flow parallel to the current sheet. This flow-induced sausage mode is called the streaming sausage mode. In the presence of a finite resistivity, the streaming sausage mode becomes a mixed sausage–tearing mode, because of the presence of magnetic field line reconnections in the current sheet. This mixed sausage–tearing mode, or simply the streaming tearing mode, has a high growth rate, γ≂0.1τ−1A, where τA is the Alfvén transit time across the current layer. This growth rate is larger than the growth rate of the pure tearing mode, which is approximately the inverse of the geometric mean of the Alfvén time τA and the diffusion time τD across the current layer.
Stability of a reversed field pinch with resistive and distant boundaries
Authors: Ho Y. L. , Prager S. C.
Published: July 2002

The linear magnetohydrodynamic stability of current-driven modes is evaluated for a reversed field pinch in which the plasma is bounded by a thin resistive shell surrounded by a vacuum region out to a radius at which a perfectly conducting wall is situated. The effects of variation of the shell resistivity and wall proximity are investigated. Growth rates of tearing modes and kink modes are calculated by analytical solution based on the modified Bessel function model for the equilibrium. Relevance to experiments is discussed.
Recent numerical results on double-layer simulation in high-intensity laser–plasma interaction
Authors: Szichman H.
Published: July 2002

Numerical studies on dynamic electric fields and double layers created inside of plasmas irradiated at laser intensities of 1017 and 1018 W/cm2 were carried out using a macroscopic two-fluid model including nonlinear forces and the complete intensity dependent optical response for heating and dielectric force effects. This was possible only by longer computation times since the temporal and spatial step sizes had to be reduced accordingly. Electrostatic fields as high as 109 and 1010 V/cm were, respectively, measured for both laser intensities and the coupling of irradiated electromagnetic waves to generate Langmuir longitudinal waves is shown to be possible for the first time. The development and production of the well-known density minima (cavitons) because of nonlinear forces is also confirmed, their prominent appearance being in direct relation to the stronger effect of the high irradiances applied.
Shock induced Rayleigh–Taylor instability in the presence of a boundary layer
Authors: Houas L. , Farhat A. , Brun R.
Published: July 2002

The aim of this work is an experimental study of the development of perturbations of a gaseous interface impulsively accelerated by a plane shock wave. The experiments are performed in a double diaphragm shock tube, where the second diaphragm is a very thin Mylar film which can be initially bulged because of a pressure difference between the two gases. The shape of the leading front of the contact zone is measured at three locations along the tube using a transversal array of heat transfer gauges. After the shock passage, the evolution of the interface is sensitive to vorticity production and boundary layer effects so that the impulsive Rayleigh–Taylor theory is inadequate for the description of this evolution. In particular, the predicted perturbation reversal when the shock wave passes from the heavy gas to the light one may not occur because of the boundary layer effect.
Electromagnetic effects on parametric instabilities of Langmuir waves
Authors: Akimoto K.
Published: July 2002

Electromagnetic effects on parametric instabilities of Langmuir waves in unmagnetized plasmas are investigated. A fully electromagnetic treatment of these instabilities removes discontinuities of frequencies that are found to be present in the wave vector space of the electrostatic dispersion equation. Furthermore, it was found that a pair of novel parametric instabilities of Langmuir pump waves emerge owing to the electromagnetic effects. Both of them excite electromagnetic plasma waves near the plasma frequency. One of them is the hybrid modulational instability, which is a four-wave up-conversion process. As the wave vector of the pump wave increases the hybrid parametric decay instability becomes dominant. This is a three-wave down-conversion instability, which has been investigated previously [Space Sci. Rev. 26, 3 (1980); Phys. Rev. A 27, 552 (1983); Astrophys. J. 308, 954 (1986)].
Reversed-field pinch Ohmic equilibria during current decay and termination
Authors: Caramana E. J. , Nebel R. A.
Published: July 2002

The possible current decay and termination of reversed-field pinch discharges via stable, Ohmic, self-similar states that do not require any instabilities or dynamo effect for their maintenance are investigated. The equations that describe such states are derived; numerical solutions that are functions of the form of the resistivity profile, the current decay rate, and the pinch parameter are presented. Relevant constraints on stable termination are discussed.
Isotropic Cartesian tensors of arbitrary even orders and velocity gradient correlation functions
Authors: Phan-Thien N. , Antonia R. A.
Published: July 2002

A recursive relation for the unit isotropic tensor of an arbitrary even order is derived from a rotational Brownian motion of the unit vector. An expression for the eighth-order velocity gradient correlation function is derived from the eighth-order isotropic tensors, after preserving the solenoidal property of the velocity field. This correlation function is compared with measurements in a turbulent wake.
The internal structure of lateral intrusions in a continuously stratified heat/salt system
Authors: McDonald Ellen Thomas , Koseff Jeffrey R.
Published: July 2002

Laboratory experiments have been performed for a double diffusive system in which opposing vertical gradients of temperature and salinity are heated from one side. Details of the internal structure of the intrusions that form along the heated endwall are discussed. Fingering motions and convective overturns are prominent characteristics of the internal intrusion structure, particularly when the rate of lateral heating is high relative to the strength of the ambient vertical density gradient. Analysis of the overturning scale indicates that the RMS size of the overturns is typically 10%–30% of the total layer thickness. Comparison of the flow inside the convective layers with that which develops in a long box heated and cooled at opposite sides based on the analysis of Jeevaraj and Imberger [J. Fluid Mech. 222, 565 (1991)] shows poor agreement when molecular values of the diffusivity and viscosity are used in the theory. However, moderate increases in the diffusivity values (to account for increased vertical mixing) give good agreement between the experiments and theory. Building on the results of Schladow et al. [J. Fluid Mech. 236, 127 (1992)], further evidence of the ability of the intrusions to continue propagating following removal of the endwall heating is presented. Modification of the flow field ahead of the intrusion fronts can create conditions for which the stability ratio, Rρ, drops below a critical value, resulting in continued propagation of the intrusions.
Direct numerical simulation tests of eddy viscosity in two dimensions
Authors: Chekhlov A. , Orszag S. A. , Sukoriansky S. , Galperin B. , Staroselsky I.
Published: July 2002

Two-parametric eddy viscosity (TPEV) and other spectral characteristics of two-dimensional (2-D) turbulence in the energy transfer subrange are calculated from direct numerical simulation (DNS) with 5122 resolution. The DNS-based TPEV is compared with those calculated from the test field model (TFM) and from the renormalization group (RG) theory. Very good agreement between all three results is observed.
Exact description of the spectrum of elliptical vortices in hydrodynamics and magnetohydrodynamics
Authors: Lifschitz Alexander
Published: July 2002

A method for studying natural oscillations of fluids and plasmas in the neighborhood of two-dimensional elliptical flows is presented. The method uses scaling combined with the Fourier transformation to reduce the spectral stability problem for such flows to a spectral problem for an ordinary differential operator. This reduction is used to obtain a complete description of the spectrum for fluid flows and a qualitative description of the spectrum (including bounds for the complex part of the spectrum) for plasma flows. It is shown that a steady planar fluid flow with elliptical streamlines is spectrally unstable. It is also shown that all planar magnetized plasma flows with elliptical streamlines are spectrally unstable, except for the case when the magnitudes of the fluid velocity and the Alfvén velocity are exactly equal to each other.
On the local topology evolution of a high-symmetry flow
Authors: Boratav Oluş N. , Pelz Richard B.
Published: July 2002

The local topology evolution of a high-symmetry, high resolution (effective maximum resolution of 10243 grid points, maximum wave number of 341) incompressible flow simulation having a Reynolds number (=1/ν) of 1000 is investigated. The Q–R invariants of the velocity gradient tensor Aij, the enstrophy, ΩijΩij and the mean-square strain rate SijSij are computed at an interval when the local maximum vorticity increases drastically. All the analysis of the computations are done on the z=0 plane, where the maximum vorticity and strain are located during the evolution. In the Q–R plane, most of the collocation points evolve towards the lower right corner, a region where strain dominates over vorticity. The pressure Hessian tensor components are computed in the 0 planes. Points with very large strain and no vorticity, which are located along the boundaries separating oppositely signed vortices, are found to have a diagonal pressure Hessian tensor. It is discussed how such a Hessian tensor form can result in a singularity formation in strain (and Q invariant). Relevance of the results to turbulence is discussed. Results are compared to the predictions of a singular model by Léorat (Ph.D. thesis, Université de Paris VII, pp. 125–129, 1975), Vieillefosse [J. Phys. 43, 837 (1982)], and Cantwell [Phys. Fluids A 5, 2008 (1992)].
Comments on ‘‘Extension of the Mott-Smith method to denser gases’’ [Phys. Fluids A 4, 1856 (1992)]
Authors: Cercignani Carlo , Frezzotti Aldo , Sgarra Carlo
Published: July 2002

This Brief Communication is devoted to a discussion of Orlov’s extension of the Mott-Smith method to study the propagation of a shock wave in a moderately dense hard sphere gas. It is shown that, at least in the present form, the method is not compatible with the conservation of momentum and energy.
Scaling properties of vortex ring formation at a circular tube opening
Authors: Nitsche Monika
Published: July 2002

A vortex sheet model is applied to study vortex ring formation at the edge of a circular tube, for accelerating piston velocities Up∼tm. We determine properties of the vortex ring as a function of the piston motion and investigate the extent to which similarity theory for planar vortex sheet separation applies. For piston strokes up to half the tube diameter, we find that the ring diameter, core size and circulation are well predicted by the planar similarity theory. The axial ring translation is a superposition of an upstream component predicted by the theory and a downstream component which is linear in the piston stroke. The front of the fluid volume exiting the tube is also linear in the piston stroke and travels with 75% of the piston velocity. The core size decreases and the distribution of fluid near the core becomes more asymmetric as the parameter m increases.
Vapour cavitation in very confined spaces for Newtonian and non Newtonian fluids
Authors: Ouibrahim A. , Fruman D. H. , Gaudemer R.
Published: July 2002

Experiments were conducted in very confined spaces comprised between a rotating cylinder and a stationary flat plate, with a minimum gap down to 5 microns, using water and a 600 ppm aqueous solution of Polyox WSR 301. The conditions for cavitation occurrence as well as the morphology of the developed cavities were determined. In the case of water, onset of cavitation is in the form of isolated spots randomly distributed along a cylinder generatrix. If the local pressure is further reduced, spots increase in size to form larger cavities, become less random and, finally, form a string of cavities whose length, in the direction of the flow, is larger than the width. As compared to the solvent, the polymer solution delays cavitation inception, decreases the length of developed cavities, and eliminates the interstitial film between successive cavities. These effects can be related to the strong elongational flow prevailing in the confined space and the viscoelastic characteristics of the polymer solution. From a comparison of the Newtonian and non Newtonian inception cavitation numbers, the elongational viscosity of the polymer solution is estimated.
X-ray measurements of growth rates at a gas interface accelerated by shock waves
Authors: Bonazza R. , Sturtevant B.
Published: July 2002

A new experimental technique to measure the density of a high atomic number gas at a shock-accelerated interface has been developed and demonstrated. It is based on the absorption of x rays by the high atomic number gas, and it was implemented in a vertical square shock tube. The object of the study was the turbulent entrainment and mixing of shock-accelerated air/xenon interfaces prepared by retracting a metal plate, initially separating the two gases, prior to the release of the shock wave. Interfaces of two types, quasi-sinusoidal and nominally flat, were examined. The amplitude of large wavelength (25–100 mm) perturbations on the interface, and the thickness of the interface were measured. An integral definition for the interface mean line was adopted, making it possible to study and time evolution of the individual Fourier modes of the perturbations. A new integral definition for the interface thickness was proposed, making it feasible to study for the first time the time evolution of the thickness of quasi-sinusoidal interfaces. Images of interfaces after interacting with a series of weak waves reverberating between the interface and the shock tube end wall were obtained. The perturbations are studied at the late stages of their evolution, when their amplitude is no longer small compared to their wavelength. Consequently, the measured growth rates of the modal amplitudes are smaller than those predicted by the impulsive model based on the small amplitude approximation. In the case of nominally flat interfaces, the thickness is observed to grow linearly at rates comparable to values previously reported.
The near wake region of a high solidity mesh strip
Authors: Kopp G. A. , Keffer J. F.
Published: July 2002

A pattern-recognition analysis of the near region of a plane turbulent wake generated by a high solidity mesh strip reveals a markedly regular vortex street. In fact, the ratio of the ‘‘coherent’’ to ‘‘incoherent’’ (or ‘‘random’’) fluctuations is significantly larger than for many other plane turbulent wakes of similar Reynolds number. Since these incoherent fluctuations are so weak, the vortex street persists. This is in contrast to what is observed to happen in many other wakes, where secondary vortices, which are associated with the incoherent fluctuations, act to deform the main vortices of the vortex street into horseshoe-like vortices very early in the development. Here, the secondary structures must be too weak in the near region to influence the vortex street to any significant effect.
Stability of source-vortex and doublet flows
Authors: Shusser M. , Weihs D.
Published: July 2002

A linear stability analysis is performed for steady source-vortex and sink-vortex flows for viscous and inviscid incompressible fluids. The analysis is based on a method recently developed by the authors [Phys. Fluids 7, 2345 (1995)], which utilizes the irrotational nature of the basic flow and takes vorticity as a perturbation. It is shown that source-vortex flows are always unstable. Sink-vortex flows are found stable except for low flow-rate flows of viscous fluid. The potential vortex is unstable for three-dimensional perturbations, but stable for two-dimensional perturbations if the fluid is inviscid. For inviscid fluid the linear stability of doublet and higher-order singularities for plane perturbations is also studied. The general integral of the linearized vorticity equations is found and used for stability analysis. Only doublet flow is found stable. A mathematical criterion for stability of certain types of steady two-dimensional flows of inviscid incompressible fluid is formulated.
Thermal inertial waves in a rotating fluid layer: Exact and asymptotic solutions
Authors: Zhang Keke , Roberts Paul H.
Published: July 2002

The problem of the onset of convective instability in a rapidly rotating fluid layer heated from below with various velocity boundary conditions is investigated by constructing exact solutions and by asymptotic analysis. It is shown that convective motions at sufficiently small Prandtl numbers are described in leading order by a thermal inertial wave. It is at the next order that buoyancy forces drive the wave against the weak effect of viscous dissipation. On the basis of the perturbation of the thermal inertial wave, asymptotic convection solutions for rigid boundaries can be expressed in simple analytic form. A new asymptotic power law between the critical Rayleigh number and the Ekman number is derived. In addition, solutions for both stationary and time-dependent convection are calculated numerically. Comparison between the numerical and asymptotic solutions is then made to show that a satisfactory quantitative agreement has been achieved.
Experimental assessment of Taylor’s hypothesis and its applicability to dissipation estimates in turbulent flows
Authors: Dahm Werner J. A. , Southerland Kenneth B.
Published: July 2002

Results are presented from an assessment of the applicability of Taylor’s hypothesis for approximating streamwise derivatives and obtaining dissipation estimates in turbulent flows. These are based on fully resolved measurements of a conserved scalar field ζ(x,t) throughout a four-dimensional spatio-temporal volume in a turbulent flow. The data allow simultaneous evaluation of all three components of the true gradient vector field ∇ζ(x,t) and the time derivative field (∂/∂t)ζ(x,t) at the small scales of a turbulent shear flow. Streamwise derivatives obtained from Taylor’s frozen flow hypothesis yield a correlation of 0.74 with the true streamwise derivative field at the present measurement location in the self-similar far field of an axisymmetric turbulent jet. Direct assessments are also presented of approximations invoking Taylor’s hypothesis to estimate energy dissipation rates in turbulent flows. The classical single-point time series approximation yields a correlation of 0.56 with the true scalar energy dissipation rate, while a mixed estimate that combines one spatial derivative and the time derivative gives a correlation of 0.72. A general analytical formulation is presented for assessing various dissipation estimates, and for determining the optimal dissipation estimate that maximizes the correlation with the true dissipation rate. The resulting optimal mixed dissipation estimate yields a correlation of 0.82 at the point of maximum turbulence intensity in a jet, and a value of 0.92 on the jet centerline.
On the spectrum of hyperbolic flows
Authors: Lifschitz Alexander
Published: July 2002

By using a previously developed technique [A. Lifschitz, Phys. Fluids A 7, 1626 (1995)], it is shown that the spectrum of linear hyperbolic flows in the plane occupies a strip in the complex plane along the real axis which is independent of the geometry of the basic flow and that all the points in this strip are simple eigenvalues. The relevance of this result to the stability theory is explained.
Downstream pressure induced hysteresis in the regular ↔ Mach reflection transition in steady flows
Authors: Ben-Dor G. , Elperin T. , Li H. , Vasiliev E.
Published: July 2002

The regular ↔ Mach reflection transition in steady flows was investigated numerically using the W-modified Godunov’s scheme. In addition to the incident-shock-wave-angle-induced hysteresis, which was discovered a few years ago and reconfirmed in the present study, a new downstream-pressure-induced hysteresis was found to exist.
Second- and third-order longitudinal velocity structure functions in a fully developed turbulent channel flow
Authors: Antonia R. A. , Zhou T. , Romano G. P.
Published: July 2002

Second- and third-order moments of temporal increments of the longitudinal velocity fluctuation have been measured using hot wires in a fully developed turbulent channel flow and analyzed using values of the mean energy dissipation rate inferred from direct numerical simulation data for the same flow and Reynolds numbers. The results indicate that dissipative range scales approach isotropy relatively rapidly when the mean shear is negligible. For larger inertial range type scales, the approach is slower. The rate at which isotropy is approached seems slower for third-order than second-order structure functions. This rate depends more on the mean shear than on the turbulent Reynolds number. Two-point laser Doppler anemometry measurements provide reasonable support for the use of Taylor’s hypothesis, at least outside the buffer region.
An algebraic preclosure theory for the Reynolds stress
Authors: Parks S. M. , Weispfennig K. , Petty C. A.
Published: July 2002

An algebraic preclosure theory for the Reynolds stress 〈u′u′〉 is developed based on a smoothing approximation which compares the space–time relaxation of a convective-diffusive Green’s function with the space–time relaxation of turbulent correlations. The formal preclosure theory relates the Reynolds stress to three distinct statistical properties of the flow: (1) a relaxation time τR associated with the temporal structure of the turbulence; (2) the spatial gradient of the mean field; and, (3) a prestress correlation related to fluctuations in the instantaneous Reynolds stress and the pressure field. Closure occurs by using an isotropic model for the prestress. For simple shear flows, the theory predicts the existence of a nonzero primary normal stress difference and an eddy viscosity coefficient which depends on the temporal relaxation of the turbulent structure and a characteristic time scale associated with the mean field. The asymptotic state of homogeneously sheared turbulence shows that τRS∼1, where S represents the mean shear rate. The Reynolds stress model and a set of recalibrated k−ε transport equations predict that the relaxation of homogeneously sheared turbulence to an asymptotic state requires development distances larger than 20 ×〈uz〉(0)/S, a theoretical result consistent with experimental observations.
Motions of anisotropic particles: Application to visualization of three-dimensional flows
Authors: Gauthier G. , Gondret P. , Rabaud M.
Published: July 2002

The aim of the paper is to get insight into flow patterns visualized by suspended anisotropic reflective particles. The motion of triaxial ellipsoids embedded in a three-dimensional flow, i.e., which cannot be reduced to a local plane Couette flow, is calculated. Both the asymptotic trajectory and the transient time to reach it are discussed. These results are used to simulate laser sheet visualizations of two classical three-dimensional flows (Taylor–Couette vortices and flow between rotating disks) where the particle history is shown to be negligible. The simulated visualizations are well compared to experimental ones but the paper addresses the fact that the legitimate question of what shows the visualization does not have a simple answer. Nevertheless, these results open the way for quantitative comparisons between computational fluid dynamics and experimental visualizations.
On the modification of the near-wall coherent structure in a three-dimensional turbulent boundary layer on a free rotating disk
Authors: Kang Hyung Suk , Choi Haecheon , Yoo Jung Yul
Published: July 2002

An experimental study has been performed on a shear-driven three-dimensional turbulent boundary layer in equilibrium over a rotating disk. The objective of the present study is to investigate the modification of the near-wall coherent structure in the three-dimensional turbulent boundary layer developed in this flow. Two-point velocity measurements are carried out with two X-wire probes which are aligned in the local wall-parallel mean velocity direction, which show that strong asymmetries exist in the velocity cross-correlation coefficient in the spanwise direction, and also in the conditionally averaged velocity signals in the vicinity of a strong ejection or sweep, as was shown by Littell and Eaton [J. Fluid Mech. 266, 175 (1994)]. However, a quadrant analysis reveals that the Reynolds-shear-stress-producing eddies are nearly symmetric in the spanwise direction and those asymmetries are attributed to the changes in the negative-Reynolds-shear-stress-producing motions which have less relation to the streamwise coherent structures.