bluuebunny/crossref_metadata_2025 huggingface dataset:
Low Reynolds number flow over cavities
Authors: Shen C. , Floryan J. M.
Published: July 2002

Low Reynolds number flow over rectangular cavities is analyzed. The problem is posed to simulate towing tank experiments of Taneda [J. Phys. Soc. Jpn. 46, 1935 (1979)]. A very good agreement exists between numerical and experimental results. The dividing streamline separates from the cavity side wall below the upper corner. The separation point moves toward this corner when the aspect ratio decreases. Flow structure inside the cavity changes considerably with the aspect ratio. Only corner vortices exist in a cavity of aspect ratio W/h=4.0. A decrease of the aspect ratio leads to the enlargement and eventual merger of these vortices. The merger begins with the formation of a stagnation point separating two vortex centers inside the cavity. These vortex centers become progressively weaker and merge to form a single central vortex in a cavity of aspect ratio W/h=2.0. Further decrease of the aspect ratio results in the enlargement of the new corner vortices and their eventual merger. This process begins in a cavity of aspect ratio between 0.6 and 0.575 and is finished in a cavity of aspect ratio 0.5, where two central vortices have been identified. The further decrease of the aspect ratio leads to the sequential repetition of this process and creation of additional central vortices.
Effects of viscosity variation on the stability of film flow down heated or cooled inclined surfaces: Long-wavelength analysis
Authors: Goussis D. , Kelly R. E.
Published: July 2002

The linear stability of liquid film flow, when the viscosity depends exponentially on temperature, is investigated here for the case of heating or cooling from below by means of an analysis valid for long waves. It is shown that cooling stabilizes the flow, while heating destabilizes it. For the case of cooling, a cutoff Prandtl number exists, above which the flow is stable with respect to long waves.
Solitary waves in a magnetic flux tube
Authors: Roberts B.
Published: July 2002

Magnetic flux tubes (slabs or cylinders) are of considerable physical interest because of their occurrence in the sun’s atmosphere. The propagation of weakly nonlinear, long-wavelength (weakly dispersive), sound waves in both a magnetic slab and a magnetic cylinder is discussed. The slab geometry leads to the Benjamin–Ono equation, viz., ∂v/∂t+cT(∂v/∂z) +βv(∂v/∂z) +(α/π)(∂2/∂z2) ×∫/∞−∞[v(s,t)ds/(s−z)]=0, and the cylindrical geometry yields its allied form, viz., ∂v/∂t+cT(∂v/∂z)+βv(∂v/∂z) +α′(∂3/∂z3)∫∞−∞{v(s,t)ds/ [λ2+(s−z)2]1/2}=0, an equation known also to arise in waves on concentrated vortices in fluids. The magnetic flux tube thus provides a simple illustration of these two equations, hitherto only considered in separate physical systems.
Electron-cyclotron maser instability in relativistic plasmas
Authors: Pritchett P. L.
Published: July 2002

The electron-cyclotron maser instability is studied for the case of an anisotropic electron velocity distribution in the regime where the relativistic corrections to the wave dispersion are significant. Solution of the linear dispersion relation reveals that when the plasma frequency–gyrofrequency ratio ωpe/Ωe<vte/c, the instability is localized just below k⊥c/Ωe=1. The growth rate is then strongly peaked for emission at 90° to the magnetic field and is considerably larger than would be the case if the cold-plasma dispersion theory were valid. These features are confirmed by electromagnetic particle simulations. The simulations also show that saturation results from perpendicular diffusion in velocity space and that the saturation level increases as ωpe/Ωe is decreased. A quasilinear analysis predicts that the saturation level scales as (Ωe/ωpe)2 ωmaxI, where ωmaxI is the maximum linear growth rate. Applications of the maser instability to the generation of the Earth’s auroral kilometric radiation are discussed.
Two-dimensional simulation of high Mach number plasma interactions
Authors: Thomas V. A. , Brecht Stephen H.
Published: July 2002

In this paper a hybrid particle–fluid simulation code is used to examine the large-scale (λ∼c/ωpi) low-frequency (ω∼ωci) formation and evolution of a collisonless shock in two dimensions where the shock is caused by a plasma slug of finite thickness traveling perpendicular to the ambient magnetic field in the presence of a uniform background plasma. During the evolution of the shock structure, background ions are energized in the perpendicular direction and then isotropized. The isotropization process is associated with the presence of large-amplitude, primarily electromagnetic, waves propagating parallel to the ambient magnetic field that are created by the self-consistent plasma interaction. High Mach number shocks are found to be inherently two-dimensional objects.
Plasma flows and radial electric field in nonaxisymmetric toroidal plasmas
Authors: Shaing K. C.
Published: July 2002

The ambipolarity of the plasmas in nonaxisymmetric toroidal systems is studied by considering the momentum relaxation on a flux surface. A set of two time-dependent equations for two chosen independent variables, the parallel plasma flow velocity U∥ and the radial electric field Er, is employed to describe the momentum relaxation process. In general, these two variables are coupled through plasma viscosities. At the steady state, one of the equations produces the viscous relaxation criterion ∑a〈B ⋅ ∇ ⋅ Πa〉=0, and the other gives rise to the well-known ambipolarity constraint ∑aeaΓana=0, where Πa, ea, and Γana are the viscous tensor, electric charge, and nonambipolar particle flux, respectively, for species a, and B is the magnetic field. After U∥ and Er are determined, the plasma is in the ambipolar state; that is, both electrons and ions diffuse at the same rate across the flux surface.
The alpha dynamo parameter and measurability of helicities in magnetohydrodynamic turbulence
Authors: Matthaeus W. H. , Goldstein M. L. , Lantz S. R.
Published: July 2002

Alpha, an important parameter in dynamo theory, is shown to be proportional to either the kinetic, current, magnetic, or velocity helicities of the fluctuating magnetic field and fluctuating velocity field. The particular helicity to which alpha is proportional depends on the assumptions used in deriving the first-order smoothed equations that describe the alpha effect. In two cases, viz., when alpha is proportional to either the magnetic helicity or velocity helicity, alpha can be determined experimentally from two-point measurements of the fluctuating fields in incompressible, homogeneous turbulence with arbitrary rotational symmetry. For the other two possibilities, alpha can be determined if the turbulence is isotropic.
Laser interaction in long-scale-length plasmas
Authors: Gardner J. H. , Herbst M. J. , Young F. C. , Stamper J. A. , Obenschain S. P. , Manka C. K. , Kearney K. J. , Grun J. , Duston D. , Burkhalter P. G.
Published: July 2002

Absorption of a short-pulse, high-intensity Nd-laser beam (vacuum irradiance of 1014 to 1015 W/cm2) by preformed plasmas of different density scale lengths is investigated. Increased effects of plasma instabilities are found at longer scale lengths. The amount of backscattered light increases with plasma scale length and limits the absorption fraction at the longest scale length. The onset of suprathermal electron production, deduced from observations of energetic (20 to 50 keV) x rays, occurs at lower laser irradiance for longer-scale-length plasmas. A correlation between energetic x rays and 3ω0/2 emission suggests that the suprathermal electrons are produced by a plasma instability at quarter-critical density. At higher intensities there is evidence for severe perturbations of the preformed plasma and for self-focusing of the incident beam.
A computational study of ion cyclotron frequency stabilization of the m=1 interchange mode in mirror geometry
Authors: Myra J. R. , D’Ippolito D. A. , Francis G. L.
Published: July 2002

A cylindrical plasma model is used to study the stabilizing effect of electromagnetic ion cyclotron frequency range (ICRF) waves on the m=1 magnetohydrodynamic interchange mode. The fast wave eigenmodes of the column and the near-field antenna pattern are calculated numerically for a diffuse plasma profile when ω>Ωi. The resulting ponderomotive force and sideband contributions to global interchange stability are then determined using a rigid shift trial function. For far-field stabilization it is verified that the direct ponderomotive and sideband contributions cancel exactly as the conducting wall supporting the fast wave eigenmode moves out to infinity. The near-field stabilization effect is related numerically to the driven k∥ spectrum of the waves and their radial profiles. The numerical model is employed to calculate threshold ICRF wave amplitudes for the stabilization experiments in the Phaedrus tandem mirror [Phys. Rev. Lett. 51, 1955 (1983)].
Single-particle analysis of the free-electron laser sideband instability for primary electromagnetic wave with constant phase and slowly varying phase
Authors: Davidson Ronald C. , Wurtele Jonathan S.
Published: July 2002

Use is made of the single-particle orbit equations together with Maxwell’s equations and appropriate statistical averages to investigate detailed properties of the sideband instability for a helical-wiggler free-electron laser with wiggler wavelength λ0=2π/k0=const and normalized wiggler amplitude aw=eB̂w/mc2k0 =const. The model describes the nonlinear evolution of a right-circularly polarized primary electromagnetic wave with frequency ωs, wavenumber ks, and slowly varying amplitude âs(z,t) and phase δs(z,t) (eikonal approximation). The orbit and wave equations are analyzed in the ponderomotive frame (‘‘primed’’ variables) moving with velocity vp=ωs/(ks+k0) relative to the laboratory. Detailed properties of the sideband instability are investigated for small-amplitude perturbations about a quasisteady equilibrium state characterized by â0s =const (independent of z′ and t′). Two cases are treated. The first case assumes constant equilibrium wave phase δ0s =const, which requires (for self-consistency) both untrapped- and trapped-electron populations satisfying 〈∑j exp[ik′pzj0(t′) +iδ0s]/γ′j〉=0.

Here kp=(ks+k0)/γp is the wavenumber of the ponderomotive potential, z′j0(t′) is the equilibrium orbit, and γjmc2 is the electron energy. The second case assumes that all of the electrons are deeply trapped, which requires a slow spatial variation of the equilibrium wave phase, ∂δ0s/∂z′=2Γ0(Γ0ck0/ΩB)2 k′p≠0. The resulting dispersion relations and detailed stability properties are found to be quite different in the two cases. Both the weak-pump and strong-pump regimes are considered.
Ballooning mode stability of elongated high-beta tokamaks
Authors: Mauel Michael E.
Published: July 2002

The variational principle derived by Choe and Freidberg [Phys. Fluids 29, 1766 (1986)] and used to estimate the geometry of high-beta tokamak equilibria is extended to include elongation. Ballooning mode stability is then investigated, illustrating the influence of elongation on local and global stability.
The evolution of a decaying spheromak
Authors: Sgro A. G. , Mirin A. A. , Marklin G.
Published: July 2002

The evolution of a low beta spheromak initially in a two-dimensional stable equilibrium having a constant J/B (the so-called minimum energy state) is calculated within the context of resistive magnetohydrodynamics. Since the initial equilibrium is stable, the spheromak at first resistively evolves through a sequence of stable quasiequilibria. This phase of the evolution is calculated with a transport code in which the resistivity is assumed to be largest at the wall and lowest at the magnetic axis. Resistive diffusion causes the safety factor q to decrease everywhere while decreasing fastest near the wall. The quasiequilibria through which the spheromak evolves are tested for stability with both an ideal linear stability code and a resistive one. The results of both stability codes are in basic agreement and show that when q drops to below (1)/(2) everywhere the spheromak becomes unstable to an n=2 mode. The agreement of the stability codes implies that the unstable mode is a resistively modified ideal mode. The unstable equilibrium is used as the initial

condition in a 3-D nonlinear magnetohydrodynamic simulation. This simulation shows that after the unstable mode saturates, the spheromak resistively evolves through a sequence of three-dimensional quasiequilibria until it reaches another unstable configuration, after which it approaches the 2-D minimum energy state again. This evolutionary cycle can conceivably start again, unless the cycle time becomes comparable to the configuration decay time, which happens at high S. One consequence of the evolutionary cycle is that as the 3-D spheromak approaches the minimum energy state, the magnetic axis and hot plasma near it approach the wall and a new magnetic axis is formed. At high enough S, when the cycle time is comparable to the configuration lifetime, this convective heat loss mechanism is minimized. The 3-D code predicts that only the n=0 and n=2 modes are active. Simulations in which the n=1, 3, and 4 modes are present show that these modes decay while the n=2 grows and saturates. Closed flux surfaces are present over most of the domain so that heat loss along stochastic field lines should not be large. When the Hall term is included a toroidal rotation of the magnetic configuration is induced which most likely corresponds to an experimentally measured rotation. The results of this calculation are in qualitative agreement with various experimental data.
Resistive interchange instability criterion in anisotropic toroidal systems
Authors: Johnson J. L. , Hastie R. J.
Published: July 2002

Ideal (Mercier) and resistive criteria for localized magnetohydrodynamic instabilities are derived for general toroidal systems with anisotropic pressure.
Streak-line motion during steady and unsteady axisymmetric vortex breakdown
Authors: Neitzel G. P.
Published: July 2002

Numerical calculations of vortex breakdown generated within a closed circular cylinder by rotation of one of the end walls have been performed. The solutions are used to compute steady streak-line patterns for dye introduced both symmetrically and asymmetrically about the symmetry axis upstream of the breakdown bubble. Beginning from such a steady state, the end-wall angular speed is impulsively increased and the asymmetric streak-line pattern is observed during a portion of the subsequent period of unsteady flow.
Ponderomotive force at the onset of chaos
Authors: Kono Mitsuo , Iwano Ryuichiro
Published: July 2002

An analytical expression for the ponderomotive force is derived in a system with a standing wave. The ponderomotive force first increases with the wave amplitude, then decreases and becomes zero at a certain value of the amplitude above which chaos is initiated. The result is confirmed by numerical experiments.
Sheath and presheath in a collisionless plasma with a Maxwellian source
Authors: Scheuer J. T. , Emmert G. A.
Published: July 2002

Bissell and Johnson [Phys. Fluids 30, 779 (1987)] have calculated the electrostatic potential variation in the sheath and presheath regions of a collisionless plasma in which the source of ions is assumed to be Maxwellian. To do this, they imposed the generalized Bohm criterion as a boundary condition. In this paper the plasma equation is solved numerically without imposing the Bohm criterion as a boundary condition. The results compare well with their results. In addition, the ion distribution function throughout the plasma region is calculated. Because of this particular source model, the ion distribution at the center of the plasma has a spiked non-Maxwellian shape.
Generalization of the synchrotron absorption–emission coefficient in plasmas to arbitrary direction of propagation
Authors: Nassri A. , Heindler M.
Published: July 2002

A new analytical formulation of the synchrotron absorption and emission coefficient in plasmas, for wave propagation perpendicular to the magnetic field, has been derived previously [Phys. Fluids 29, 3275 (1986)]. These coefficients were shown to be both accurate and analytically simple. Their generalization to arbitrary directions of propagation with respect to the magnetic field is presented here. Based on the analytical formulas for perpendicular propagation and on the exact sum–integral formulation of the coefficients for arbitrary propagation, this generalization is achieved by empirical data fit. Hereby the exact formulation serves as target function for the fitting procedure and subsequently as reference for determination of the accuracy of the results. The generalized analytical representations for the coefficients are presented here, one for each polarization mode and for the low and high temperature domain (above and below a few tens of kilo-electron-volts).
‘‘Flicker’’ in small scale laser–plasma self-focusing
Authors: Coggeshall S. V. , Mead W. C. , Jones R. D.
Published: July 2002

Small amplitude, short wavelength ion acoustic waves in laser-produced plasmas cause fluctuations in the trajectories of light rays that can lead to time-dependent, self-sustaining shifting of focal spots and a somewhat random redistribution of the light near the critical surface. This flickering is seen in simulations involving small scale beam inhomogeneities over a uniform background laser profile, which model the center of a realistic laser beam. The effect can cause significant intensity multiplication in long scale length high-Z plasmas with only modest beam imperfections.
A statistical model of electron heating in localized Langmuir fields
Authors: Rozmus W. , Samson J. C.
Published: July 2002

It is shown that the interaction of charged particles with localized, coherent, electrostatic wave packets can be described by a diffusion model, provided that the modes of each wave packet overlap. A theoretical model for the diffusion coefficient is proposed that takes into account the existence of large adiabatic islands, embedded within stochastic regions of the phase space. The model is based on the observation that particles in the stochastic regions interact independently with each wave packet, and consequently a time-localized diffusion model can be used. Solutions of the diffusion equation, which use theoretical values for the diffusion coefficient, give very good predictions of the temporal evolution of the particle distribution functions and kinetic energy.
Flow regimes in two-dimensional mixed convection with spatially periodic lower wall heating
Authors: Zhang Sara Q. , Tangborn Andrew V.
Published: July 2002

Two-dimensional numerical simulations of flow through a channel with spatially periodic temperature boundary conditions at the lower wall have been carried out. A spectral method with a Fourier series expansion in the streamwise direction and a Chebyshev expansion in the vertical direction is employed. A bifurcation to a limit cycle occurs at Reynolds numbers as low as Re=4 and Rayleigh numbers as low as Ra=14 500. The frequency of oscillation decreases with Re and is essentially independent of Ra. Maps of flow regimes for varying periodicities have been created. Regimes with periodicities longer than the imposed temperature boundary condition have been found.
Effects of body curvature and nonparallelism on the stability of flow over a swept cylinder
Authors: Masad Jamal A. , Malik Mujeeb R.
Published: July 2002

The linear stability of three-dimensional incompressible flow over an infinite swept cylinder is considered. In particular, the effects of convex body curvature and nonparallelism on both stationary and traveling disturbances are studied. Both an exact approach and a perturbation approach are used to account for the body-curvature effect and the results from both approaches agree very well. The nonparallel effects are accounted for by using a perturbation method. The influence of convex body curvature and nonparallelism with variation in the sweep angle, the unit Reynolds number, the cylinder radius, the location on the cylinder, and the disturbance spanwise wave number and frequency is studied. Both stationary and traveling disturbances are destabilized by the nonparallel effects and are stabilized by the convex body-curvature effects. This is in agreement with the results obtained by solving linear parabolized stability equations. The effect of convex body curvature is gradually less stabilizing as the disturbance frequency increases. The variation of the combined effects of convex body curvature and nonparallelism in the parameter space is controlled mainly by the variation (in the parameter space) of the convex body-curvature effects.
Nonlinear interaction of small-scale Rossby waves with an intense large-scale zonal flow
Authors: Manin Dmitrii Yu. , Nazarenko Sergey V.
Published: July 2002

The system of Rossby waves is unstable with respect to modulations. This instability results in the generation of a large-scale zonal flow with zero mean vorticity. It is shown that in both stable and unstable situations, a finite-time singularity formation takes place in the system. Such a singularity has the form of peaks on the vorticity profile of the zonal flow. The situation is also considered when some zonal flow with nonzero mean vorticity is initially present. Solitary-wave solutions appropriate for the description of nonlinear behavior of such systems are found. In the case of weak mean vorticity of the zonal flow, the solitons break and the singularities develop. If the mean vorticity is strong, then the evolution of the system can be considered as the dynamics of a soliton gas. Soliton dynamics possesses some interesting properties, such as formation of soliton pairs and annihilation of solitons during collision.
The effects of viscosity on the stability of a trailing-line vortex in compressible flow
Authors: Stott Jillian A. K. , Duck Peter W.
Published: July 2002

We consider the effects of viscosity on the inviscid stability of the Batchelor [J. Fluid Mech. 20, 645 (1964)] vortex in a compressible flow. The problem is tackled asymptotically, in the limit of large (streamwise and azimuthal) wavenumbers, together with large Mach numbers. This problem, with viscous effects neglected, was discussed in Stott and Duck [J. Fluid Mech. 268, 323 (1994)]. The authors found that the nature of the solution passes through different regimes as the Mach number increases, relative to the wave number. This structure persists when viscous effects are included in the analysis. In the present study, as in that mentioned above, the mode present in the incompressible case ceases to be unstable at high Mach numbers and a center mode forms, whose stability characteristics are determined primarily by conditions close to the vortex axis. We find generally that viscosity has a stabilizing influence on the flow, whilst in the case of center modes, viscous effects become important at much larger Reynolds numbers than for the first class of disturbance.
Stokes drag on conglomerates of spheres
Authors: Cichocki B. , Hinsen K.
Published: July 2002

The Stokes drag coefficients for conglomerates of between two and 167 spheres are obtained from a recently developed scheme for numerical calculations of hydrodynamic interactions [J. Chem. Phys. 100, 3780 (1994)]. Experimental data for these conglomerates were provided by Lasso and Weidmann [Phys. Fluids 29, 3921 (1986)]. The numerical results and the experimental data agree very well. It is shown that in numerical calculations of hydrodynamic interactions, all long-range contributions must be included exactly.
Photographic study of the shock-induced dispersion of microscopic gas bubbles
Authors: Szumowski A. P. , Falkowski K.
Published: July 2002

Separated and attached microscopic air bubbles excited by a sequence of expansion and compression (shock) waves are considered. It was found out that the expanded bubbles break up into clusters of air nuclei, under certain conditions, due to the shock wave-induced collapses.
Nonlinear waves and turbulence in Marangoni convection
Authors: Kazhdan D. , Shtilman L. , Golovin A. A. , Pismen L. M.
Published: July 2002

In the paper we present a numerical study of a new type of nonlinear waves in Marangoni convection. The waves are caused by nonlinear interaction between long-scale deformational instability and short-scale convection. It is shown that, due to a nonlinear coupling with the deformation of the free liquid–gas interface, the primary convection pattern can undergo oscillatory instability generating various kinds of long surface waves which modulate the short-scale convection. The numerical analysis of the system of nonlinear coupled equations describing these waves confirms the predictions of weakly nonlinear analysis and shows the existence of either standing or travelling waves in the proper parametric regions, at low supercriticality. With increasing supercriticality, the waves undergo various transformations leading to the formation of pulsating travelling waves, aharmonic standing waves as well as irregular wavy behavior resembling ‘‘interfacial turbulence.’’ We map regions in the parameter space where various kinds of waves can be observed, and describe some characteristics of irregular wavy behavior.
An explicit example with non-Gaussian probability distribution for nontrivial scalar mean and fluctuation
Authors: McLaughlin Richard M. , Majda Andrew J.
Published: July 2002

Recently, one of the authors, studying a model for turbulent diffusion involving a large-scale velocity field rapidly fluctuating in time, rigorously demonstrated intermittency in a diffusing scalar field by exhibiting broader than Gaussian tails in the scalar PDF. Here, we explore this model further with exact formulas within the context of general initial data possessing both a mean and a fluctuating component. Several new phenomena due to the presence of a nonzero scalar mean are documented here. We will establish that the limiting long time scalar PDF has long tails, as well as persisting skewness. Further, we show that the limiting PDF depends on the large-scale energy of initial temperature fluctuations and exhibits long time memory of the initial data. Additionally, we will exhibit an explicit phase transition occurring in the scalar PDF as this large scale energy is varied, whereby the limiting PDF switches between states arising from deterministic initial data and states dominated by fluctuation.
Phase dynamics of Kármán vortices in cylinder wakes
Authors: Monkewitz P. A. , Williamson C. H. K. , Miller G. D.
Published: July 2002

The temporal evolution of Kármán vortex shedding patterns in the wake of a cylinder placed at right angles to a uniform flow is studied for Reynolds numbers (based on cylinder diameter) between 80 and 140. Focusing on the dynamics of the vortex shedding phase in the wake planview (the plane spanned by the free-stream direction and the cylinder axis) we study experimentally and model the response of shedding patterns to time-dependent boundary conditions imposed at the cylinder ends. By appropriate impulsive changes of end conditions, spanwise wave number ‘‘shocks’’ can be produced that travel along the cylinder span. These shock experiments, together with data from steady oblique shedding patterns, are used to determine the parameters for the spanwise Ginzburg–Landau model, which has already been used successfully to describe many of the phenomena observed in cylinder wakes. We then demonstrate experimentally that, in analogy to gasdynamics, it is also possible to produce ‘‘expansion waves’’ of the spanwise wave number, which are well described by the Ginzburg–Landau model without further adjustment of its parameters.
Transition in flow over a swept cylinder: Correlation with experimental data
Authors: Masad Jamal A. , Abdelnaser Ahmad S.
Published: July 2002

Linear stability analysis, which includes the effects of nonparallelism and body curvature, is used to calculate the N factors of stationary and traveling disturbances for the same experimental conditions measured by Poll for flow over a long swept cylinder. The correlating N factors for traveling disturbances have less scatter than the correlating N factors of stationary disturbances. The mean value of the correlating N factor for traveling disturbances is 14.9 and 7.4 for stationary disturbances. Therefore, for an initial amplitude of a stationary disturbance that is 100 times larger than that of a traveling disturbance, the amplitude of the traveling disturbance is 18 times larger than the amplitude of a stationary disturbance at the location of transition onset. The calculations indicate that transition is due to traveling disturbances; this result is in agreement with the experimental observations.
The separation of particle pairs in the eddy-damped quasinormal Markovian approximation
Authors: Thomson David J.
Published: July 2002

The implications of the eddy-damped quasinormal Markovian (EDQNM) approximation for the separation of particle pairs in (three-dimensional) inertial subrange turbulence are explored. In particular the EDQNM equations are solved for the particle separation probability distribution, without making the usual approximation of replacing the damping time scales by their large time asymptotic form. A number of properties of the separation probability distribution that are of significance for the prediction of concentration fluctuations are calculated. The values show quite large departures from the values obtained with the large time form of the damping time scales.
A DNS study of turbulent mixing of two passive scalars
Authors: Juneja A. , Pope S. B.
Published: July 2002

We employ direct numerical simulations to study the mixing of two passive scalars in stationary, homogeneous, isotropic turbulence. The present work is a direct extension of that of Eswaran and Pope from one scalar to two scalars and the focus is on examining the evolution states of the scalar joint probability density function (jpdf) and the conditional expectation of the scalar diffusion to motivate better models for multi-scalar mixing. The initial scalar fields are chosen to conform closely to a ‘‘triple-delta function’’ jpdf corresponding to blobs of fluid in three distinct states. The effect of the initial length scales and diffusivity of the scalars on the evolution of the jpdf and the conditional diffusion is investigated in detail as the scalars decay from their prescribed initial state. Also examined is the issue of self-similarity of the scalar jpdf at large times and the rate of decay of the scalar variance and dissipation.
Renormalization group theory for turbulence: Eddy-viscosity type model based on an iterative averaging method
Authors: Nagano Yasutaka , Itazu Yoshihiro
Published: July 2002

The renormalization group (RNG) theory of turbulence is often used for the forced Navier–Stokes equation in order to investigate turbulence models in Fourier space. The strong point of this kind of theory is the ability to construct turbulence models with the aid of the Kolmogorov −5/3 power law for the energy spectrum. In this paper, we have made use of an iterative averaging method proposed by McComb (1990), which does not have the misleading ε-expansion technique developed by Yakhot and Orszag (1986), then applied this method to the derivation of an eddy-viscosity type turbulence model. Using the exact Navier–Stokes equation excluding artificial external forces, we have obtained the eddy-viscosity type turbulence model which is equivalent to the Boussinesq postulate, and its model constant Cμ is determined from only a Kolmogorov constant α.
Comments on ‘‘Weakly nonlocal gravity-capillary solitary waves’’ [Phys. Fluids 8, 1506 (1996)]
Authors: Vanden-Broeck J.-M.
Published: July 2002

An apparent contradiction between the results of Yang and Akylas [Phys. Fluids 8, 1506 (1996)] and those of Vanden-Broeck [Phys. Fluids 3, 2669 (1991)] is clarified by comparing the cnoidal and solitary waves predicted by the Korteweg–de Vries theory. In particular the rate at which the cnoidal waves approach a solitary wave as the wavelength is increased, is discussed.
Vortex formation in mixing layers: A weakly nonlinear stability approach
Authors: Plaschko Peter
Published: July 2002

This paper is concerned with the stability of two-dimensional incompressible mixing layers with small transversal velocity gradients. Using the approach of slight flow divergence, a boundary layer type of approximation of solutions to the steady mixing layer flow is obtained. We derive in the limit of small velocity gradients a velocity profile of an error function type. To gain an insight into the problem of the spatial instability of this flow we apply a model involving perturbations with only a single frequency component. A generalized approach, however, is outlined in the Appendix. There the interaction of a fundamental mode with its subharmonic, oscillating at one-third the frequency, is analyzed. First numerical results show that under certain conditions the subharmonic can represent the dominant disturbance. A multiple scales expansion of the disturbance streamfunction is constructed with variables chosen to derive a Landau-type equation with cubic nonlinearities governing an amplitude function A. Scaling spatial and temporal variables and the Reynolds number we obtain in leading order a generalized Rayleigh equation. We solve the associated eigenvalue problem for spatially growing modes, whereas the calculation of damped modes is beyond the scope of our approach. The solution to this equation can be separated into a shape function and the amplitude A. An investigation of the second-order terms yields a rederivation of the boundary layer approximation of the steady flow, an equation governing second harmonics of the disturbance and an equation determining the mean flow correction. At third order we have to apply a resonance condition, which demands small linear spatial growth rates. This restriction is consistent with the limit of small velocity gradients and we can thus derive a cubic amplitude equation governing the space–time evolution of A. This equation can be cast into a separated first-order ODE. The numerical results show that the combined effect of nonlinearity and flow divergence strongly influences the amplitudes such that they reach a maximum and decay farther downstream. The study is based on an essentially inviscid approach. The regime of amplitude decay is therefore restricted and the integrations have to be terminated when the limit of neutral growth is reached. Comparison with experimental data is difficult because the latter are taken for higher values of the velocity gradients. Yet typical experimental trends are predicted by the findings of the present study. We found in particular in the numerical study of vortex contours structural instabilities in terms of breakup of sinusoidal lines to create vortex patches and the phenomenon of cut-and-connect of vortices near ‘‘saddle points.’’
A new instability for finite Prandtl number rotating convection with free-slip boundary conditions
Authors: Ponty Y. , Passot T. , Sulem P. L.
Published: July 2002

Rolls in finite Prandtl number rotating convection with free-slip top and bottom boundary conditions are shown to be unstable with respect to small angle perturbations for any value of the Crotation rate. This instability is driven by the horizontal mean flow whose estimation requires a special singular perturbation analysis.
The effect of surface roughness on flow structures in a neutrally stratified planetary boundary layer flow
Authors: Lin Ching-Long , Moeng Chin-Hoh , Sullivan Peter P. , McWilliams James C.
Published: July 2002

The effects of surface roughness on the structures of a neutrally stratified planetary boundary layer flow are investigated by the large-eddy simulation technique. Our numerical model, which assumes horizontal periodicity, shows that the growth of an internal boundary layer (IBL) in response to an abrupt change of surface roughness (either smooth-to-rough transition or rough-to-smooth transition) obeys the 4/5th power of the time, similar to that along the downwind fetch. A sudden increase or decrease in the surface shear stress during the transition is also observed. A quadrant analysis shows that during the transition, ejections and sweeps are altered significantly. Flow visualization further illustrates that the distribution density and the strength of coherent vortical structures and ejection eddies increase substantially during the smooth-to-rough transition. Conversely, these parameters decrease in the rough-to-smooth transition. The mean velocity profile has an inflection point at the IBL top, but the coherent vortical motions and ejection eddies affected by the change of the roughness are inside the IBL, suggesting that this inflection point is more static than dynamic. We also compare the quasi-steady coherent flow structures of different surface roughness values after the transition period. Streak spacing appears to increase with increasing surface roughness. Ejection eddies and vortical structures increase in scale as well as in strength as the surface roughness increases. The correlation between drag coefficient and flow structures in boundary layer flows is discussed.
Strong echo effect and nonlinear transient growth in shear flows
Authors: Vanneste J. , Morrison P. J. , Warn T.
Published: July 2002

The nonlinear interaction of two disturbances excited successively in a two-dimensional Couette flow is shown to lead to a transient energy growth. This phenomenon, which is called the echo effect and exists in several other physical systems, is interesting because the energy growth appears long after the energy associated with the original disturbances has decayed. Here, the echo effect is studied analytically and numerically in a situation where the nonlinear response has the same order of magnitude as the two excitations. A system of amplitude equations describing the nonlinear interactions between three sheared modes is derived and employed to examine the physical mechanism of the echo. The qualitative validity of this system is confirmed by numerical simulations. The influence of viscous dissipation on the echo effect is also considered.
Transition to turbulence of the flow in a straight pipe downstream of a helical coil
Authors: Hon R. , Humphrey J. A. C. , Champagne F.
Published: July 2002

This investigation is concerned with the (re) transition to turbulence of the flow in a straight pipe downstream of a long helical coil where the flow has previously laminarized. The pipe is tangent to the coil exit and they are both of constant diameter D=2R0. The coil diameter to curvature ratio is D/RC=1/10.64 and the coil pitch is small. The Reynolds number of the flow, defined as Re=DUb/ν, where Ub is the bulk average streamwise velocity of the fluid and ν its kinematic viscosity, ranges between 2 500 and 17 700. A laser-Doppler velocimeter is used to measure time records, mean, and rms values of the streamwise velocity component over the pipe cross section at various axial locations 2<x/D<45 downstream of the coil–pipe juncture. The flow in the coil is laminar up to Re≈5200. That in the straight pipe has transitioned by x/D=45 when Re=4600 and, with increasing Re, the transition location moves upstream while the flow rapidly evolves towards the turbulent state. Analysis of the results suggests that transition to turbulence in the straight pipe may be occurring in two ways; (a) through the growth of disturbances induced at the pipe wall; and (b) through an inflectional velocity instability in the core flow.
The effects of curvature on wake-dominated incompressible free shear layers
Authors: Zhuang Mei
Published: July 2002

Instability characteristics of curved incompressible free shear layers, with mean velocity profiles having a wake component, are studied using linear inviscid stability theory in spatial formulation. Both two- and three-dimensional disturbances are considered. The shear layer mode and the wake mode, previously found in a plane shear layer with a wake component in the mean velocity profile, are also found in the corresponding curved shear layer. Results of unstably curved shear layers with a wake component are consistent with those of previous investigations of a curved shear layer without a wake component. Results for a stably curved shear layer with a wake component show that the growth rate of the wake mode increases with increasing shear layer curvature and an oblique wake mode can become dominant compared to its corresponding two-dimensional wake mode. A wake-dominated shear layer, therefore, can become unstable as its curvature increases, regardless of whether the shear layer is stably or unstably curved regarding the corresponding monotonic mixing layer profile. The amplification rates of the shear layer mode and the wake mode could become comparable by varying the free-stream density ratio. For a wake-dominated shear layer under three-dimensional disturbances, the centrifugal modes are found. These modes are developed out of the wake mode for a stably curved shear layer and developed out of the shear layer mode for an unstably curved shear layer. Since the stability behavior is governed by the wake behavior, the wake-dominated shear layer could support the centrifugal instability regardless of the sense of curvature regarding the corresponding monotonic mixing layer profile.
Charge and current neutralization in the formation of ion rings in a background plasma
Authors: Oliver B. V. , Ryutov D. D. , Sudan R. N.
Published: July 2002

For typical field-reversed ion ring experiments, an intense ion beam is injected across a plasma-filled magnetic cusp and propagated into a solenoidal field downstream. The characteristic time τ satisfies 2π/Ωe≪τ≤2π/Ωi and the background plasma can be modeled as an electron magnetohydrodynamic (EMHD) fluid. In the nearly collisionless regime, such that νe≪Ωe, the plasma response is governed by the whistler mode. The role of the wall boundaries in such experiments to control the charge and current neutralization of the injected beam is considered for axisymmetric ∂/∂θ=0 geometry. It is found that for close enough conducting walls, such that the whistler transit time to the wall is short compared to the beam transit time, effective control of the return currents can be established such that current neutralization can be suppressed while maintaining good charge neutralization (νe is the electron collision frequency and Ωe is the corresponding gyrofrequency).
Excitation of electromagnetic waves by relativistic electron beam in a plasma filled rippled wall waveguide
Authors: Choyal Y. , Maheshwari K. P.
Published: July 2002

An analytical and numerical study is presented herewith to get an insight into the excitation of forward and backward waves caused by an intense relativistic electron beam in a rippled wall plasma filled waveguide with weak modulation. The numerical results of growth rate are derived in the case of weak modulation at kz=π/z0 (the π point). Numerical results also show that no excitation of waves takes place if relativistic factor of the beam γ<(1+μ20s/R20k20)1/2. For γ≳(1−μ20s/R20k20)−1/2, the beam excites both forward and backward waves, and only forward waves if (1+μ20s/R20k20)1/2<γ< (1−μ20s/R20k20)−1/2. The dependence of the frequency of the generated forward waves on beam energy is also studied numerically and the results are compared with those of the experiment [IEEE Trans. Plasma Sci. PS-18, 490 (1990)]. The effect of corrugation depth of rippled wall plasma filled backward wave oscillator (BWO) on minimum frequency generated is also studied.
Overview of International Thermonuclear Experimental Reactor (ITER) engineering design activities*
Authors: Shimomura Y.
Published: July 2002

The International Thermonuclear Experimental Reactor (ITER) [International Thermonuclear Experimental Reactor (ITER) (International Atomic Energy Agency, Vienna, 1988), ITER Documentation Series, No. 1] project is a multiphased project, presently proceeding under the auspices of the International Atomic Energy Agency according to the terms of a four-party agreement among the European Atomic Energy Community (EC), the Government of Japan (JA), the Government of the Russian Federation (RF), and the Government of the United States (US), ‘‘the Parties.’’ The ITER project is based on the tokamak, a Russian invention, and has since been brought to a high level of development in all major fusion programs in the world. The objective of ITER is to demonstrate the scientific and technological feasibility of fusion energy for peaceful purposes. The ITER design is being developed, with support from the Parties’ four Home Teams and is in progress by the Joint Central Team. An overview of ITER Design activities is presented.
Kinetic resonance damping rate of the toroidal ion temperature gradient mode
Authors: Kim J. Y. , Kishimoto Y. , Horton W. , Tajima T.
Published: July 2002

The linear damping rates of the toroidal ion temperature gradient (ηi) mode due to the toroidal resonance are calculated in the local kinetic limit. The well-known Landau contour method is generalized to treat the analytic continuation problem of the guiding center dispersion function in the toroidal resonance system where the resonance occurs from both the magnetic ∇B-curvature drift and the parallel ion transit drift. A detailed numerical analysis is presented for the dependence of the damping rate of the toroidal ηi mode on various parameters such as εn, ky, and the trapped electron fraction. In addition, a consideration is presented on the decay problem of the ballistic response by phase mixing in the toroidal system, which is directly related to the kinetic damping problem of the normal modes by the toroidal resonance.
On the theory of field line resonances in plasma configurations
Authors: Fedorov E. N. , Mazur N. G. , Pilipenko V. A. , Yumoto K.
Published: July 2002

The theoretical justification of the basic principles of Alfvén field line resonance in two-dimensional inhomogeneous plasma is given. The problem has recently been discussed by Hansen and Goertz [Phys. Fluids B 4, 2713 (1992)]. They suggested that the qualitative nature of magnetohydro- dynamic wave transformation in the region of field line resonance must be radically modified in multidimensional systems. A more correct treatment of the problem with the use of the Frobenius method proves the inconsistency of the criticism put forward by Hansen and Goertz. The singular behavior of the wave field near a resonant field line is maintained for two-dimensionally inhomogeneous configurations as well.
Improving regular acceleration in the nonlinear interaction of particles and waves
Authors: Pakter R. , Corso G.
Published: July 2002

In this work one studies the effects arising from the inclusion of a stationary extraordinary mode in the resonant interaction of magnetized particles and perpendicularly propagating electrostatic waves. It is found that for a stationary mode frequency of the order of the Larmor frequency and with a suitably chosen amplitude, one is able to suppress the resonance which drives the weakly relativistic dynamics into chaos. Improved regular acceleration of initially low energy particles is thus attained. Analytical estimates of the optimal stationary mode amplitude is presented. A detailed study of the topological effects due to resonance suppression based on bifurcation analysis is performed. The main results are verified with the help of single particle numerical simulations.