bluuebunny/crossref_metadata_2025 huggingface dataset:
Turbulent deposition and trapping of aerosols at a wall
Authors: Brooke John W. , Kontomaris K. , Hanratty T. J. , McLaughlin John B.
Published: July 2002

The trajectories of aerosols are computed in a high-resolution direct numerical simulation of turbulent flow in a vertical channel. The aerosol equation of motion includes only a Stokes drag force and the influence of the aerosols on the gas flow is assumed to be negligible. Since the flow is vertical, aerosols deposit as a consequence of the turbulent fluctuations and their own inertia. It is shown that the eddies which are responsible for aerosol deposition are the same eddies that control turbulence production. Typical aerosol trajectories are shown and related to eddy structure. A free-flight theory suggested by Friedlander and Johnstone [Ind. Eng. Chem. 49, 1151 (1957)] is found to be based on reasonable assumptions about typical velocities of depositing aerosols as they pass through the viscous sublayer, but the theory is shown to be deficient in other respects. The distribution of normal velocities of the aerosols that deposit is compared to the distribution of fluid particle velocities in the viscous sublayer and some support is found for the notion that the probability distribution of Eulerian velocities may be useful in predicting deposition.
An experimental study of helicity density in turbulent flows
Authors: Wallace James M. , Balint Jean-Louis , Ong Lawrence
Published: July 2002

Databases for a turbulent boundary layer at Rθ=2685, a turbulent two-stream mixing layer at Rθ=5800, and a turbulent grid flow at RM=23 400 have been examined for properties of the relative helicity density, h=(U⋅Ω)/‖U‖‖Ω‖. The velocity and vorticity vectors U and Ω were simultaneously measured in these flows using a miniature probe with nine hot-wire sensors with a spatial resolution of a few Kolmogorov microscales. The results of this analysis are in generally good agreement with a similar analysis of a direct numerical channel flow simulation of Rogers and Moin [Phys. Fluids 30, 2662 (1987)]. The results do not support the suggestion that there is a high probability for the flows locally to achieve a Beltrami-like state with the velocity and vorticity vectors often nearly aligned. Such preferred alignment does not occur in the grid flow and only slightly occurs in regions of the shear flows where it is known that the mean velocity is somewhat aligned with coherent vortices. A joint probability analysis does provide some indication that alignment of the vectors is associated with lower turbulent kinetic energy dissipation. Residual mean helicity density, which previously has been explained by conjectured ‘‘spontaneous symmetry breaking,’’ is shown here likely to be due to small measurement errors. Joint probability density plots show that the two parts of the convective acceleration term in the Navier–Stokes equation, the Lamb vector, Ω×U, and ∇[(U⋅U)/2], are highly correlated with each other and are similarly associated with the turbulent kinetic energy dissipation.
Atmospheric interfacial waves
Authors: Forbes Lawrence K. , Belward Shaun R.
Published: July 2002

Waves at the interface of a two-layer fluid are considered. The fluid in the lower layer is incompressible with constant density and is flowing irrotationally. In the upper layer, the fluid is stationary but compressible, and corresponds to an isothermal atmosphere with a density profile that decreases exponentially with height. The interface between the two fluids is assumed sharp. The formation of waves at the interface would come about typically as a result of the interaction of the moving lower layer of fluid with local topographical features, as with the classical problem of the generation of waves on the lee side of a mountain range. It is shown that the present model is capable of supporting the formation of interfacial waves that are similar in many respects to the classical gravity wave of Stokes, and that are ultimately limited in every case by the formation of a 120° angle at the wave crest. The highly nonlinear wave profiles are computed numerically and compared with the predictions of linearized theory. An extended perturbation analysis is given near the point at which the interfacial waves break down as a result of the Kelvin–Helmholtz instability.
Excitation of kinetic Alfvén waves by resonant mode conversion and longitudinal heating of magnetized plasmas
Authors: Tanaka Motohiko , Sato Tetsuya , Hasegawa A.
Published: July 2002

Simulation of the kinetic Alfvén wave is performed using a two-and-one-half-dimensional (2 (1)/(2) -D) macroscale particle [magnetohydrodynamic (MHD) scale kinetic] simulation code. An oscillating antenna current is applied in one of the boundary regions to launch MHD perturbations into an inhomogeneous plasma in which a sheared magnetic field is present. It is shown that the applied perturbation is mode converted into the kinetic Alfvén wave at the Alfvén resonance layers, resulting in resonant heating of both the ions and electrons. When the plasma beta is relatively low, only the electrons are heated along the ambient magnetic field. The electron heating rate is found to be scaled as dTe∥/dt∝β1/2e 〈δB2y〉, where βe is the electron beta and 〈δB2y〉 is the wave magnetic field intensity. In contrast, ion heating occurs when the ion beta is close to unity and the temperature ratio satisfies Te/Ti>1. Besides plasma heating, it is found that the plasma particles are accelerated along the ambient magnetic field in the direction of the wave propagation through Landau resonance with the kinetic Alfvén wave.
Analysis of Z-pinch dynamics with application to fibers
Authors: Rosenau Philip , Nebel Richard A. , Lewis H. Ralph
Published: July 2002

A computer-aided study of Z-pinch plasma transport reveals a high level of structured behavior. The equations asymptote into time and space separable forms, with the profiles of all the variables determined solely by the time dependence of the plasma current. Plasma profiles (normalized with respect to their values on the axis and to the plasma radius) are almost independent of the level of Bremsstrahlung radiation and thus can be determined using the self-similar pattern of a nonradiating plasma. Radiation causes the plasma column to collapse within a finite time and is accompanied by a rapid growth in the density and pressure. The temporal growth of the temperature initially follows that of the current, but if the current crosses the Pease limit, the temperature also rapidly grows.
Weak turbulence theory of collisionless trapped electron driven drift instability in tokamaks
Authors: Hahm T. S. , Tang W. M.
Published: July 2002

The toroidal collisionless trapped electron modes are analyzed in the weak turbulence regime treating both ions and trapped electrons nonlinearly in the presence of ion and electron temperature gradients. The spectral intensity of the density fluctuations in the nonlinearly saturated state is analytically obtained from the steady-state solution of the wave-kinetic equation. Distant nonlinear interactions between low-kθ and high-kθ modes of similar frequencies via trapped electron scattering (the resonance between the beat wave and the trapped electron precession drift frequencies) suppress the low-kθ [kθρs ≪(Ln/R)1/2] modes while close interactions via ion Compton scattering (nonlinear ion Landau damping) produce a monotonically decreasing spectrum from kθρs ≂(Ln/R)1/2 to kθρs≂1 according to an approximate power law k−3θ. Various fluctuation amplitudes at saturation and the fluctuation-induced anomalous particle and heat fluxes are found to be smaller than the mixing length estimates. The plasma confinement is predicted to improve with higher Ti/ Te, more peaked density profile, larger aspect ratio, and higher plasma current. Also, a significant dependence of transport on the electron temperature gradient is found which could contribute to the rigidity of the electron temperature profile often experimentally observed.
Self-focusing of whistler waves
Authors: Karpman V. I. , Kaufman R. N. , Shagalov A. G.
Published: July 2002

The theory of axially symmetric self-focusing of whistler waves, based on the full system of Maxwell equations, is developed. The plasma is described by the magnetohydrodynamic equations including the ponderomotive force from rf field. The nonlinear Schrödinger equations (NSE) for arbitrary azimuthal modes of whistler waves are derived. It is shown that they differ from the NSE for a scalar field; this is connected with an intrinsic angular momentum due to the rotating polarization of whistlers. It is shown that the self-focusing, as described by the NSE, differs in its final stage from the results following from the full set of Maxwell equations. The latter gives defocusing after sufficient narrowing of the initial wave beam, due to transformation of the trapped wave into a nontrapped branch which is not contained in the NSE description. The oscillatory character of the defocusing is demonstrated.
Excitation of plasma waves by electromagnetic waves in magnetized plasmas
Authors: Shukla P. K.
Published: July 2002

Three-dimensional equations for the plasma wake fields in the presence of a single frequency, intense circularly polarized electromagnetic (CPEM) wave in a two-component magnetoplasma are derived. For a given CPEM envelope, the axial electric fields of plasma waves are obtained for a one-dimensional model problem in which all the waves are aligned along the magnetic-field lines. It is found that the presence of an external magnetic field can significantly enhance the strength of the plasma wake fields when the right-hand CPEM wave is used for the excitation purposes.
Analysis of the effects of elongation and triangularity on the propagation of lower-hybrid waves
Authors: Cardinali A. , Micozzi P. , Barbato E. , Romanelli F.
Published: July 2002

Lower-hybrid (LH) wave propagation is studied for a general magnetic-field configuration. The ray-tracing equations in the geometric optics approximation are analytically and numerically solved in flux surface coordinates by using asymptotic techniques. In particular, the effects of elongation, triangularity, and the Shafranov shift on wave penetration are pointed out. Numerical applications devoted to the study of current drive generation for the International Thermonuclear Experimental Reactor (ITER) [Nucl. Fusion 31, 1135 (1991)] plasma parameters will also be presented.
Cascade properties of shear Alfvén wave turbulence
Authors: Bondeson Anders
Published: July 2002

Nonlinear three-wave interactions of linear normal modes are investigated for two-dimensional incompressible magnetohydrodynamics and the weakly three-dimensional Strauss equations in the case where a strong uniform background field B0 is present. In both systems the only resonant interaction affecting Alfvén waves is caused by the shear of the background field plus the zero frequency (ω=k ⋅ B0=0) components of the perturbation. It is shown that the Alfvén waves are cascaded in wavenumber space by a mechanism equivalent to the resonant absorption at the Alfvén resonance. For large wavenumbers perpendicular to B0, the cascade is described by Hamilton’s ray equations, dk/dt=−∂ω/∂r, where ω includes the effects of the zero frequency perturbations.
Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks
Authors: Jenkins J. T. , Richman M. W.
Published: July 2002

Grad’s method of moments is employed to derive balance laws and constitutive relations for plane flows of a dense gas consisting of identical, rough, inelastic, circular disks. Two temperatures are involved; these are proportional to the kinetic energies associated with fluctuations in translational velocity and spin, respectively. When the single particle velocity distribution function is assumed to be close to a two-temperature Maxwellian, two distinct theories are obtained. One applies when the particles are almost smooth and the collisions between them are nearly elastic; the other applies to nearly elastic particles that, in a collision, almost reverse the relative velocity of their points of contact. I both cases energy is nearly conserved in collisions.
The evolution of nonlinear Alfvén waves subject to growth and damping
Authors: Spangler Steven R.
Published: July 2002

Results of a numerical study of Alfvén waves are presented subject to nonlinearity, dispersion, growth, and damping. The model presented is the derivative nonlinear Schrödinger equation, modified to include linear growth and damping processes. The processes that are considered are wave amplification by streaming particle distributions, and damping resulting from ion-cyclotron resonance absorption. These growth and damping mechanisms are dominant in different portions of wavenumber space. The primary role of nonlinearity is the transfer of wave energy from growing or amplified wavenumbers to those which are damped. A nonlinear saturation mechanism thereby results, in which instability of low wavenumber modes may be quenched. A simple phenomenological model is developed, which accounts for many of the salient features of the numerical calculations. The application of these results to observations of Alfvén waves upstream of the Earth’s bow shock is briefly considered. It is suggested that the short wavelength ‘‘shocklet’’ structures resemble the soliton-like pulses that emerge from the driven derivative nonlinear Schrödinger equation. However, the nonlinear effects discussed in this paper do not seem responsible for limiting the amplitude of the ‘‘low-frequency’’ waves in the foreshock region.
Reflection of ion-acoustic waves from an ion sheath at a grid
Authors: Schott L.
Published: July 2002

The reflection of continuous sinusoidal waves from a grid is investigated experimentally. It is found that the reflection coefficient has a distinct maximum in contrast to the prediction of the theory. The electron components of the incident and reflected waves are observed to vanish within the quasineutral layer close to the grid where the plasma density rapidly drops. Furthermore it is shown that the reflected wave is a downstream wave that propagates on the ion beam that originates on the other side of the grid.
Two-point theory of current-driven, ion-cyclotron turbulence
Authors: Chiueh T. , Diamond P. H.
Published: July 2002

An analytical theory of current-driven, ion-cyclotron turbulence that treats incoherent phase-space density granulations (clumps) is presented. In contrast to previous investigations it focuses on the physically relevant regime of weak collective dissipation, where waves and clumps coexist. The threshold current for nonlinear instability is calculated and is found to deviate from the linear threshold by up to 7%. A necessary condition for the existence of stationary wave-clump turbulence is derived and shown to be analogous to the test-particle model, fluctuation–dissipation theorem result. The structure of three-dimensional magnetized clumps is characterized. It is proposed that nonlinear instability is saturated by collective dissipation due to ion-wave scattering. For this wave-clump turbulence regime, it is found that the fluctuation level (eφ/Te)rms≤0.1, and that the modification of anomalous resistivity to levels predicted by conventional nonlinear wave theories is moderate. In marked contrast to the quasilinear prediction, it is also shown that ion heating significantly exceeds electron heating, and that a drag force on electrons sustains a steady current and is set up to counteract the accelerating electric field along field lines.
Asymptotic analysis of lower hybrid wave propagation in tokamaks
Authors: Cardinali A. , Romanelli F.
Published: July 2002

An asymptotic analysis of the lower hybrid wave propagation in toroidal geometry is presented which relies on the difference in magnitude between the parallel and perpendicular wave vectors when the wave frequency is of the order of the ion plasma frequency. Using the method of matched asymptotic expansions, the equation for the radial position of the ray is solved and the effects of the toroidal corrections are discussed. Moreover, the equation for the parallel wave vector is derived and analytically solved by using a multiple scale analysis. The latter solution is asymptotically matched to a local exact solution near the plasma edge where the multiple scale analysis breaks down. The result of the asymptotic analytical treatment is compared with the findings of a numerical integration of the starting set of equations. Finally, using the previous results, the equation for the variation of the electric field amplitude along the trajectory is analytically solved.
Scanning laser anemometer measurements of a forced cylinder wake
Authors: Williams David R. , Economou Manthos
Published: July 2002

It is demonstrated that a scanning laser anemometer is capable of measuring rapid and randomly occurring flow events. Mean and instantaneous velocity profiles in the near wake of a cylinder at Reynolds number of 155 are shown together with spatial correlations. In addition, the scanning laser anemometer has been used to show that the mean velocity defect behind the cylinder can be substantially reduced, when the wake is disturbed by unsteady forcing with a line of small pulsating jets emanating from the trailing edge of the cylinder.
The cusp map in the complex-frequency plane for absolute instabilities
Authors: Kupfer K. , Bers A. , Ram A. K.
Published: July 2002

It is well known that absolute instabilities can be located by prescribed mappings from the complex-frequency plane to the wavenumber plane through the dispersion relation D(ω,k)=0. However, in many systems of physical interest the dispersion relation is polynomial in ω while transcendental in k, and the implementation of this mapping procedure is particularly difficult. If one maps consecutive deformations of the Fourier integral path (originally along the real k axis) into the ω plane, points having (∂D/∂k)=0 are readily detected by the distinctive feature of their local maps. It is shown that a simple topological relationship between these points and the image of the real k axis determines the stability characteristics of the system, without mapping from the ω plane back into the k-plane.
Image systems for a Stokeslet inside a rigid spherical container
Authors: Maul Christine , Kim Sangtae
Published: July 2002

This Brief Communication derives a more compact form of the fundamental solution to the Stokes equations for a point force (Stokeslet) in a fluid domain bounded by a rigid spherical container. Although equivalent to Oseen’s (1927) solution, the present form is more useful in subsequent applications in boundary integral equation methods.
The rheology of bimodal hard-sphere dispersions
Authors: Chang Chingyi , Powell Robert L.
Published: July 2002

The viscosity of a monolayer of a suspension of bimodally distributed hard spheres is determined for area fractions, φa, from 0.15 to 0.74 with different particle size ratios, λ (diameter of large sphere/diameter of small spheres=1, 2, and 4), and different fractions of small spheres of total solids, ξ (0.07, 0.27, 0.49, 0.64, and 0.83). Particle distributions are generated by a Monte Carlo technique and the hydrodynamic interactions are calculated by Stokesian dynamics. These results, which correspond to the high-frequency dynamic viscosities, are compared with those from the dynamic simulation of hydrodynamically interacting spherical particles [Chang and Powell, J. Fluid Mech. 253, 1 (1993)]. Dynamic simulation is found to yield higher relative viscosities, ηr, as compared with the results of Monte Carlo simulation at high concentrations. This results from the absence of long clusters that completely cross a periodic cell in the Monte Carlo simulations that are present in the dynamic simulations. When φa is normalized by the maximum packing fraction, φm2-D, all the viscosity data fall onto a master curve. This is the same trend as that found in dynamic simulations, except that the Monte Carlo simulation gives lower relative viscosities for φa/φm2-D ≳ 0.3. When λ and φa are fixed, ηr decreases as ξ increases from zero, reaches a minimum, and then increases as ξ→1, similar to the trend found in the dynamic simulations. Good agreement is found among the results of two-dimensional simulations, experiments, and three-dimensional simulations for monodispersed suspensions.
Measurements of turbulent velocity fluctuations in a planar Couette cell
Authors: Malerud Stein , Målo/y Knut Jo/rgen , Goldburg Walter I.
Published: July 2002

The anisotropy of turbulent velocity fluctuations in a planar Couette cell has been investigated by using homodyne photon correlation spectroscopy (HCS). We find that 〈δvq(l)〉, the mean velocity difference between two points separated by a distance l, is consistent with the scaling behavior 〈δvq(l)〉∝l0.55. These measurements were made at a Reynolds number Re much greater than Rec, where the subcritical transition first occurs. The HCS technique was also used to measure Rec itself.
The linear stability of an oscillatory two-phase channel flow in the limit of small Stokes numbers
Authors: Chen Yen-Cho , Chung J. N.
Published: July 2002

The effects of particles on the linear stability of an oscillatory two-phase plane channel flow are examined for small Stokes numbers. The results in this note are valid for the condition that the dimensionless oscillation frequency is of the order of unity or smaller. The particles are found to have a destabilizing effect at all flow oscillation frequencies except in the high-frequency region and the extent of the destabilization increases with increasing particle mass fraction. The critical Reynolds number for a gas–particle flow may be significantly changed by the flow oscillation.
The spreading of volatile liquid droplets on heated surfaces
Authors: Anderson D. M. , Davis S. H.
Published: July 2002

A two-dimensional volatile liquid droplet on a uniformly heated horizontal surface is considered. Lubrication theory is used to describe the effects of capillarity, thermocapillarity, vapor recoil, viscous spreading, contact-angle hysteresis, and mass loss on the behavior of the droplet. A new contact-line condition based on mass balance is formulated and used, which represents a leading-order superposition of spreading and evaporative effects. Evolution equations for steady and unsteady droplet profiles are found and solved for small and large capillary numbers. In the steady evaporation case, the steady contact angle, which represents a balance between viscous spreading effects and evaporative effects, is larger than the advancing contact angle. This new angle is also observed over much of the droplet lifetime during unsteady evaporation. Further, in the unsteady case, effects which tend to decrease (increase) the contact angle promote (delay) evaporation. In the ‘‘large’’ capillary number limit, matched asymptotics are used to describe the droplet profile; away from the contact line the shape is determined by initial conditions and bulk mass loss, while near the contact-line surface curvature and slip are important.
Columnar vortex generation and interaction with a clean or contaminated free surface
Authors: Hirsa A. , Harper J. E. , Kim S.
Published: July 2002

The interaction of a columnar vortex with a free surface is studied experimentally. The vortex is generated by a pair of corotating flaps and is visualized by planar laser-induced fluorescence. When the surface is clean, the vortex is unaffected and remains essentially two dimensional. However, when the surface is contaminated by a relatively viscous monomolecular layer, the vortex dynamics can be significantly altered, resulting in a downward axial flow followed by vortex breakdown.
The interaction of a shock with a vortex: Shock distortion and the production of acoustic waves
Authors: Ellzey Janet L. , Henneke Michael R. , Picone J. Michael , Oran Elaine S.
Published: July 2002

Numerical simulations of a shock interacting with a compressible vortex are presented for shocks and vortices of various relative strengths. The simulations show the effects of the vortex on the shock structure and the structure of the acoustic field generated by the shock–vortex interaction. A relatively weak vortex perturbs the transmitted shock only slightly, whereas a strong vortex leaves the transmitted shock with a structure corresponding to either a regular or Mach reflection. The acoustic wave generated by the interaction consists of two components: a ‘‘quadrupolar’’ component produced by the initial shock–vortex interaction and the complex reflected shock system. When these waves merge, they form the asymmetric structure seen in experiments.
Determination of surface tension from the shape oscillations of an electromagnetically levitated droplet
Authors: Bayazitoglu Y. , Sathuvalli U. B. R. , Suryanarayana P. V. R. , Mitchell G. F.
Published: July 2002

In the fundamental (l=2) mode, the frequency spectrum of a magnetically levitated inviscid droplet exhibits three distinct peaks. If the modes that correspond to each of these peaks is known, the surface tension of the droplet may be calculated. In experiments that make use of this principle, there is no unambiguous method of assigning mode numbers to these peaks. The dynamics of the oscillating droplet depend on the magnetic pressure on the droplet surface. Consequently, the order of the peaks in the l=2 mode oscillations is determined by the magnetic pressure distribution. In this paper, the magnetic pressure distribution on the surface of the droplet is calculated as a function of the parameters that govern the external magnetic field. The frequencies of the droplet oscillation and its static shape deformation are also expressed in terms of these same parameters. The frequencies of oscillation are used to determine the surface tension of the liquid droplet. Finally, the magnetic pressure distribution on the droplet is shown to yield the well-known ‘‘pear-like’’ shape that is assumed by liquid metal droplets in a conical levitator.
Internal gravity wave radiation into weakly stratified fluid
Authors: Sutherland B. R.
Published: July 2002

It is shown by way of nonlinear numerical simulations of flow restricted to two dimensions that a compact wavepacket of large-amplitude internal gravity waves incident upon a weakly stratified region in which the buoyancy frequency is less than the frequency of the wavepacket may partially transmit energy into this region through the generation of a wavepacket of lower frequency. In part, the transmission of waves occurs due to the transient nature of the forcing by the incident wavepacket, but if the amplitude of the wavepacket is moderately large, weakly nonlinear effects may act to significantly increase the proportion of the wavepacket that is transmitted. For a range of simulations initialized with wavepackets of different amplitude and vertical extent, the characteristics of the reflected and transmitted waves are analyzed and reflection coefficients are calculated. An explanation for how the nonlinear transmission mechanism operates is given by demonstrating that the wave induced mean-flow, which is shown to be approximately equal to the horizontal wave pseudomomentum expressed in Eulerian variables, acts to adjust the frequency of the incident waves.
Stable and unstable singularities in the unforced Hele-Shaw cell
Authors: Almgren Robert , Bertozzi Andrea , Brenner Michael P.
Published: July 2002

We study singularity formation in the lubrication model for the unforced Hele-Shaw system, describing the breaking in two of a fluid droplet confined between two narrowly spaced glass plates. By varying the initial data, we exhibit four different scenarios: (1) the droplet breaks in finite time, with two pinch points moving toward each other and merging at the singular time; (2) the droplet breaks in finite time, with two asymmetric pinch points propagating away from each other; (3) the droplet breaks in finite time, with a single symmetric pinch point; or (4) the droplet relaxes to a stable equilibrium shape without a finite time breakup. Each of the three singular scenarios has a self-similar structure with different scaling laws; the first scenario has not been observed before in other Hele-Shaw studies. We demonstrate instabilities of the second and third scenarios, in which the solution changes its behavior at a thickness that can be arbitrarily small depending on the initial condition. These transitions can be identified by examining the structure of the solution in the intermediate scaling region.
Dynamics of drops in cavity flows: Aggregation of high viscosity ratio drops
Authors: Manga Michael
Published: July 2002

The interactions of deformable drops in cavity flows is studied numerically in the limit of low Reynolds numbers for a two-dimensional model. Flow in a square cavity is driven by the steady motion of one of the walls. Deformable drops will migrate across streamlines until they reach an equilibrium trajectory or equilibrium position; the rate and direction of migration depend on both the viscosity ratio and capillary number. High viscosity ratio deformable drops have a tendency to aggregate and form clusters. The presence of a deformable dispersed phase results in an elastic behavior of the suspension.
Transition to chaotic natural convection in tall Hele–Shaw slots
Authors: Hu Wenjie , Steen Paul H.
Published: July 2002

Numerical simulations show that natural convection in tall Hele–Shaw slots has a dynamics similar to that of the convection loop. A Hopf bifurcation followed by homoclinic explosion is the route of transition to chaotic flow. The Hopf bifurcation leads to one-sided periodic motion while the homoclinic bifurcation point is the origin of the two-sided diagonal oscillation. Periodic regimes are separated by a Lorenz-type strange attractor. The instability of an internal boundary layer is the physics underlying the diagonal oscillation.
Singularity formation in Hele–Shaw bubbles
Authors: Almgren Robert
Published: July 2002

We provide numerical and analytic evidence for the formation of a singularity driven only by surface tension in the mathematical model describing a two-dimensional Hele–Shaw cell with no air injection. Constantin and Pugh have proved that no such singularity is possible if the initial shape is close to a circle; thus we show that their result is not true in general. Our evidence takes the form of direct numerical simulation of the full problem, including a careful assessment of the effects of limited spatial resolution, and comparison of the full problem with the lubrication approximation.
Unsteady Couette granular flows
Authors: Babic Marijan
Published: July 2002

Unsteady Couette granular flows are investigated both theoretically and by the means of the discrete element method (DEM). Theoretical formulation of the problem is based on the kinetic theory for smooth, nearly elastic particles. The resulting boundary value problem is solved numerically for two particular types of flows: (a) transient Couette flows, in which the wall velocity instantaneously changes from one constant value to another, and (b) cyclic Couette flows, in which the wall velocity is a harmonic function of time. The behavior of granular fluids in these flows is found to critically depend on the ratios of time scales that characterize the rate of change of the wall velocity and processes of momentum diffusion and energy relaxation. The limiting case in which the momentum diffusion time scale is much smaller than the energy relaxation time scale is also analyzed analytically by perturbation methods. In this limit granular materials behave as nearly incompressible non-Newtonian fluids. Hence, under appropriate conditions, which correspond to small Mach numbers, mathematical analysis of rapid granular flows can be tremendously simplified. For both transient and cyclic Couette flows, predictions of the kinetic theory for disks are found to be in a very good agreement with the corresponding DEM simulations at all time scales as long as the coefficient of restitution is close to unity. However, as the coefficient of restitution decreases, the agreement deteriorates due to a gradual breakdown of assumptions used in the development of the nearly elastic kinetic theory.
Drag reduction of turbulent pipe flows by circular-wall oscillation
Authors: Choi Kwing-So , Graham Mark
Published: July 2002

An experimental study on turbulent pipe flows was conducted with a view to reduce their friction drag by oscillating a section of the pipe in a circumferential direction. The results indicated that the friction factor of the pipe is reduced by as much as 25% as a result of active manipulation of near-wall turbulence structure by circular-wall oscillation. An increase in the bulk velocity was clearly shown when the pipe was oscillated at a constant head, supporting the measured drag reduction in the present experiment. The percentage reduction in pipe friction was found to be better scaled with the nondimensional velocity of the oscillating wall than with its nondimensional period, confirming a suggestion that the drag reduction seem to be resulted from the realignment of longitudinal vortices into a circumferential direction by the wall oscillation.
Laminar buoyant magnetohydrodynamic flow in vertical rectangular ducts
Authors: Bühler L.
Published: July 2002

The buoyancy-driven laminar magnetohydrodynamic flow in long vertical channels is investigated. It is assumed that the channels have a rectangular cross section with one pair of walls aligned with the strong uniform magnetic field. The walls may have arbitrary electrical conductance. Using asymptotic methods, solutions are derived for general temperature distributions inside the ducts. Results are shown for different values of the control parameters. One finds the typical subregions for the flow inside the duct, namely the inviscid core, surrounded by viscous Hartmann layers and side layers. The character of the solution inside these regions may deviate from what is expected by a comparison with the classical solutions for pressure-driven duct flows. The main difference is that the flow in the core not necessarily exhibits a two-dimensional behavior. Most surprising, however, is the fact, that high-velocity jets are observed for the first time along perfectly conducting sidewalls. These jets are able to carry a major part of the flow rate.
Asymptotic solution of the equation for the probability distribution of a passive scalar in grid turbulence with a uniform mean scalar gradient
Authors: Sabel’nikov Vladimir A.
Published: July 2002

A fully explicit asymptotic solution of the (simplified) equation for the probability density function (pdf) of a passive scalar in grid turbulence with a uniform mean cross-stream scalar gradient is obtained (the equation considered is exact for homogeneous turbulence). The asymptotic pdf is a function of the conditional expectations of the scalar dissipation and the transverse velocity. The solution generalizes the well-known asymptotic solution of Sinai and Yakhot [Phys. Rev. Lett. 63, 1962 (1989)] for homogeneous turbulence in the absence of a mean scalar gradient. An exact expression that relates the conditional expectations of molecular diffusion and transverse velocity is derived. This expression generalizes the result of Valiño et al. [Phys. Rev. Lett. 72, 3518 (1994)] for the zero mean gradient case.
A theoretical study of the turbulent diffusion in incompressible shear flows and in passive scalars
Authors: Shimomura Yutaka
Published: July 2002

The triple velocity, the pressure–velocity, and the scalar–scalar–velocity correlations in incompressible turbulent shear flows and in passive scalar fields are studied by using the two-scale direct-interaction approximation, which satisfies the solenoidal condition of the velocity fields and systematically introduces the cutoff wave numbers. As a result, we obtain their expressions of the gradient diffusion type involving the effect of cross-diffusion. The model constants in the obtained expressions for the triple velocity and the pressure–velocity correlations are close to the values used in the turbulence models. The derived expression for the scalar–scalar–velocity correlation shows the complex dependence on the ratio R of the velocity length scale to the scalar one. As a special case of R=1, we obtain its explicit expression whose model constant also agrees well with the numerically optimized value.
Parametrically driven surface waves in viscoelastic liquids
Authors: Kumar Satish
Published: July 2002

When a container of liquid is subject to vertical sinusoidal oscillation, the free surface becomes unstable at a critical driving acceleration and gives rise to standing waves. Here, we consider containers of finite depth, neglect the influence of lateral boundaries, and perform a linear stability analysis for viscoelastic liquids. Floquet theory is applied to transform the linearized governing equations into a recursion relation for the temporal modes of the free surface deformation. In the absence of external forcing, the recursion relation yields the dispersion equation for free surface waves on viscoelastic liquids. In the presence of external forcing, the recursion relation is studied both numerically and analytically for the case where the polymer stresses are described by a single-mode Maxwell model. When surface tension forces are sufficiently strong relative to elastic forces, the numerical results show that the standing waves respond subharmonically to the driving frequency. However, the instability threshold increases less rapidly with the driving frequency than that for a Newtonian liquid of the same zero-shear viscosity. When elastic forces become sufficiently strong relative to surface tension forces, the standing waves can respond harmonically within certain ranges of the driving frequency if the product of the driving frequency and the liquid relaxation time is not too large or too small. Dramatic changes are seen in the behavior of the neutral stability curves, dispersion relations, and instability thresholds. In the case where the viscous boundary layer thickness is much less than the disturbance wavelength, the viscoelastic recursion relation is simplified to yield a Mathieu equation which is nonlocal in time. The method of multiple scales is then applied to determine the instability threshold analytically. The results of this study indicate that the behavior of parametrically driven surface waves is very sensitive to the liquid relaxation time, and suggest that such waves may serve as a useful tool for the measurement of rheological properties.
Characteristics of chemically reacting compressible homogeneous turbulence
Authors: Jaberi F. A. , Livescu D. , Madnia C. K.
Published: July 2002

Direct numerical simulations (DNS) are conducted to study the turbulence-chemical reaction interactions in homogeneous decaying compressible fluid flows. The reaction is of a single-step irreversible Arrhenius type. The results indicate that the heat of reaction has a noticeable influence on the solenoidal and the dilatational turbulent motions. The effect of reaction on the solenoidal velocity field is primarily due to variation of the molecular diffusivity coefficients with temperature and appears at small scales. However, the dilatational motions are affected more than the solenoidal motions and are intensified at all length scales. The decay rate of the turbulent kinetic energy is dependent on the molecular dissipation and the pressure-dilation correlation. In isothermal reacting cases, the net contribution of the pressure-dilatation is small and the turbulent energy decays continuously due to viscous dissipation. In the exothermic reacting cases, the pressure-dilatation tends to increase the turbulent kinetic energy when the reaction is significant. Analysis of the flow structure indicates that the flow is dominated by strain in the reaction zones. Also, consistent with previous studies, the scalar gradient tends to align with the most compressive strain eigenvector and the vorticity vector tends to align with the intermediate strain eigenvector. The heat of reaction weakens this preferential alignment, primarily due to variation in molecular transport coefficients. The spatial and the compositional structure of the flame are also affected by the modification of the turbulence and the molecular coefficients.
Analytical treatment of Alfvén resonances and singularities in nonuniform magnetoplasmas
Authors: Wright Andrew N. , Thompson Michael J.
Published: July 2002

The linear resonant excitation of Alfvén waves in a cold plasma permeated by a nonuniform magnetic field is considered. The equilibrium magnetic field is irrotational and possesses an invariant coordinate perpendicular to the direction of the field. By solving for the coefficients in a Generalized Frobenius Series the regular and singular solutions may be generated. The singular solution is logarithmic and produces a net absorption of energy at the resonant field line. The efficiency of coupling between the fast mode and the resonant Alfvén mode is determined by the following overlap integral along the resonant field line, ∫(ξβrbγ0/hβ)dl; ξβr is the resonant eigenfunction, bγ0 is the compressional/parallel magnetic field perturbation, and hβ is proportional to the separation of background lines of force in the invariant direction. The amplitude of the singular solution is proportional to this integral, while the rate of energy absorption at the resonance is proportional to its square. It is also shown how the analytical solution at the resonance may be used to avoid problems encountered in numerical solutions.
Wall stabilization of high beta plasmas in DIII-D
Authors: Taylor T. S. , Strait E. J. , Lao L. L. , Mauel M. , Turnbull A. D. , Burrell K. H. , Chu M. S. , Ferron J. R. , Groebner R. J. , La Haye R. J. , Rice B. W. , Snider R. T. , Thompson S. J. , Wròblewski D. , Lightly D. J.
Published: July 2002

Detailed analysis of recent high beta discharges in the DIII-D [Plasma Physics Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] tokamak demonstrates that the resistive vacuum vessel can provide stabilization of low n magnetohydrodynamic (MHD) modes. The experimental beta values reaching up to βT=12.6% are more than 30% larger than the maximum stable beta calculated with no wall stabilization. Plasma rotation is essential for stabilization. When the plasma rotation slows sufficiently, unstable modes with the characteristics of the predicted ‘‘resistive wall’’ mode are observed. Through slowing of the plasma rotation between the q=2 and q=3 surfaces with the application of a nonaxisymmetric field, it has been determined that the rotation at the outer rational surfaces is most important, and that the critical rotation frequency is of the order of Ω/2π=1 kHz.
Response to ‘‘Comment on ‘Landau-fluid simulation of laser filamentation’ ’’ [Phys. Plasmas 1, 1287 (1994)]
Authors: Kaiser T. B. , Cohen B. I. , Berger R. L. , Lasinski B. F. , Langdon A. B. , Williams E. A.
Published: July 2002

The authors disagree with the assertions in Ref. 1. The authors think that the expression for the electron heat flux is fairly general and the appropriate electron damping rage, eq. (56) of Ref. 2 is correct. (AIP)
The plasma transport equations derived by multiple time-scale expansions. II. An application
Authors: Edenstrasser J. W. , Kassab M. M. M.
Published: July 2002

A multiple time scale derivative expansion scheme has been employed to reveal some aspects of Taylor’s relaxation theory, which states that a ‘‘slightly imperfect’’ plasma relaxes under the conservation of the overall magnetic helicity K toward a state of minimum magnetic energy. The purpose of this paper is to investigate the time evolution of K on the ideal magnetohydrodynamic (IMHD), the MHD-collision (CMHD), and resistive diffusion (RDMHD) time scales. On the ideal MHD time scale, it is found, just as expected, that K is an invariant of motion for each single flux tube. On the MHD-collision time scale Taylor’s conjecture is explicitly proven, namely that only the overall K is an invariant of motion. Finally for the resistive diffusion time scale, it is found that the time derivative is proportional to the resistivity, however, with additional terms arising from the MHD fluctuation spectrum.
Magnetization and other characteristics of exact relativistic dispersion of circularly polarized radiation in a magnetized plasma
Authors: Sarkar Susmita , Chakraborty B. , Khan Manoranjan , Dutta Debjani
Published: July 2002

A relativistic determination has been made of the zero frequency magnetic moment field [the inverse Faraday effect (IFE)], synchrotron radiation, and other consequences of the exact dispersion relation of a circularly polarized wave propagating in a two-component, cold, magnetized plasma. The relativistically correct Faraday angle of rotation of the plane of polarization of the electromagnetic (EM) wave due to the variation of the dispersion rates of the right- and left-circularly polarized components of the wave has been obtained. For Alfvén wave frequencies (wave frequency less than the ion gyrofrequency), a relativistically correct analysis of the interesting new features which appear due to the predominance of the wave-induced ion dynamics over electron motion is also presented.
Stability of a thermal plasma jet
Authors: Singh A. P. , Talwar S. P.
Published: July 2002

The stability of a slab model of a jet moving in an external plasma is investigated, assuming the configuration to be characterized by a general heat-loss function. Numerical results are obtained for the growth rates of unstable modes, both for symmetric and asymmetric perturbations for equal parallel magnetic fields along or transverse to the propagation vector in the wide and slender jet approximations. Special configurations of an incompressible jet moving past a thermal plasma and also of a thermal plasma moving past an incompressible static plasma are also considered.
Kinetic model of collective scattering off fast ion generated electromagnetic fluctuations in magnetized Vlasov plasma
Authors: Heikkinen J. A. , Dumbrajs O.
Published: July 2002

From the general three-wave coupling formalism in magnetized nonrelativistic Vlasov plasma, an expression is derived that gives the differential cross section for the scattering of incident radiation off of thermal fluctuations induced by ions in a hot magnetized plasma. The model is valid to any order in thermal parameters, and can thus generalize the previous theory models to regimes where either the electron Larmor radius or the electron cyclotron resonance are significant for the scattered wave.
Velocity and magnetic field structures in a magnetohydrodynamic dynamo
Authors: Kageyama Akira , Sato Tetsuya
Published: July 2002

Computer simulation of the magnetohydrodynamic dynamo in a rotating spherical shell geometry is performed. The convection velocity and the magnetic field structures are investigated in detail when the magnetic field is exponentially growing. It is found that the magnetic energy is strongly localized in space. The energy is generated when toroidal field lines are stretched by the fluid flows in columnar convection cells.
Measurement and interpretation of current transmission in a crossed-field diode below cutoff
Authors: Vanderberg Bo H. , Eninger Jan E.
Published: July 2002

Measurements on the current-voltage-magnetic field characteristics of a space-charge-limited cylindrical cross-field diode below cutoff are presented. The measured current is found to be lower than predicted by simple cold-fluid theory. This reduction combined with observed oscillations in the current can be explained by secondary electron emission from the anode, leading to an increase of space charge in the diode.
Near-forward scattering in magnetized plasma: Are laser spots whistling?
Authors: Mourenas D.
Published: July 2002

Near-forward scatter of laser light off lower hybrid and whistler waves in hot magnetized plasmas is investigated. Important gains might be obtained at relatively high intensity, as well for low (≪ωpi) as for high (≫ωpi) frequency waves, leading to unexpected features in the scattered light spectrum.