bluuebunny/crossref_metadata_2025 huggingface dataset:
Instabilities and vortex dynamics in shear flow of magnetized plasmas
Authors: Tajima T. , Horton W. , Morrison P. J. , Schutkeker J. , Kamimura T. , Mima K. , Abe Y.
Published: July 2002

Gradient-driven instabilities and the subsequent nonlinear evolution of generated vortices in sheared E×B flows are investigated for magnetized plasmas with and without gravity (magnetic curvature) and magnetic shear by using theory and implicit particle simulations. In the linear eigenmode analysis, the instabilities considered are the Kelvin–Helmholtz (K–H) instability and the resistive interchange instability. The presence of the shear flow can stabilize these instabilities. The dynamics of the K–H instability and the vortex dynamics can be uniformly described by the initial flow pattern with a vorticity localization parameter ε. The observed growth of the K–H modes is exponential in time for linearly unstable modes, secular for the marginal mode, and absent until driven nonlinearly for linearly stable modes. The distance between two vortex centers experiences rapid merging while the angle θ between the axis of the vortices and the external shear flow increases. These vortices proceed toward their overall coalescence, while shedding small-scale vortices and waves. The main features of vortex dynamics, the nonlinear coalescence and the tilt or the rotational instabilities of vortices, are shown to be given by using a low-dimension Hamiltonian representation for interacting vortex cores in the shear flow.
Coherent structures in shear flow-driven plasma microturbulence
Authors: Jovanovic D. , Shukla P. K. , de Angelis U. , Horton W.
Published: July 2002

Nonlinear electromagnetic perturbations whose characteristic scale length is shorter than the ion Larmor radius are studied using a hydrodynamic description for the electrons, and a kinetic description for the ions, in nonisothermal, nonuniform, magnetized plasma. It is shown that ion drift-Alfvén perturbations may be linearly unstable in the presence of a parallel shear plasma flow. In the fully nonlinear regime a solution in the form of a moving double vortex is found.
Relativistic plasma microwave electronics: Studies of high-power plasma-filled backward-wave oscillators
Authors: Carmel Y. , Lou W. R. , Antonsen T. M. , Rodgers J. , Levush B. , Destler W. W. , Granatstein V. L.
Published: July 2002

The area of relativistic plasma microwave electronics has only recently generated renewed interest. New experimental data are presented demonstrating that the presence of a low-density background plasma in a relativistic backward-wave oscillator leads to several beneficial effects, including (a) enhanced interaction efficiency (40%), (b) operation at very low and possibly zero guiding magnetic field, (c) tunability by controlling the plasma density, (d) high degree of spectral coherency, and (e) operation well above the vacuum limiting current.
The collision-frequency and reaction rate
Authors: Chang Yongbin , Huo Yuping , Yu Guoyang
Published: July 2002

The collision-frequencies between pairs of particles in a steady state for both smooth rigid elastic and Coulomb interaction are obtained by a uniform method. In addition, the results for smooth rigid elastic interaction are the same as that obtained previously [S. Champman and T. C. Cowling, in The Mathematical Theory of Non-Uniform Gas (Cambridge U.P., Cambridge, 1970), Chap. 5]. A momentum change distribution for collision frequency is obtained. It cannot only be used as an exact means for the description of Coulomb collision frequency but can also be used for calculating reaction rates. In the case of smooth rigid elastic interaction, the reaction rate proved to be of Arrhenius formula [D. H. Charles and G. A. Rayford, Fundamentals of Chemical Reaction Engineering (Prentice–Hall, Englewood Cliffs, NJ, 1979), Chap. 12]. For Coulomb interaction, a formula for the fusion reaction rate between deuterium and tritium as 〈σvDT〉 = 0.24T−3/2Γ(−1, 17.3/T) cm3/sec (with T in keV) is obtained, which is in agreement with the empirical data over a large temperature region (10 keV<T<1000 keV).
Characteristics of obliquely propagating, nonlinear Alfvén waves
Authors: Spangler Steven R. , Plapp Brendan B.
Published: July 2002

Properties of obliquely propagating (with respect to the large scale magnetic field) nonlinear Alfvén and fast magnetosonic waves as described by the derivative nonlinear Schrödinger equation are considered. Attention is restricted to those waves which in the parallel-propagating limit are circularly polarized, exact solutions to the magnetohydrodynamic (MHD) equations. A study is made of the changes in the structure of these waves as the propagation angle is increased. In addition, numerical studies are made of the evolution of initial conditions which do not correspond to stationary wave solutions. The principal conclusions of this investigation are as follows. (1) As the propagation angle with respect to the mean field increases, the functional forms of the wave magnetic field components in the two directions orthogonal to the propagation direction become increasingly dissimilar. This fact may be the basis for the ‘‘polarization evolution’’ of large amplitude MHD waves observed in space. (2) The angle about the mean field within which stationary waves resemble parallel-propagating, circularly polarized waves becomes smaller as the wavelength increases. (3) Numerical investigations of the evolution of large amplitude, circularly polarized wave packets show that if the ‘‘initial condition’’ wave train is close to parallel-propagating (where the criterion for ‘‘close’’ is developed in this paper), then there is little subsequent evolution in its form. However, if the propagation angle is sufficiently large, the wave steepens, undergoes polarization evolution, and can generate high-frequency wavelets. The relevance of these results for the large amplitude MHD waves near the Earth’s bow shock is briefly discussed.
Rescaling methods and plasma expansions into vacuum
Authors: Manfredi G. , Mola S. , Feix M. R.
Published: July 2002

The problem of a two-component, collisionless plasma expansion into vacuum is investigated from the viewpoint of the Vlasov–Poisson model. The set of equations is treated both analytically (through the rescaling transformations) and numerically, using a one-dimensional Eulerian code. In planar geometry, the rescaling allows to conjecture the existence of a self-similar expansion over long times. Numerical results subsequently confirm the conjecture and show that the plasma becomes neutral over a smaller and smaller scale. A few thermodynamical properties are studied: the temperature is shown to decrease as t−2; the polytropic relation (d/dt)(pn−γ)=0 (with γ=3) is verified asymptotically via a semianalytical argument. Finally, the same problem is studied in a spherical one-dimensional geometry. The time-asymptotic solution is again self-similar. Numerical simulations show that a non-neutral, multiple-layer structure appears, which is proved to be stable over long times.
Revisiting the validity of quasilinear theory
Authors: Liang Y.-M. , Diamond P. H.
Published: July 2002

The weak turbulence theory of Langmuir waves in a one-dimensional, one-species plasma is discussed. Analytic calculations using the theory of two-point correlations show that in the weak turbulence regime, τac≪min(τtr,γ−1k) (where τac is the field autocorrelation time and τtr is the particle decorrelation time), the nonlinear enhancement of the mode growth rate γk beyond the linear, Landau growth rate γkL is small, additive, and higher order in the weak turbulence expansion parameter. This result thus supports the validity of the quasilinear theory for Langmuir wave turbulence, and disagrees with the predictions of Adam, Laval, and Pesme [Phys. Rev. Lett. 43, 1671 (1979)], which indicate a non-negligible, multiplicative enhancement in the regime τac≪τtr≪γ−1k. Analysis shows that their result comes from the use of an invalid source term for the fluctuations.
Current sheet profiles in two-dimensional magnetohydrodynamics
Authors: Biskamp D.
Published: July 2002

Numerical simulations of current sheet formation in a two-dimensional ideal incompressible magnetohydrodynamic system reveal that sheets evolve self-similarly with cross-sheet profiles close to j(ψ)∝exp(−2αψ). This current profile has previously been derived by several authors as the most probable state in a current-carrying plasma. A critical review of the different theoretical approaches is given.
High poloidal beta long-pulse experiments in the Tokamak Fusion Test Reactor*
Authors: Kesner J. , Mauel M. E. , Navratil G. A. , Sabbagh S. A. , Bell M. , Budny R. , Bush C. , Fredrickson E. , Grek B. , Janos A. , Johnson D. , Mansfield D. , McCune D. , McGuire K. , Park H. , Ramsey A. , Synakowski E. , Taylor G. , Zarnstorff M. , Batha S. H. , Levinton F. M.
Published: July 2002

Experiments have been performed in the Tokamak Fusion Test Reactor [D. M. Meade et al. in Plasma Physics Controlled Nuclear Fusion Research, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 9] with neutral beam injection of up to 4 sec. duration, which is comparable to the time scale for resistive redistribution of the plasma current profile. These plasmas were created using a rapid decrease of the plasma current which initially created a plasma with enhanced stability and confinement. As the current profile evolved, a significantly reduced beta limit was observed. The high εβp plasmas had up to 90% of the current driven noninductively which significantly broadened the current profile during the long pulse lengths. These experiments demonstrated that high βN plasmas could not be sustained for times longer than the resistive relaxation of the outer current region which at early times after the current ramp-down carried negative current. At later times in lower βN discharges, beta collapses were sometimes observed as the current profile broadened at βN∼1.5. The appearance of disruptions was consistent with the predictions of ideal magnetohydrodynamics (MHD) stability analyses.
Cusp catastrophe in flow acoustics
Authors: Rehberg Ingo
Published: July 2002

The transonic flow in a tube following an abrupt enlargement of the cross section produces self-induced flow oscillations which generate sound (whistler). The frequency of the oscillation is influenced by the tube length: increasing length leads to a frequency decrease, but only up to a critical length lc of the tube. If this length is further increased, the frequency will jump to higher values. This jump shows hysteresis: decreasing the tube length again leads to a jump to the lower frequency at a length lc1<lc. Having presented details of the above phenomenon, the two mathematical models are then presented, in which the transonic oscillator is represented by two simple nonlinear equations which behave harmonically, and the acoustic resonator, i.e., the tube, is represented by a term including a time lag. It is shown that the hysteresis vanishes for both the experiment and the model if the sound reflection at the end of the tube is decreased below a certain critical value. This behavior is one of the few reported examples of a cusp catastrophe in an oscillating system.
Nonlinear mode conversion and anomalous absorption processes during radio-frequency heating of bumpy torus plasmas
Authors: Stefan V. , Krall N. A.
Published: July 2002

The theory of nonlinear mode conversion is reviewed and applied to the ELMO Bumpy Torus (EBT) [Proceedings of the 5th International Conference on Plasma Physics and Controlled Nuclear Fusion Research 1974 (IAEA, Vienna, 1975), Vol. 2, p. 141] environment in the electron-cyclotron, upper-hybrid, lower-hybrid, and ion-cyclotron frequency ranges. A variety of parametric excitations in these frequency ranges is studied. Based on cascade saturation mechanisms, the parametric turbulence levels and corresponding anomalous absorption rates of the excited modes are evaluated. The relevance of nonlinear mode conversion for contemporary and future EBT experiments is discussed.
Considerations of temperature stability in a cylindrical plasma
Authors: Rasband S. N. , Xu Yao-Hui
Published: July 2002

A variational formulation is used to consider thermal equilibrium and stability for a cylindrical plasma modeled by dissipative magnetohydrodynamics. The parameter dependence of equilibrium solutions and their stability is followed using homotopy techniques. Solution branches and their connections are studied in relation to the applied fields.
Experiments with deceleration from a Taylor-vortex flow
Authors: Squire T. H. , Jankowski D. F. , Neitzel G. P.
Published: July 2002

The behavior of a Taylor-vortex structure during a constant deceleration has been studied experimentally. As expected, the results show a return to circular Couette flow at an instantaneous Reynolds number below the steady critical value.
Stability and Bäcklund transform of the forced Burgers equation
Authors: Pasmanter R. A.
Published: July 2002

A proof is given of the neutral (absolute) stability of the Burgers equation driven by time-independent external forces (boundary conditions). A Bäcklund transform of the forced Burgers equation is presented that is valid even when the external force is time dependent.
Solutions to the nonlinear Boltzmann equation for particle transport in a host medium
Authors: Rupp D. , Nonnenmacher T. F.
Published: July 2002

Analytical solutions for nonlinear diffusion of test particles (mass m) into a background system of field particles (mass m̂) are available only for the mass ratio α=m/m̂=0. This physical situation for α≠0 and numerical solutions for the moments and the distribution function  f (v,τ) are investigated.
Kinetic theory of parametric excitation of electromagnetic waves propagating along a constant magnetic field
Authors: Matsuda Kyoko
Published: July 2002

A nonlinear dispersion relation for a circularly polarized electromagnetic wave of a finite wavelength propagating along a constant magnetic field is derived by a kinetic theory. The dispersion relation includes an important correction term to the dispersion relation previously obtained for the ion cyclotron range frequency and may be applied to problems in any range of frequency. Using this dispersion relation, parametric instabilities relevant in a finite-amplitude right circularly polarized wave (r wave), that is, excitations of newly found branches of a strongly damped r wave, the Raman scattering to a damped r wave, and the Brillouin scattering, have been studied.
Kink stability of a field-reversed ion layer in a background plasma
Authors: Ishida A. , Sudan R. N. , Rosenbluth M. N. , Engquist M. G.
Published: July 2002

By means of the two-fluid energy principle, the kink stability boundary of a field-reversed ion layer of arbitrary thickness immersed in a dense low-temperature background plasma is investigated theoretically. This system is found to have a stability window against kinks. The dependence of the kink stability regime on the equilibrium properties of the system is also shown. In the thin layer limit, a comparison is made between the previous theories and the present theory.
Electrostatic instabilities near the lower-hybrid frequency excited by a large-amplitude pump
Authors: Rambo P. W. , DeGroot J. S.
Published: July 2002

Instabilities of a magnetized plasma subjected to a large-amplitude dipole field oscillating at a frequency near the lower-hybrid frequency are investigated by numerically solving the linear dispersion relation. Besides the usual parametric instabilities, additional modes are driven unstable at higher harmonics of the pump frequency. The relevance of these modes to plasma heating is discussed.
Cross-field resonance effects near the f
q2 frequency
Authors: Thiel J. , Hamelin M.
Published: July 2002

The cross-field radiation from a point source in a warm magnetoplasma is studied near the fq2 frequency where the group velocity of cross-field waves vanishes, between the upper hybrid frequency or the second electron gyroharmonic, whichever is the higher, and the third gyroharmonic. Calculations are made of the electrostatic wave potential created by an alternating point charge in a Maxwellian magnetoplasma, neglecting collisions and forced ion motion. The integral which gives the potential is evaluated both analytically and numerically by using the least-damped-root approximation which involves considering only three roots of the dispersion equation for electrostatic waves. The good agreement between the approximate analytical and the exact numerical calculations in a cross-field direction permits one to understand physically the behavior of the three-wave interference pattern which depends on the excitation frequency, the distance of observation, and the electron density and temperature. Two new theoretical effects are primarily studied: (i) the potential becomes infinite at fq2 when collisions are neglected, and (ii) an oscillatory structure can occur at frequencies less than fq2. The main characteristics of these effects are derived as functions of the plasma parameters. In particular, it is found that the fq2 resonance arises with extremely sharp outlines and neatly differentiates between two frequency ranges with quite different potential patterns. Finally, the possibility of observing these resonance effects in the laboratory and by space experiments is discussed.
A scalar model of turbulent convection
Authors: Legait A.
Published: July 2002

A scalar model of turbulent incompressible convection is presented in which transfer of energy between modes at different scales or between horizontal and vertical vorticity modes is represented by quadratic nonlinear interactions. The growth rate of the modes is parametrized in order to take into account the buoyancy force and the mean temperature gradient. At a small Prandtl number (which is of astrophysical interest) it is found that the Nusselt number scales as (Rσ)1/3. The form of the spectrum at large wavenumbers is that of three-dimensional turbulence (Kolmogoroff spectrum). At small wavenumbers the spectrum is determined by the growth rate of the unstable modes.
Analytical model for the perpendicular temperature enhancement in lower-hybrid current drive
Authors: Hizanidis K. , Bers A. , Fuchs V. , Cairns R. A.
Published: July 2002

The enhancement of the perpendicular temperature inside the resonant region, observed in numerical studies of the two-dimensional Fokker–Planck equation, combined with unidirectional rf quasilinear diffusion, is modeled on the basis of the collisional relaxation equations. Strong rf diffusion is assumed and relativistic effects are taken into account. The resulting enhanced perpendicular temperature is a function of the position and the width of the applied rf spectrum. Good agreement with two-dimensional Fokker–Planck numerical results has been found.
Interaction of an intense relativistic electron beam with preformed channels
Authors: Murphy D. P. , Raleigh M. , Pechacek R. E. , Greig J. R.
Published: July 2002

The interaction of an intense relativistic electron beam (REB) with preformed channels in gaseous atmospheres has been analyzed in order to delineate the effects of reduced density, avalanche ionization, preexisting conductivity, and channel currents. The REB for these experiments was produced from a field emission diode driven by the ≈1.4 MV pulse from a pulse forming line. Relativistic electron beam currents up to ≈16 kA with current densities up to ≈2 kA/cm2 were achieved and the REB current was approximately a half sine wave of width 27 nsec (FWHM). Preformed channels in the atmosphere were created using laser-guided electric discharges. Current-carrying reduced density channels were produced by applying a second discharge to the reduced density channel produced by the first discharge. Reduced density (≤ρ0/80), nonconducting channels were produced by the absorption of radiation from a pulsed CO2 laser in ammonia gas at background pressures of ≈40 Torr (ρ0/20). The results show that reduced density had little effect on REB propagation except for a decrease in scattering until the density within the channel had been reduced to such a low level that the dominant mechanism by which conductivity is generated shifted from direct collisional ionization to avalanche ionization. Avalanche ionization in a uniform atmosphere increases the growth of REB instabilities but when it is limited to the reduced density channel region the REB was always repelled or expelled from the channel. Preexisting channel conductivity (σ≥0.1 S/m) also caused the REB to be repelled or expelled from the channel. The presence of a parallel channel current permitted the REB to be readily injected into the channel and guided along it with minimal losses. All of these effects and the thresholds at which they occurred are consistent with the present understanding of the interaction of intense REB’s with gaseous atmospheres.
Oscillatory Marangoni–Bénard interfacial instability and capillary–gravity waves in single- and two-component liquid layers with or without Soret thermal diffusion
Authors: Garcia-Ybarra P. L. , Velarde M. G.
Published: July 2002

Shown here are the dispersion relation, the oscillation frequency, and the critical Marangoni number for the onset of oscillatory interfacial instability in a horizontal single- or two-component liquid layer heated from above or below when the upper deformable surface is open to the ambient air. It is shown that for vanishingly small gravity the temperature gradient for the onset of instability also becomes negligibly small thus indicating the major importance and the potential danger of Marangoni–Bénard instability in experiments under microgravity conditions.
Calculation of neoclassical fluxes in the plateau regime for nonaxisymmetric toroidal plasmas
Authors: Rodriguez-Solano Ribeiro E. , Shaing K. C.
Published: July 2002

An analytic calculation of the neoclassical fluxes in the plateau regime in the absence of momentum and energy sources is carried out with a general model field, B=B0[1+∑iεi cos(liθ−miζ)], following the moment-equation approach. It is shown that the radial particle and heat fluxes resulting from each harmonic (εi) are additive and have the same sign. Consequently, the neoclassical fluxes in a stellarator in the plateau regime are larger than those in the corresponding ‘‘equivalent’’ tokamak (same aspect ratio and rotational transform). Numerical calculations performed with a drift kinetic equation solver agree to within 10% with the analytic results for the examples considered.
Propagation of charge-neutral beams in space: Modifications when negative ions are present
Authors: Winglee R. M. , Pritchett P. L.
Published: July 2002

Two-dimensional (three velocity component) electrostatic simulations are used to investigate the properties of a charge-neutral beam consisting of H+, H−, and electrons which will be used in the Beams on R_ockets (BEAR) experiment to be launched in late 1987 or early 1988. For cross-field injection and beam densities much greater than the ambient plasma density, the beam splits into two approximately charge-neutral beams: a H+–e− beam that propagates down the field lines and a H+–H− beam that propagates at nearly the initial beam velocity on time scales less than the ion gyroperiod. Because of this splitting, space-charge oscillations are induced in the H+–H− component, which lead to its breakup. At lower beam denisties, particularly when the beam electron density is less than about the density of the ambient plasma, the ambient plasma response reduces the space-charge fields as the beam splits and the space-charge oscillations are suppressed.
Evidence of turbulence in a current disrupted region in a plasma focus
Authors: Hirano Katsumi , Yamamoto Toshikazu
Published: July 2002

Immediately after the current disruption in a plasma focus discharge, emission of neutrons, soft x rays, ions, and electrons are observed for several tens of nanoseconds. Using a laser scattering diagnostic and a Schlieren technique, it is shown that the plasma in the disrupted region is in a superthermal level in this phase. In the Schlieren technique, the same laser pulse used for the scattering system was used for the light source. The experiment showed that only in the disrupted region did enhanced scattering occur. The measured duration of the superthermal level is ∼10 nsec. When a probe gas is mixed with the working gas, D2, spectral lines of highly charged ions of probe gas are obtained in the disrupted region.
Nonlinear equilibration of two-dimensional optimal perturbations in viscous shear flow
Authors: Butler Kathryn M. , Farrell Brian F.
Published: July 2002

Two-dimensional perturbations configured for maximum energy growth in laminar viscous shear flow are shown to develop into quasisteady finite amplitude structures, provided that the initial perturbation has sufficient energy and a nearby nonlinear mode exists. For Poiseuille flow, which supports finite amplitude equilibria for Reynolds numbers above ∼2900, an optimal perturbation with initial energy density equal to or greater than 0.1% of the mean flow energy density closely approaches the quasiequilibrium state within 10 advective time units. For Couette flow, which has no finite amplitude solution, the optimal perturbations decay rapidly after reaching maximum amplitude unless the configuration is sufficiently close to a linear mode with slow exponential decay rate. While the quasiequilibrium structure for Poiseuille flow is locally inflectional, it supports only weak instabilities with scales larger than the local region.
The dissipation rate of fluctuating kinetic energy in a fluid–solid flow
Authors: Liljegren Lucia M.
Published: July 2002

An analysis is performed to determine the relationship between the Taylor microscale for total velocity and the dissipation rate for fluctuating kinetic energy in a fluid–solid mixture.
Spin coating of viscoelastic and nonvolatile fluids over a planar disk
Authors: Borkar A. V. , Tsamopoulos J. A. , Gupta S. A. , Gupta R. K.
Published: July 2002

Spin coating of two commercially used polymer solutions is studied both theoretically and experimentally. Physical and rheological characterization of these solutions indicates that under the spinning conditions currently used they behave as nonvolatile, viscoelastic fluids with constant viscosity and elasticity. The corresponding Reynolds (Re) and Deborah (De) numbers are up to order unity. The theoretical analysis demonstrates and explains why, at very short times after the inception of impulsive spinning, the velocity and stress fields in such fluids develop in an oscillatory manner. The amplitude of these oscillations increases with the ratio of the retardation parameter to the Deborah number, whereas their damping rate gets smaller as De increases. Since these oscillations dissipate very rapidly, and before substantial thinning of the film takes place, the thinning rate, velocity, and shear stress components do not deviate eventually from those of a Newtonian fluid. Such a complete explanation of similar experimental findings has not been offered before. The radial normal stress component does increase considerably over its Newtonian value, and this explains certain ‘‘experimental practices.’’ Similar oscillatory development early on occurs even at higher Re, as long as Re∼De, but it is dissipated again, this time because of the abrupt thinning of the film. The theoretical results are in good agreement with experimental measurements of ‘‘dry film’’ thickness and with dynamical measurements of ‘‘wet film’’ thickness during spinning, which are reported herein for the first time. Care must be taken in reporting ‘‘dry film’’ thickness because the commercial solutions under study retain part of the solvent after ‘‘soft baking’’ over a hotplate. Complete solvent removal produces dry films, but requires treatment in a vacuum oven, higher temperatures, and longer heating times.
Stochastic characteristics of a point-source plume diffusion field upstream of a sphere
Authors: Liu Shengjian , Sakai Yasuhiko , Tsunoda Hiroyuki , Nakamura Ikuo
Published: July 2002

This research aimed to clarify the disturbance generated by a sphere in a point-source diffusing plume developing in grid-generated turbulence. Of special concern is the effect of the distortion of the mean stream near the forward stagnation point on the diffusion. Some results from statistical processing of experimental data are given. It was found that, because of the strong distortion of the mean stream, molecular diffusion in the vicinity of the stagnation point is greatly accelerated. As a result, as the stagnation point is approached, the conditioned probability density function for near-zero concentration shows a remarkable slump. This result is explained qualitatively with the help of the probability density function (PDF) budget equation. A new concept, smeariness, is defined and used to effectively explain the experimental results.
Kinetic alpha effect in viscosity stratified creeping flows
Authors: Kliakhandler Igor , Sivashinsky Gregory
Published: July 2002

It is shown that viscosity stratified plane Poiseuille flow may exhibit a long-wavelength instability of a purely kinetic nature formally resembling the so-called alpha effect known in magnetohydrodynamics or in anisotropic three-dimensional flows of homogeneous fluids. In the absence of the alpha effect, the system may display a peculiar type of long-wavelength instability, where the latter is controlled by the surface tension. The weakly nonlinear equation for the evolving interfaces is derived and solved numerically.
Dispersion in zero-mean periodic flows
Authors: Jones Scott W.
Published: July 2002

The dispersion of tracer particles in zero-mean shear flows with no-slip boundaries is found to be diffusive when the particle trajectories are chaotic and ergodically explore the flow domain. This diffusive spreading occurs even when the molecular diffusivity vanishes. The long-time behavior for zero-mean shear flows thus differs quantitatively from non-zero mean shear flows. A model problem is formulated and the moment equations solved using techniques from the theory of random walks. Dispersion of ‘‘perfect’’ tracers in oscillatory Rayleigh–Bénard convection is also found to behave diffusively.
Arbitrarily oriented capillary-viscous planar jets in the presence of gravity
Authors: Goodwin Ralph T. , Schowalter William R.
Published: July 2002

Numerical solutions for the steady flow of an arbitrarily oriented incompressible capillary-viscous jet in the presence of gravity are presented. A combination of the finite element method and an elliptic mesh generation technique are used to compute solutions over a wide range of the four relevant physical parameters: Reynolds number, Stokes number, capillary number, and angle of the jet nozzle with respect to gravity. It is shown that both gravity and surface-tension forces can be instrumental in the mechanism of jet turning. In addition, it is found that multiple solutions are possible when the jet nozzle is directed close to vertically upward. The linear stability of the steady solutions to two-dimensional disturbances is briefly considered.
Terminal structure of unsteady classical and interacting boundary layers
Authors: Xiao Z. , Adams E. C. , Conlisk A. T.
Published: July 2002

The terminal structure of the unsteady boundary-layer equations is investigated for the problem of impulsive flow past a circular cylinder. It is known that both the classical and interacting boundary-layer equations for this problem are singular and the singular structure for the interacting boundary layer on a circular cylinder has not been properly resolved using the classical finite difference approach within an Eulerian framework. The objective of this paper is to resolve the singular structure for both the classical and interacting boundary layers for the impulsively started flow past a cylinder. An adaptive-grid scheme, coupled to a panel method for the interacting case, is employed to resolve the extremely small time and length scales associated with a terminal structure defined by the emergence of a singularity. Calculations performed in an Eulerian coordinate system show that interacting boundary-layer calculations terminate sooner than the classical boundary-layer calculation, and as the Reynolds number decreases, the singularity occurs earlier in time and closer to the rear stagnation point of the circular cylinder. Comparisons with previous Lagrangian and fixed-grid Eulerian results are discussed.
Three-dimensional subharmonic waves during transition in the near-wake region of a cylinder
Authors: Williams D. R. , Mansy H. , Abouel-Fotouh A.
Published: July 2002

Detailed quantitative measurements of three-dimensional subharmonic waves have been obtained with a scanning laser anemometer in the near-wake region of a circular cylinder. A spatial decomposition technique has been used to separate the secondary three-dimensional flow from the primary Strouhal vortex flow. The appearance of subharmonic frequencies in the spectrum of the secondary instability field at Reynolds numbers of 300 and above provides experimental evidence consistent with the scenario of a period-doubling route to turbulence. The basic flow structure of the secondary field responsible for producing the subharmonics is shown to be pairs of counter-rotating streamwise vortices, which alternate the direction of rotation every Strouhal period.
Modeling nearly incompressible turbulence with minimum Fisher information
Authors: Cocke W. J.
Published: July 2002

The principle of minimum Fisher information (MFI) is used to work out the joint distribution function of the density and velocity in homogeneous, isotropic, stationary, nearly incompressible turbulence. We assume that the Mach number is very low. It is shown that simple constraints on the minimization may be chosen to give a good fit to the pressure distribution function found in recent direct numerical simulations and experiments, where the PDF is exponential for negative p and roughly exp[−(p/p0)3/2]p−1/2 for positive p. The appropriate constraints in the MFI problem are on the skewness of the PDF both by itself and weighted by the internal energy density of the fluid. MFI then predicts that in the limit of very low Mach number, the pressure and the fluid velocity u are independent of each other, as random variables; i.e., P(p,u)→P(p)P(u). Also, P(u) is a Gaussian.
A normal multimode decomposition method for stability experiments
Authors: Tumin Anatoli , Amitay Michael , Cohen Jacob , De Zhou Ming
Published: July 2002

A method for decomposition of an experimental signal that contains several normal modes with a prescribed frequency, is proposed. The method is based on an expansion of solutions for small-amplitude spatially growing disturbances in a biorthogonal eigenfunction system. It is shown that data of one velocity component at a given cross-stream section of the flow are in some cases, sufficient for the decomposition. The method is applied successfully to analyze small-amplitude periodic disturbances in a transitional wall-jet flow.
Thermal singularities in film rupture
Authors: Oron Alexander , Bankoff S. George , Davis Stephen H.
Published: July 2002

Long-wave approximation for the spatiotemporal evolution of thermal and evaporative instabilities of a thin liquid film lying on a ‘‘thick’’ solid substrate is considered. It is shown that accounting for a nonzero thermal resistance of the solid eliminates the emergence of temperature, heat and mass flux singularities at the rupture point.
Chaotic heat transfer enhancement in rotating eccentric annular-flow systems
Authors: Ganesan Venkat , Bryden Michelle D. , Brenner Howard
Published: July 2002

Thermal Taylor dispersion theory for time-periodic systems was used to study the extent of chaotic laminar heat transfer enhancement and axial thermal dispersion occurring during combined transverse and axial annular flow between two nonconcentric circular cylinders undergoing alternate rotations. A local Newton’s “law of cooling” heat transfer boundary condition was used on the outer cylinder, whereas the inner cylinder was supposed insulated. The effective heat transfer coefficient H̄* describing the global rate of heat loss from the system (differing in general from the true microscale Newton’s law heat transfer coefficient h on the outer cylinder) was calculated as a function of the system parameters, thereby serving to quantify the extent of chaotic heat transfer enhancement. The axial thermal Taylor dispersivity provided an independent measure of the effects of chaotic mixing, as too did the axial thermal velocity. Calculations were performed for three different cases: (i) concentric cylinder rotation (for which case the resulting circular transverse flow has no effect upon the effective transport properties); (ii) nonconcentric counter-rotating circular cylinders, each undergoing a steady rotation, thereby creating a time-independent transverse flow field; (iii) nonconcentric counter- and co-rotating circular cylinders, each undergoing time-periodic alternate rotation while the other remains at rest. A “regular” enhancement of the heat transfer rate over the concentric cylinder case was observed in case (ii), arising from the presence of a secondary-flow recirculation region. Enhancement due to chaotic advection was observed in case (iii) [about 50% more than that of case (ii) and more than double that of case (i), all other things being equal]. Concomitant values of the axial thermal Taylor dispersivity and axial thermal velocity confirmed the existence of enhanced transverse transport due to chaotic advection. It was observed that the functional dependence of the enhanced heat transfer rate upon the system parameters does not consistently display the same trends as are qualitatively suggested by the “degree of chaoticity” of the comparable Poincaré plots. This observation signals the need for caution in simply assuming that the greater the degree of chaotic “mixing” implicit in the Poincaré plot the greater will be the corresponding global transport rate. By simple redefinition of the symbols used in the present paper, our energy transport results may be re-interpreted so as to apply to the case of reactive-species transport involving a first-order irreversible chemical reaction occurring on the outer-cylinder surface; explicitly, the Nusselt number quantifying the local heat transfer coefficient rate is simply replaced by a comparable Damköhler number quantifying the local kinetics of the surface reaction.
Conduction in the small gap between two spheres
Authors: Solomentsev Yuri , Velegol Darrell , Anderson John L.
Published: July 2002

A solution to the conduction equation has been developed for two equal size, nonconducting spheres with the line between centers perpendicular to the applied field. The solution, valid when the gap between the spheres is small compared to their radius, is based on a matched asymptotic expansion. For the case when the conductivity is uniform everywhere (i.e., Laplace’s equation), the solution agrees well with numerical results obtained from an infinite series solution in bispherical coordinates. An example with a nonuniform conductivity in the gap is presented to demonstrate how the method can be extended to more general conduction problems.
Analytic solutions for Stokes flow past a partially encapsulated droplet
Authors: Palaniappan D. , Kim Sangtae
Published: July 2002

The Stokes flow past the unusual geometry of two fused (overlapping) spheres, somewhat surprisingly, has an exact analytic solution, provided that the spheres intersect orthogonally. The problem of flow past a partially encapsulated droplet is considered, to illustrate the basic idea. The simple nature of the analytical solution is of some interest in biophysical models of molecular assemblies involving a combination of stick and slip surfaces.
Local similarity solutions in the presence of a slip boundary condition
Authors: Salamon Todd R. , Bornside David E. , Armstrong Robert C. , Brown Robert A.
Published: July 2002

The local solution behavior near corners formed by the intersection of a slip surface with either a no-slip or a shear-free boundary is analyzed by finite element calculations of the two-dimensional flow of an inertialess Newtonian fluid in several model flow geometries; these flows are the flow in a tapered contraction, a sudden expansion and the extrudate swell from a planar die. Local finite element mesh refinement based on irregular, embedded elements is used to obtain extremely fine resolution of the velocity and pressure fields near the region where there is a sudden change in boundary condition. The calculations accurately reproduce the expected asymptotic behavior for a shear-free surface intersecting a no-slip boundary, where the solution is given by a self-similar form for the velocity and pressure fields. Replacing the shear-free condition with a slip condition yields a similar form for the local velocity and pressure fields and indicates that the slip boundary behaves, to leading order, as a shear-free surface. Calculations for a slip boundary intersecting a shear-free surface yield similar results, with the local behavior being given by asymptotic analysis for two shear-free surfaces intersecting to form a wedge. These results suggest that replacing the no-slip boundary condition in planar Newtonian die swell with a slip boundary condition can give rise to local behavior of velocity gradients and pressure which is more singular than the flow created with no-slip boundary conditions. This prediction is confirmed by calculations of Newtonian die swell with slip. These calculations also demonstrate that the local solution in Newtonian die swell is sensitive to the details of the numerical method.
An intermittency model for passive-scalar turbulence
Authors: Cao Nianzheng , Chen Shiyi
Published: July 2002

A phenomenological model for the inertial range scaling of passive-scalar turbulence is developed based on a bivariate log-Poisson model. An analytical formula of the scaling exponent for three-dimensional passive-scalar turbulence is deduced. The predicted scaling exponents are compared with experimental measurements, showing good agreement.
Periodic vortex breakdown in wide spherical gaps
Authors: Yuan Li , Fu Dexun , Ma Yanwen
Published: July 2002

The flow field with vortex breakdown in wide spherical gaps was studied numerically by a finite difference method under the axisymmetric condition. The result shows that the flow bifurcates to periodic motion as the Reynolds number or the eccentricity of the spheres increases.
Thermocapillary and buoyant flows with low frequency jitter. I. Jitter confined to the plane
Authors: Grassia P. , Homsy G. M.
Published: July 2002

A temperature gradient is applied along a fluid filled slot with a flat upper interface, establishing flow via thermocapillarity and/or buoyancy. There is a known parallel flow along the slot, in which the fluid velocity varies vertically, and there is a known convected temperature profile. This parallel flow is then subjected to gravitational modulation or “jitter” which is applied at low frequency and in various directions. For gravity modulations in the plane of the basic flow, analytic solutions for velocity and temperature profiles are obtained for jitter of arbitrary amplitude. These solutions involve modifications to the earlier parallel flow solutions. Jitter in the vertical direction generates vorticity due to coupling with the applied horizontal temperature gradient. This alternately cooperates or competes with the steady basic flow over a cycle of the modulation, but does not qualitatively change the flow or temperature profiles. Jitter applied along the slot produces vorticity only when coupled to vertical convected temperature gradients and so is important when the basic flow is sufficiently strong (large Marangoni and/or Rayleigh number). Various cases are considered for the basic flow, which may be driven by thermocapillarity alone, by vertical gravity alone or by a mixture of thermocapillarity and vertical gravity. When strong streamwise jitter is added to any of these cases, the flow profile alternates during the modulation cycle between boundary layer structures and vertically stacked cells. The type of structure selected depends on the sense of the horizontal thermal stratification with respect to the jitter, and in that part of the cycle where this stratification is unstable, there are particular amplitudes of jitter which can give strong cellular motions or runaways. These runaways represent a resonant interaction with stationary Rayleigh-Bénard cells.
Chaotic heat transfer in a periodic two-dimensional flow
Authors: Saatdjian E. , Leprevost J. C.
Published: July 2002

Chaotic heat transfer in the annular region between two confocal ellipses is analyzed with tools developed in previous mixing studies as well as specific ones presented here. In particular, we show that even though the Eulerian temperature field is periodic, the Lagrangian temperature of a particle can be either periodic or chaotic depending on its initial position. A potential mixing zone, very similar to the one defined by Kaper and Wiggins, is defined for modulated heteroclinic trajectories. The geometry and modulation protocol can be optimized so that a greater than 100% increase of heat transfer over that of conduction is obtained.
Temporal instability of gas jets injected in viscous liquids to three-dimensional disturbances
Authors: Parthasarathy R. N. , Chiang Kai-Ming
Published: July 2002

A temporal linear stability analysis of an inviscid incompressible gas jet injected into a co-flowing viscous liquid was conducted to study the growth of small three-dimensional disturbances that lead to the break-up of the gas jet. The primary flow parameter that governed the growth of the disturbances was the gas Weber number. At small Weber numbers, only the two-dimensional varicose disturbances were unstable; at high Weber numbers, three-dimensional disturbances became unstable with growth rates comparable to the sinuous and varicose disturbances. The phase velocity of the disturbances in the gas jet was small, on the order of the co-flowing liquid velocity.
Stability of the axisymmetric buoyant-capillary flows in a laterally heated liquid bridge
Authors: Chénier E. , Delcarte C. , Labrosse G.
Published: July 2002

The axisymmetric steady-states solutions of buoyant-capillary flows in a cylindrical liquid bridge are calculated by means of a pseudo-spectral method. The free surface is undeformable and laterally heated. The working fluid is a liquid metal, with a Prandtl number value Pr=0.01. Particular care was taken to preserve the physical regularity in our model, by writing appropriate flux boundary conditions. The location and nature of the bifurcations undergone by the flows are investigated in the space of the dimensionless numbers (Marangoni, Ma∈[0,600]; Rayleigh, Ra∈[0,5×104]). Saddle-node and Hopf bifurcations are found. By analyzing the steady state structures and the energy budgets, the saddle-node bifurcations are observed to play a determinant role. Only two sets of stable steady-states, connected by saddle-nodes, are allowed by the coupling of buoyancy and capillarity. Most of the solutions of the explored part of the (Ma, Ra) plane belong to these states.