bluuebunny/crossref_metadata_2025 huggingface dataset:
Entrainment and stirring in viscous plumes
Authors: Griffiths R. W.
Published: July 2002

Buoyant plumes in very viscous fluids, although laminar, entrain their surroundings as a result of conduction of heat. Once heated, the fluid takes part in the plume motion and is stirred within the plume by internal circulation. Entrainment modifies the behavior of plumes by enlarging and cooling them. Similarity solutions for several cases, including isolated ‘‘thermals’’ having fixed buoyancy, thermals having a constant internal heat generation, the initial stages of a plume formed by a continuous volume flux (a starting plume), and steady plume conduits fed by a constant source flux are reviewed. Both laboratory experiments and computations of particle paths show that stirring in thermals and starting plumes also leads to well-defined shapes for passive tracers, shapes that depend upon the magnitude of an appropriate Rayleigh number. The computations of particle paths are extended to the case of a steady plume conduit ascending through a horizontal shear flow in order to show the internal structure of the plume. Implications of these models for mantle plumes and volcanic hotspots are discussed briefly. It is possible that the structured chemical heterogeneities produced by stirring within plumes may contribute to observed chemical variability of lavas generated by plume activity.
Transport by capillary waves. Part II: Scalar dispersion and structure of the concentration field
Authors: Ramshankar R. , Gollub J. P.
Published: July 2002

Experiments on the transport of passive scalar tracers on capillary waves generated by the Faraday instability are presented. A spot of fluorescent dye is placed just below the fluid surface and the evolution of the dye concentration field is studied. Substantial transport is found over large distances, consistent with earlier observations of particle motion on the fluid surface. The time evolution of the radial distribution of impurity is characterized on a coarse-grained scale. At large driving amplitudes ε, where the wave pattern is time-dependent with only short-range spatial correlations, the diffusion may be described as a normal Brownian process. At lower ε, where the patterns are well ordered (but modulated), this approximation fails though there is still significant transport. For large ε, the isoconcentration contours are well described as fractals with a dimension that approaches 1.40±0.05 at long times. The scalar gradient field may be described as a multifractal. These results are surprisingly similar to those obtained for transport in turbulent shear flows.
Air-blown waves on thin viscous sheets
Authors: King A. C. , Tuck E. O. , Vanden-Broeck J.-M.
Published: July 2002

A model based upon lubrication and thin airfoil theories permits steady periodic waves on the surface of a thin inclined layer of viscous fluid, when an upward stream of air flows over its surface. The flow in the layer is rotational, and is sustained by a balance between the lubrication force in the fluid and a surface shear and pressure gradient supplied by the airflow over it. An analytic small-amplitude expansion, and a numerical large-amplitude solution, are used to describe some of the features of these waves. There is a long-wave limit of a solitary waveform.
Vertical diffusion of the far wake of a sphere moving in a stratified fluid
Authors: Chomaz J. M. , Bonneton P. , Butet A. , Hopfinger E. J.
Published: July 2002

The far wake of a sphere towed horizontally in a linearly stratified fluid with Froude numbers F ∈ (0.25,12.7) and Reynolds numbers Re ∈ [150,30 000] is investigated. Regardless of the initial Froude number, the wake becomes quasi two dimensional at times large compared with the Brunt–Väisälä period. For F≤4.5, the horizontal motions are coherent over the whole depth of the wake. The wake takes the form of a regular von Kármán street for F≤1.5 but is irregular at larger F. For F≥4.5 the far wake consists of, vertically incoherent, horizontal motions in several layers. The transition occurs smoothly by a vertical decorrelation of the horizontal motion in the depth of the far which starts at F=4.5. The most novel result is that the horizontal velocity and vertical vorticity diffuse vertically in a time much shorter than predicted by a viscous diffusion law. The ratio of the observed diffusion time to the viscous diffusion time is expected to depend on Reynolds number as is indicated by a simple model.
Chaotic scattering of two identical point vortex pairs
Authors: Price Tim
Published: July 2002

The scattering dynamics of two vortex pairs with equal circulations ±κ have hitherto been thought to be regular, in contrast to the case of nonidentical pairs where a hierarchy of resonant states gives rise to chaotic behavior. However, no rigorous explanation could be found for such regularity occurring in a nonintegrable Hamiltonian system. This was recently posed as an open problem [H. Aref et al., Fluid Dyn. Res. 3, 63 (1988)], and in this paper the problem is resolved by presenting a counter-example mechanism which yields chaotic scattering dynamics when the initial pair spacings differ markedly. Alternative modes of scattering are characterized by symbolic sequences. These predictions are confirmed by numerical experiments which also show that the chaos persists even when the initial spacings are nearly equal, although the physical origin of the irregular scattering is less clear. Regular behavior is seen only in the integrable case of equal initial pair spacings.
On modeling three-dimensional turbulent wall layers
Authors: Durbin P. A.
Published: July 2002

A Reynolds stress model with a modification to the ε equation is shown to reproduce the essential new features observed by Moin et al. [Phys. Fluids A 2, 1846 (1990)] in three-dimensional turbulent channel flow. Perhaps the most significant of these features is an initial drop of turbulent kinetic energy; previous turbulence models do not predict this. The effect of the three-dimensional modification on the infinite swept-wing boundary layer is assessed. It is not large and is primarily restricted to a region near to the surface. A three-dimensional homogeneous shear flow is formulated and turbulence statistics are computed by solving a simple Reynolds stress model.
A complete set of resistive compressive ballooning equations for two-dimensional flow equilibria
Authors: Grassie K. , Krech M.
Published: July 2002

Based on the linearized compressible resistive magnetohydrodynamic equations a system of five equations describing the time-dependent behavior of ballooning modes in equilibria with sheared flow is derived. The subsequent ordering scheme is based on the method of slowly varying amplitudes, where the fast variation is prescribed by an appropriately chosen eikonal. This method bears some resemblance to a scale expansion, where at the end only the first two scales are kept.
Explosive instability of a lower hybrid wiggler free-electron laser
Authors: Sharma Anamika , Tripathi V. K.
Published: July 2002

Lower hybrid wave wigglers appear to have some advantages over Langmuir wave wigglers in generating shorter wavelengths in a free-electron laser. However, the oscillating two-stream instability of the wiggler is a potential threat to the device, limiting the operation regime to high plasma temperatures and high beam currents. At large beam currents the free-electron laser instability is explosive and may be used for the generation of intense short pulses.
Propagation of neutralized plasma beams
Authors: Wessel F. J. , Rostoker N. , Fisher A. , Rahman H. U. , Song J. H.
Published: July 2002

Beams of neutralized plasma will cross a transverse magnetic field, magnetized plasma, and neutral gas, by a combination of single particle and collective-plasma processes. At low density the beam will deflect; at higher density the beam will exhibit undeflected motion by the E×B drift or diamagnetic (high-beta) exclusion of the magnetic field. In the high-beta regime, where β>1 (β is the ratio of plasma-beam energy density to magnetic field energy density), beam magnetization occurs on a time scale orders of magnitude faster than the classical Spitzer time scale. Recent studies of fast magnetization suggest that transport processes in large ion gyroradius beams, y/ρi<1, are dominated by ion motion rather than electron motion as previously understood for small gyroradius beams, y/ρi>1, where y and ρi are the beam transverse width and ion gyroradius, respectively. Although quantitative aspects of the small gyroradius propagation physics theory are still valid, most notably the E×B drift, much work remains to fully understand fast magnetic diffusion processes, beam-trapping mechanisms, and long-range propagation limits.
A tearing mode energy principle for an axisymmetric finite beta plasma
Authors: Chu M. S. , Chance M. S. , Greene J. M. , Jensen T. H.
Published: July 2002

A self-adjoint, gauge invariant stability functional δWTG for determination of a sufficient condition of tearing mode stability is obtained for a plasma with arbitrary current and pressure profiles. The plasma is stable if there is no free energy available to support energy flux into the singular layer. The pressure gradient near the singular layer is found to be stabilizing. The tearing mode energy drive is extracted by casting the problem into its nonlinear context, demanding that both large and small solutions be continuous across the singular layer.
The space potential in the tokamak text
Authors: Yang X. Z. , Zhang B. Z. , Wootton A. J. , Schoch P. M. , Richards B. , Baldwin D. , Brower D. L. , Castle G. G. , Hazeltine R. D. , Heard J. W. , Hickok R. L. , Li W. L. , Lin H. , McCool S. C. , Simcic V. J. , Ritz Ch. P. , Yu C. X.
Published: July 2002

A heavy ion beam probe has been used to measure the plasma space potential profiles in the tokamak TEXT [Nucl. Fusion Technol. 1, 479 (1981)]. The Ohmic discharges studied were perturbed by externally produced resonant magnetic fields (an ergodic magnetic limiter or EML). Without these perturbations the plasma central potential is generally consistent with the value calculated from radial ion momentum balance, using experimental values of density and ion temperature and assuming a neoclassical poloidal rotation velocity. Exceptions to the agreement are found when operating with reduced plasma parameters. Possible reasons for this discrepancy are explored, in particular, the effects of intrinsic magnetic field fluctuations, and modifications to the self-consistent radial electric sheath. With the application of the EML fields the edge electric field and potential increase during periods of magnetic island overlap. A test particle calculation of electron transport shows increases in diffusivity also occur during periods of magnetic island overlap. These calculated changes in diffusivity are interpreted in terms of a stochastic layer width, which is itself used to predict a potential change for comparison with the experimental results.
Theory of ionization-driven drift wave turbulence
Authors: Ware A. S. , Diamond P. H. , Biglari H. , Carreras B. A. , Charlton L. A. , Leboeuf J.-N. , Wootton A. J.
Published: July 2002

The theory of ionization-driven drift wave turbulence is presented in the context of a quasilocal model. Linear analysis reveals that ionization effects can destabilize collisional drift waves and can possibly induce parallel shear flow instabilities, as well. Nonlinear analysis indicates that energy is transferred from large to small stable scales and converted to ion kinetic energy. Results indicate mode coupling effects are dominant. Large fluctuation levels, in excess of mixing length expectations, are predicted. The ionization source drives a purely inward particle flux, which can explain the anomalously rapid uptake of particles that occurs in response to gas puffing.
Resonance broadening theory of plasma turbulence
Authors: Ishihara Osamu , Xia Huajuan , Hirose Akira
Published: July 2002

Motion of charged particles in random electric fields is studied analytically. It is shown that the velocity increments of particles are described as a nonstationary stochastic process that results in the time dependency of the Fokker–Planck diffusion coefficient. The diffusion rate of particles in velocity space is analyzed by different methods. Direct calculation of the Fokker–Planck diffusion coefficient based on particle trajectories reveals that the turbulent collisions broaden the resonance region in velocity space and that the turbulent collision frequency is proportional to the square root of velocity variance. Calculation of a transition probability by quantum mechanical approach supports the above conclusion in which fluctuations in the coordinate due to random fields are considered in the Hamiltonian. The Vlasov approach clarifies the subtle point of erroneous assumption made earlier to derive conventional (Dupree–Weinstock) resonance broadening theory. The diffusion rate in strong turbulence is found to be much lower than both the quasilinear and the conventional resonance broadening predictions and scales as D∼E4/3.
Sawtooth stabilization by localized electron cyclotron heating in the WT-3 tokamak
Authors: Hanada K. , Maehara T. , Makino K. , Kishigami Y. , Kishino T. , Minami T. , Tanaka H. , Iida M. , Nakamura M. , Maekawa T. , Terumichi Y. , Tanaka S.
Published: July 2002

The effect on sawtooth oscillations (STO) by localized electron-cyclotron-resonance heating (ECH) on the WT-3 tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1988 (International Atomic Energy Agency, Vienna, 1989), Vol. 1, p. 563] is studied. STO are strongly modified or stabilized by ECH near the q=1 surface, where q refers to the safety factor. The effect of ECH is much stronger when it is applied on the high-field side as compared to the low-field side. Further, even when ECH is applied outside the q=1 surface, the amplitude of STO decreases and STO stabilizes. In the very high qL discharge, the excitation of STO can be obtained by applying ECH.
Two novel applications of bootstrap currents: Snakes and jitter stabilization
Authors: Thyagaraja A. , Haas F. A.
Published: July 2002

Both neoclassical theory and certain turbulence theories of particle transport in tokamaks predict the existence of bootstrap (i.e., pressure-driven) currents. Two new applications of this form of noninductive current are considered in this work. In the first, an earlier model of the nonlinearly saturated m=1 tearing mode is extended to include the stabilizing effect of a bootstrap current inside the island. This is used to explain several observed features of the so-called ‘‘snake’’ reported in the Joint European Torus (JET) [R. D. Gill, A. W. Edwards, D. Pasini, and A. Weller, Nucl. Fusion 32, 723 (1992)]. The second application involves an alternating current (ac) form of bootstrap current, produced by pressure-gradient fluctuations. It is suggested that a time-dependent (in the plasma frame), radio-frequency (rf) power source can be used to produce localized pressure fluctuations of suitable frequency and amplitude to implement the dynamic stabilization method for suppressing gross modes in tokamaks suggested in a recent paper [A. Thyagaraja, R. D. Hazeltine, and A. Y. Aydemir, Phys. Fluids B 4, 2733 (1992)]. This method works by ‘‘detuning’’ the resonant layer by rapid current/shear fluctuations. Estimates made for the power source requirements both for small machines such as COMPASS and for larger machines like JET suggest that the method could be practically feasible. This ‘‘jitter’’ (i.e., dynamic) stabilization method could provide a useful form of active instability control to avoid both gross/disruptive and fine-scale/transportive instabilities, which may set severe operating/safety constraints in the reactor regime. The results are also capable, in principle, of throwing considerable light on the local properties of current generation and diffusion in tokamaks, which may be enhanced by turbulence, as has been suggested recently by several researchers.
Ultrafast x-ray sources*
Authors: Kieffer J. C. , Chaker M. , Matte J. P. , Pépin H. , Côté C. Y. , Beaudoin Y. , Johnston T. W. , Chien C. Y. , Coe S. , Mourou G. , Peyrusse O.
Published: July 2002

Time-resolved spectroscopy (with a 2 psec temporal resolution) of plasmas produced by the interaction between solid targets and a high contrast subpicosecond table top terawatt (T3) laser at 1016 W/cm2, is used to study the basic processes which control the x-ray pulse duration. Short x-ray pulses have been obtained by spectral selection or by plasma gradient scalelength control. Time-dependent calculations of the atomic physics [Phys. Fluids B 4, 2007, 1992] coupled to a Fokker–Planck code [Phys. Rev. Lett. 53, 1461, 1984] indicate that it is essential to take into account the non-Maxwellian character of the electron distribution for a quantitative analysis of the experimental results.
Reconnection of magnetic field lines in a turbulent flow
Authors: Kleva Robert G.
Published: July 2002

The effect of a turbulent flow on the rate of reconnection of magnetic field lines by a tearing instability is calculated numerically. The reconnection rate is shown to be reduced by the turbulent flow. The turbulent flow transfers energy from the growing tearing instability into shorter wavelength electromagnetic modes that are stable, thereby reducing the rate of reconnection of magnetic field lines by the longer wavelength tearing instability. The numerical results presented contradict the prediction of a turbulence theory of Diamond et al. [Phys. Fluids 27, 1449 (1984)] that a turbulent flow causes an anomalous diffusivity (resistivity) which increases the growth rate of tearing modes.
Parallel viscosity-driven neoclassical fluxes in the banana regime in nonsymmetric toroidal plasmas
Authors: Shaing K. C. , Hirshman S. P. , Tolliver J. S.
Published: July 2002

Analytic expressions for the parallel viscosity-driven neoclassical fluxes in the banana regime in arbitrary nonsymmetric toroidal plasmas are derived without considering boundary layer effects. They can be evaluated numerically if the Fourier decomposition of the strength of the magnetic field ‖B‖ is known. Since no averaging over the high-frequency component of the Fourier decomposition of ‖B‖ has been employed, these expressions can reproduce all the known results in symmetric systems and predict the possibility of reversing the direction of the bootstrap current and Ware pinch flux in a stellarator.
Efficient proton ring trapping in an ion ring experiment
Authors: Greenly J. B. , Hammer D. A. , Pedrow P. D. , Sudan R. N.
Published: July 2002

In an 8 kG magnetic mirror, 400 keV proton rings, containing up to 3×1015 protons and 0.2 kJ energy, have been trapped. The trapping is accomplished by injecting a rotating proton ring through a 1 μsec rise-time, 1.4:1 pulsed mirror coil. Negligible loss occurs through the 1.45:1 static downstream mirror after the first bounce, when ≳90% of the injected beam is reflected. The pulsed upstream mirror traps ≳70% of the returning protons, after which there is very little particle loss for the first four ring bounces in the mirror well. Ring decay then increases as a result of slowing down and charge exchange in the >50 mTorr H2 background, and the ring is observable for >10 bounces, or ≳5 μsec.
Numerical simulation of a laminar end-wall vortex and boundary layer
Authors: Wilson Tim , Rotunno Richard
Published: July 2002

The fluid dynamics of a laminar axisymmetric end-wall vortex is investigated through high-resolution numerical integrations of the Navier–Stokes equations. The predicted velocity field is shown to be in good to excellent agreement with a concurrent laboratory investigation. The dynamics of the boundary layer and core regions are found to be mostly inviscid. Thin viscous sublayers in the boundary layer and core vanish in the vicinity of the inviscid corner region. The effectively inviscid nature of most of the flow is demonstrated by examining the balance of terms in the momentum equations and by the applicability of the inviscid swirl equation rη=r2(dH/dΨ)−(d/dΨ)(Γ2/2) to most of the flow.
Three-dimensional numerical study of convection in a cylindrical thermal diffusion cell: Inclination effect
Authors: Henry D. , Roux B.
Published: July 2002

The effect of the buoyancy-driven convection on the separation of the two constituents of a binary mixture in a long cylindrical cell is considered. This cell is designed to measure the thermal diffusion (Soret) coefficient of that mixture in a spatial (microgravity) environment. Such a cell, heated from the ends, is subjected to a nearly constant axial temperature gradient that generally presents some inclination with respect to the gravity vector, giving rise to low but three-dimensional motions. In space applications this inclination (with respect to residual gravity) is generally not known a priori. A three-dimensional simulation based on a false transient scheme with finite difference techniques is carried out in order to study the influence of the cell inclination on low convective motions. Two small values of a Grashof number, relevant for space applications (Gr=1 and Gr=3), and three values of the Soret parameter (S=−0.5, S=0, and S=0.5) have been considered. Characteristics of the flow and of its influence on the separation of constituents are given for several inclinations. Particularly interesting results are discussed for the vertical situations. Attention is focused on a molten (AgI–KI) mixture with a Prandtl number of 0.6 and a Schmidt number of 60, contained in a cylinder with an aspect ratio of 6.
A second-order closure prediction of premixed turbulent combustion in jets
Authors: Davé N. , Kollmann W.
Published: July 2002

In this paper, a numerical prediction is reported involving second-order closure of a turbulent flow of a vertically burning, lean mixture of premixed combustible gases discharging from a pipe and developing into a turbulent combusting roundjet. Classical closures are used where available. Expressions for the chemical reaction rate term and other unclosed terms related to variable density flow in the Favre-averaged turbulent transport equations are based on the Bray–Moss–Libby aerothermochemistry for premixed turbulent combustion, extended to variable enthalpy systems. Mixing of hot burned and cool ambient gases and the attendant buoyancy effects are found to be significant physical phenomena in the behavior of such lean premixed combusting jets. Results of the simulation are compared with experimental data of Yoshida [Proceedings of the Eighteenth International Symposium on Combustion (The Combustion Institute, Pittsburgh, 1981), p. 931] with which reasonable numerical agreement is obtained. Reasons for discrepancies and possible lines for future research are discussed.
Possible parametric instabilities of beat waves in a transversely magnetized plasma
Authors: Salimullah M.
Published: July 2002

The effect of an external magnetic field on the various possible parametric instabilities of the longitudinal beat wave at the difference frequency of two incident laser beams in a hot plasma has been theoretically investigated. The kinetic equation is employed to obtain the nonlinear response of the magnetized electrons caused by the nonlinear coupling of the beat wave with the low-frequency electrostatic plasma modes. It is noted that the growth rates of the three-wave and the four-wave parametric instabilities can be influenced by the external transverse magnetic field.
Thermophoresis of a spherical particle in a rarefied gas of a transition regime
Authors: Yamamoto Kyoji , Ishihara Yuji
Published: July 2002

A theoretical study is made of thermophoresis of a solid sphere in a rarefied gas in which a uniform temperature gradient and a uniform velocity at infinity exist. The analysis is carried out on the basis of the linearized Bhatnager–Gross–Krook (BGK) equation, from which simultaneous integral equations for the density, flow velocity, and temperature are derived. These equations are solved numerically over a wide range of Knudsen numbers covering the area from the slip flow to the nearly free molecular flow. A formula for the variation of the thermophoretic force acting on the sphere versus the Knudsen number is obtained for any value of thermal conductivity of the sphere when there is no imposed flow at infinity. The thermophoretic velocity of a suspended sphere in a gas is also calculated. The flow patterns as well as the distributions of temperature are shown.
The modulation of short waves riding on solitary waves
Authors: Shen I-Fan , Easson W. J. , Greated C. A. , Evans W. A. B.
Published: July 2002

The modulation of linear short waves riding on a long finite-amplitude solitary wave has been analyzed numerically. It is found that the maximum modulated wave number, frequency, and amplitude of short waves always occur at the crest of solitary waves. This paper shows that the modulated wave number on the crest of solitary waves increases significantly as the amplitude of the solitary waves increases, and that the modulated short wave frequency and amplitude on the crest increase almost linearly.
Longitudinal vortex structures in a cylinder wake
Authors: Wu J. , Sheridan J. , Welsh M. C. , Hourigan K. , Thompson M.
Published: July 2002

This paper presents the velocity field of the longitudinal vortices found in the wake of a circular cylinder, as measured using digital particle image velocimetry (PIV). Vorticity and circulation of the longitudinal vortices are presented, based on instantaneous velocity distributions in a transverse plane behind the cylinder.
Combined heat and momentum transport in a dilute gas
Authors: Tij Mohamed , Santos Andrés
Published: July 2002

The infinite hierarchy of moment equations derived from the Boltzmann equation for Maxwell molecules is analyzed in the case of steady planar Couette flow. It is proved that a solution exists that is consistent with the following hydrodynamic profiles: p=nkBT=const, T∂ux/∂y=const, (T∂/∂y)2T=const. In general, the velocity moments of order k are polynomials of degree k−2 in a scaled space variable s∝∫T−1dy. The momentum and energy transport are described by a nonlinear shear viscosity η(a)=η(0)Fη(a) and a nonlinear thermal conductivity κ(a)=κ(0)Fκ(a), respectively, where a≡∂ux/∂s is the (constant) reduced shear rate. By performing a perturbation expansion in powers of a, it is found that Fη(a)=1−1.472a2+𝒪(a4) and Fκ(a)=1−3.226a2+𝒪(a4). These numerical values are compared with those obtained from the BGK and the Liu kinetic models.
Effect of the vessel size on the hydrodynamic diffusion of sedimenting spheres
Authors: Nicolai Hélène , Guazzelli Elisabeth
Published: July 2002

Experiments are described which demonstrate that particle velocity fluctuations and hydrodynamic self-diffusivities of sedimenting non-Brownian spheres do not vary as the inner width of the vessel varies by a factor of 4.
Bifurcating jets generated with stepped and sawtooth nozzles
Authors: Longmire E. K. , Duong L. H.
Published: July 2002

A simple round jet is perturbed by attaching either a stepped or a sawtooth trailing edge that acts as a form of passive control. Flow visualization, laser Doppler anemometer, and hot-wire measurements are used to document the flow behavior in both water and air for Reynolds numbers of 7600 and 22 000, respectively. When the jet is forced, the flow bifurcates. The bifurcation requires a low forcing frequency that encourages the formation of tilted primary vortex rings with significant vorticity and axial spacing. In the step nozzle flow, the rings result from closed vortex loops. In the sawtooth nozzle flow, they develop from sections of a helix. A powerful secondary jet initiates in straining regions between primary ring cores, where closed-loop or helical structures with opposite tilt are present. The radial momentum in this jet is large enough to divert the path of the primary jet in the opposite direction. The bifurcating effect was found to be strongest when the forcing frequency was less than or equal to one-third of the natural roll-up frequency.
Horizontal jets in a rotating stratified fluid
Authors: Voropayev Sergey I. , Zhang Xiuzhang , Boyer Don L. , Fernando Harindra J. S. , Chi Wu Pok
Published: July 2002

A horizontal jet emerging continuously from a small round nozzle (concentrated source of momentum) in a rotaing stratified fluid is investigated using laboratory experiments. The jet either (i) deflects from the direction of injection, forming an anticyclonic spiral monopole (monopole regime), or (ii) propagates along the injection direction, forming a dipolar structure (dipole regime). Which of these characteristic flows occurs depends on the system parameters, the Reynolds number Re, and the buoyancy frequency to Coriolis parameter ratio N/f; a flow regime diagram is developed for the parameter ranges 40≲ Re≲200 and 0≲N/f≲35, respectively. A theoretical analysis is advanced to explain the conditions under which the monopole and dipole regimes occur, including the transition curve between the two regimes. The theory is supported by laboratory experiments. Some geophysical examples of the considered flows are discussed.
The inverse diffusion time scale of velocity gradients in homogeneous isotropic turbulence
Authors: Martin Jesus , Ooi Andrew , Dopazo Cesar , Chong M. S. , Soria Julio
Published: July 2002

The diffusion term in the velocity gradient tensor Aij evolution equation in homogeneous isotropic turbulence at moderate Reynolds number has been investigated using full direct numerical simulation (DNS) of the Navier–Stokes equations. This study also considered the diffusion terms associated with the strain rate tensor Sij and the vorticity vector ωi. The statistics of the “diffusion frequency” ω0 defined as ω0≡−ν∇2Aij/Aij, which can be thought of as an inverse of a characteristic diffusion time scale t0, has been studied both for diagonal and off-diagonal elements of this tensor, for Sij and for ωi. The probability density functions (PDF’s) of the diffusion frequency ω0 for all the variables considered in this study have a distinct peak indicating a most probable positive value. It is found that the value of the frequency increases with larger absolute values of the velocity gradient. The conditional averages of ν∇2Aij, ν∇2Sij and ν∇2ωi are found to be closely related by a cubic function of Aij, Sij and ωi respectively, which in the neighborhood of one standard deviation from the origin is very well approximated by the same linear relationship for all the variables. This latter result suggests that a linear approximation model [Dopazo et al., Ninth Symposium on Turbulent Shear Flows; J. Martin, Ph.D. dissertation] for the diffusion terms of velocity gradients may be appropriate in certain cases.
Angular dependence and growth of vorticity in the three-dimensional Euler equations
Authors: Gibbon J. D. , Heritage M.
Published: July 2002

An investigation of lower bounds on the quantities Wn(t)=∫Ω|ω|2n dV for n⩾1 for the incompressible three-dimensional (3D) Euler equations has led us to consider a set of spatially averaged weighted “eigenvalues,” λS(n)(t) and λP(n)(t), of the strain matrix S and the Hessian matrix of the pressure P={p,ij}, respectively. It is shown that these obey the simple inequality, λ̇S(n)+f(θn)(λS(n))2+λP(n)⩾0, where f(θn)=1−tan2 θn. The θn are spatially averaged weighted angles between the vorticity vector ω and the vortex stretching vector σ=ω⋅∇u. The weighting in the averaging process highlights regions of large vorticity. This is the angle considered by Tsinober, Kit, and Dracos in their analysis of data from turbulent grid flow experiments in which they noted a tendency toward alignment between ω and σ. The Burgers vortex turns out to be a sharp solution of this inequality with a corresponding angle θn=0, giving rise to exponential growth in Wn. Some special solutions for cases where θn moves between θn=0 and θn=π/2 are displayed. The work of Ohkitani and Kishiba on the alignment in 3-D Euler flows between ω and the third eigenvector of P at maximum enstrophy is also particularly relevant and is applied to the modified pressure matrix Q={p,ij−3δijp,ii} in the limit n→∞. The finite time blow-up problem is discussed in this context. In an Appendix it is shown that an identical inequality holds for the barotropic compressible Euler equations where ζ=ω/ρ and Wn(t)=∫Ωρ|ζ|2n dV replace ω and Wn, respectively.
On the motion of slender vortex filaments
Authors: Zhou Hong
Published: July 2002

Several approaches for slender vortex motion (the local induction equation, the Klein–Majda equation, and the Klein–Knio equation) are compared on a specific example of sideband instability of Kelvin waves on a vortex. Numerical experiments on this model problem indicate that all these equations yield qualitatively similar behavior, and this behavior is different from the behavior of a nonslender vortex with variable cross-section. It is found that the boundaries between stable, recurrent, and chaotic regimes in the parameter space of the model problem depend on the equation used. The boundaries of these domains in the parameter space for the Klein–Majda equation and for the Klein–Knio equation are closely related to the core size. When the core size is large enough, the Klein–Majda equation always exhibits stable solutions for our model problem. Various conclusions are drawn; in particular, the behavior of turbulent vortices cannot be captured by these approximations, and probably cannot be captured by any slender vortex model with constant vortex cross-section. Speculations about the differences between classical and superfluid hydrodynamics are also offered.
A Galilean invariant explicit algebraic Reynolds stress model for turbulent curved flows
Authors: Girimaji Sharath S.
Published: July 2002

A Galilean invariant weak-equilibrium turbulence hypothesis that is sensitive to streamline curvature is proposed. The hypothesis leads to a fully explicit algebraic expression for Reynolds stress in terms of the mean velocity field and kinetic energy and dissipation of turbulence. The model is tested in curved homogeneous shear flow which is a homogeneous idealization of the circular streamline flow. The agreement is excellent with Reynolds stress closure model and adequate with available experimental data.
Stabilization of longitudinal vortex instabilities by means of transverse flow oscillations
Authors: Hu H.-C. , Kelly R. E.
Published: July 2002

Longitudinal vortices with axes in the direction of a mean shear flow can arise due to body force instabilities associated with heating or centrifugal effects. In this paper we are concerned with possible stabilization or destabilization of such instabilities by means of a controlled flow oscillation in the spanwise direction. For the heated case, stabilization occurs up to the values of Rayleigh and Reynolds numbers at which streamwise two-dimensional disturbances become critical. For the centrifugal case, stabilization occurs only for sufficiently large values of the Reynolds number associated with the spanwise oscillation; for smaller values, destabilization occurs.
Absolute/convective transition of wake-dominated supersonic shear layers
Authors: Zhuang Mei
Published: July 2002

The absolute and convective instability characteristics of supersonic wake dominated shear layers, described by a hyperbolic-tangent profile plus a wake component represented by a Gaussian distribution, are investigated. The effects of the Mach number, the freestream temperature ratio and the wake deficit on the boundary of the absolute/convective transition and the branch point parameters (such as frequency, wave number, and the spatial growth rate) are studied using linear stability theory. For supersonic mixing layers, it is found that at a given wake deficit the amount of backflow necessary to cause absolute instability decreases as the convective Mach number increases and that all the branch point parameters vary slowly as functions of the convective Mach number as opposed to subsonic mixing layers. As the wake deficit decreases, the curve separating the absolute and the convective regions moves down to the values of more negative freestream velocity ratio for both subsonic and supersonic mixing layers and the branch point spatial growth rate decreases for a given convective Mach number. The effect of decreasing the wake deficit on the absolute/convective transition boundary is similar to that of increasing the freestream temperature ratio.
Derivation of a PDF model for turbulent flows based on principles from statistical physics
Authors: Minier Jean-Pierre , Pozorski Jacek
Published: July 2002

Classical ideas from statistical physics are used to derive a PDF model for turbulent flows. The model is built by adopting a Lagrangian point of view and by considering separately the statistical effects of the viscous and of the pressure gradient forces which act on a fluid particle. Closures are developed alternatively in terms of the pdf itself and of the trajectories of the stochastic process. The viscous force is shown to manifest itself as an anti-diffusion in phase space while modeling of the fluctuating part of the pressure gradient force is based on linear laws for non-equilibrium thermodynamics along Onsager’s regression-to-equilibrium hypothesis. The final expression is identical to a Langevin equation proposed by Pope which is thus seen to be obtained from underlying principles.
Demonstration of a rarefied gas flow induced near the edge of a uniformly heated plate
Authors: Sone Yoshio , Yoshimoto Minoru
Published: July 2002

A new type of a rarefied gas flow, which was found numerically by the research group of the first author, is demonstrated by a simple experiment. It is a steady flow induced by the edge effect of a uniformly heated plate. The experiment is carried out in a standard bell jar, and small windmills are used to detect flows. The flow found by the numerical computation is observed. The cause of the flow is discussed and attributed to the edge effect of the heated plate.
Deformation of a liquid drop adhering to a plane wall: Significance of the drop viscosity and the effect of an insoluble surfactant
Authors: Yon Steve , Pozrikidis C.
Published: July 2002

The transient deformation of a viscous drop attached to a plane wall and subjected to an overpassing simple shear flow is studied in the limit of a vanishing Reynolds number. The buoyancy force is negligible, the contact line has and retains a prescribed circular shape, and the interface is either devoid of surfactants, in which case it exhibits constant surface tension, or it is occupied by an insoluble surfactant, in which case the surface tension is related to the surfactant concentration by means of a linear constitutive equation. In the numerical procedure, the interfacial velocity is computed by solving the equations of Stokes flow using a boundary-element method in which the interface is discretized into six-node curved triangles. The convection–diffusion equation for the concentration of the surfactant is integrated in time over the evolving interface using a semi-implicit finite-volume method. In the numerical investigations, the deformation of a drop is simulated from the initial state, where the interface has the prescribed shape of a section of a sphere and a uniform surfactant distribution, to either a steady deformed shape, or up to the point where evidence for continued deformation is obtained. The results show that the presence of surfactant promotes the deformation of drops whose viscosity is low compared to that of the ambient fluid, but has a small influence on the deformation of drops whose viscosity is comparable to, or higher than, that of the ambient fluid. At a fixed capillary number, the deformation of the drop equilibrium shape for constant or varying surface tension increases monotonically with raising the drop viscosity because of the increasing importance of the image flow due to the wall. Thus, whereas a viscous drop suspended in an infinite shear flow extends indefinitely into a slender ligament only when its viscosity is less than about four times the viscosity of the ambient fluid and the shear rate is sufficiently high, an analogous threshold for a drop attached to a wall does not seem to arise.
An experimental analysis of the instability of nonaxisymmetric liquid bridges in a gravitational field
Authors: Bezdenejnykh N. A. , Meseguer J. , Perales J. M.
Published: July 2002

The stability limits of nonaxisymmetric liquid bridges between equal in diameter, coaxial disks have been determined experimentally. Experiments have been performed by working with very small size liquid bridges. The experimental setup allows any orientation of the liquid bridge axis with respect to the local gravity vector acceleration. By appropriately orienting the liquid bridge axis, the influence on the stability limits of both the lateral and the axial component of the acceleration acting on the liquid bridge has been investigated.
Interfacial instabilities of a fluid annulus in a rotating Hele–Shaw cell
Authors: Carrillo Lluı́s , Soriano Jordi , Ortı́n Jordi
Published: July 2002

We have studied the interfacial instabilities experienced by a liquid annulus as it moves radially in a circular Hele–Shaw cell rotating with angular velocity Ω. The instability of the leading interface (oil displacing air) is driven by the density difference in the presence of centrifugal forcing, while the instability of the trailing interface (air displacing oil) is driven by the large viscosity contrast. A linear stability analysis shows that the stability of the two interfaces is coupled through the pressure field already at a linear level. We have performed experiments in a dry cell and in a cell coated with a thin fluid layer on each plate, and found that the stability depends substantially on the wetting conditions at the leading interface. Our experimental results of the number of fingers resulting from the instability compare well with the predictions obtained through a numerical integration of the coupled equations derived from a linear stability analysis. Deep in the nonlinear regime we observe the emission of liquid droplets through the formation of thin filaments at the tip of outgrowing fingers.
Temporal evolution of stimulated Brillouin backscatter
Authors: Hinkel D. E. , Williams E. A. , Berger R. L.
Published: July 2002

A qualitative understanding of the time dependence of stimulated Brillouin scattering (SBS) provides estimates of the amount of temporal growth that occurs in current inertial confinement fusion and short laser pulse interaction experiments when the growth is limited by the length of the experiment or by motion of the ‘‘hot spots’’ of the laser intensity pattern induced by beam smoothing. In the weak coupling limit, the instantaneous growth rate depends upon the plasma initial conditions early in time, is proportional to t−1/2 later in time, and asymptotically approaches the absolute growth rate (in the absence of damping). When the instability is strongly coupled, the growth rate depends upon the plasma initial conditions early in time but is proportional to t−1/3 later in time. When the growth rate drops to a value comparable to that of the ion acoustic frequency, the instability becomes effectively weakly coupled. The effects of damping are also discussed.
Beam scattering and heating at the front of an electron beam injected into a plasma
Authors: Chan L. Y. , Stenzel R. L.
Published: July 2002

A dense pulsed electron beam (tr≤20 ns, Vb=200 V, ib≤2 A, nb/ne≤10%) is injected into a uniform magnetoplasma (ne=1−4×1010 cm−3, kTe≤0.5 eV, B0=90 G) to study wave–particle interactions that occur at the front of the beam on short-time scales during which the ions are regarded as fixed and immobile. Above a threshold beam density (nb/ne≳5%), the beam front is observed using optical diagnostics to rapidly erode due to beam scattering and energetic tail production, and broaden into a warm front that propagates slower than its injected speed. Using radio-frequency (RF) antennas, the beam is observed to bunch due to the streaming beam–plasma instability and create a ballistic beam mode (fB=nfpe), which collapses into broadband electrostatic turbulence during the onset of beam scattering. A low-frequency electrostatic wave mode (fpi<fLF<fpe) is also detected that is coupled to the scattering process. These measurements show that rich beam–plasma phenomena occur in this electron time-scale regime, which are not adequately addressed by current plasma theory.
Exact ion acoustic solitary waves in an impurity-containing magnetized plasma
Authors: Yinhua Chen , Yu M. Y.
Published: July 2002

Fully nonlinear ion acoustic solitary waves propagating obliquely to the external magnetic field in an impurity-containing magnetized plasma are investigated.
Kinetic theory of magnetic island stability in tokamaks
Authors: Zabiégo M. , Garbet X.
Published: July 2002

The nonlinear behavior of low- and large-wave number tearing modes is studied. The emphasis is laid on diamagnetic effects. A kinetic equation, including transport processes associated with a background of microturbulence, is used to describe the electron component. Such transport processes are shown to play a significant rôle in the adjustment of density and temperature profile, and also in the calculation of the island rotation frequency. The fluctuating electric potential is calculated self-consistently, using the differential response of electrons and ions. Four regimes are considered, related to island width (smaller or larger than an ion Larmor radius) and transport regime (electron–ion collisions or electroviscosity dominated). It is shown that diamagnetism does not influence the island stability for small island width in the viscous regime, as long as the constant Ψ constraint is maintained. It turns out that the release of this constraint may strongly modify the previously calculated stability thresholds. Finally, it is found that diamagnetism is destabilizing (stabilizing) for island width smaller (larger) than an ion Larmor radius, in both resistive and viscous regimes. A typical island evolution scenario is studied which shows that even large-scale tearing modes with positive Δ′ could saturate to island width of order of a few ion Larmor radii. Illustrative Δ′ threshold and island saturation size are calculated.
Resonance parallel viscosity in the banana regime in poloidally rotating tokamak plasmas
Authors: Shaing K. C. , Hsu C. T. , Dominguez N.
Published: July 2002

Parallel viscosity in the banana regime in a poloidally (E×B) rotating tokamak plasma is calculated to include the effects of orbit squeezing and to allow the poloidal E×B Mach number Mp to have a value of order unity. Here, E is the electric field and B is the magnetic field. The effects of orbit squeezing not only modify the size of the particle orbit, but also change the fraction of poloidally trapped particles. Resonance between the particle parallel (to B) speed u and the poloidal component of the E×B velocity can only occur for those particles with energy (v/vt)2≳M2p (with v the particle speed and vt the thermal speed). Thus, the resonance parallel plasma viscosity in the banana regime decreases exponentially with M2p when M2p≥1, and has a local maximum of M2p∼1.
High-frequency, amplitude modulation of a submillimeter wave, medium power gyrotron
Authors: Idehara T. , Shimizu Y. , Makino S. , Ichikawa K. , Tatsukawa T. , Ogawa I. , Brand G. F.
Published: July 2002

Experimental results of the amplitude modulation of the output of a submillimeter wave gyrotron are presented. The 100% modulation of the output at frequencies up to several hundred kilohertz has been achieved with anode modulation levels of only a few percent. A good account of the experimental results is given by including a small modulation of the anode voltage in an energy transfer formula and then calculating the power output.