bluuebunny/crossref_metadata_2025 huggingface dataset:
Excitation and damping of compressional hydromagnetic waves on a magnetized, high-pressure plasma column
Authors: Meuth H. , Ribe F. L.
Published: July 2002

Azimuthally symmetric (m=0) radio-frequency (rf) waves for zero and for finite axial wavenumber k are investigated in a low-compression linear theta pinch. The (k=0) modes occur spontaneously following the implosion phase of the discharge. For the k≠0 modes, a novel 100 MW, 1 MHz current drive is used to excite the plasma column in the vicinity of the lowest fast magnetoacoustic mode at various filling pressures. Phases, amplitudes, and radial mode structure are studied for both the k=0 modes and the externally driven (k≠0) modes. In the first case, the damping is determined from the e-folding time of the decaying oscillations. In the latter case, the phases and amplitudes indicate a broad resonance structure, from which we extract the damping constant. The energy deposition of the externally driven rf wave leads to a radial expansion of the plasma column, as observed by axial interferometry and by excluded flux measurements. These experimental results are compared with the predictions of two MHD-like ion-kinetic models. The characteristic and resonant frequencies, as well as the oscillatory radial mode structure, can be understood within the ideal MHD description. It is found that the viscous kinetic model overestimates the observed k=0 damping by at least an order of magnitude, while both this and the ion Landau-damping model (with and without ion-cyclotron effects) underestimate the (k≠0) damping by at least an order of magnitude. The experimentally observed damping and wave-energy deposition are consistent with the magnitude of the rf oscillations. The efficiency of the rf energy deposition is at least 27%.
Wave entropy: A derivation by Jaynes’ principle
Authors: Kaufman Allan N.
Published: July 2002

The Jaynes maximum-entropy principle [E. T. Jaynes, Papers on Probability, Statistics, and Statistical Physics (Reidel, Dordrecht, The Netherlands, 1983)] is used to derive the standard expression for the entropy of a set of weakly interacting waves.
Overtaking collision between two solitary waves
Authors: Zou Qisu , Su Chau-Hsing
Published: July 2002

Under the assumptions of long wavelength, small amplitude, and propagation in one direction, it is well known that the water wave equations in the lowest order of approximation with slow variation in time and space can be reduced to the Korteweg–de Vries (KdV) equation. Linear inhomogeneous equations with their coefficients, as well as the inhomogeneous terms depending on the solutions of the lower-order equations, have been obtained in the next order and the third order of approximation. An accurate numerical method is used to integrate these equations for an overtaking interaction between two solitary waves. It is found, up to the second order of approximation, that the collision is elastic, i.e., the solitary waves regain their original form without giving rise to any secondary wave. The results of second-order solution are in good agreement with the analytic solution of Sachs [SIAM J. Math. Anal. 15, 468 (1984)]. However, the numerical computation on the third-order equation shows a secondary wave train trailing behind the smaller wave after the collision.
Vlasov susceptibility of relativistic magnetized plasma and application to free-electron lasers
Authors: Grebogi Celso , Uhm Han S.
Published: July 2002

The Vlasov susceptibility for two interacting electromagnetic waves is derived by using an extended version of the ‘‘κ–χ theorem.’’ The plasma is relativistic and magnetized. It is allowed for arbitrary k⊥ρ, ω/Ω, k⊥/k∥, and v/c. Nonuniformities in the background quasistatic magnetic field are also included. As an application, a general expression for the free-electron laser susceptibility is derived.
Pouring flows
Authors: Vanden-Broeck Jean-Marc , Keller Joseph B.
Published: July 2002

Free surface flows of a liquid poured from a container are calculated numerically for various configurations of the lip. The flow is assumed to be steady, two dimensional, and irrotational; the liquid is treated as inviscid and incompressible; and gravity is taken into account. It is shown that there are jetlike flows with two free surfaces, and other flows with one free surface which follow along the underside of the lip or spout. The latter flows occur in the well-known ‘‘teapot effect,’’ which was treated previously without including gravity. Some of the results are applicable also to flows over weirs and spillways.
Evolution of current sheets near a hyperbolic magnetic neutral point
Authors: Shivamoggi Bhimsen K.
Published: July 2002

An exact solution for the magnetohydrodynamic equations for a time-dependent, two-dimensional flow of an incompressible plasma of finite conductivity in a hyperbolic magnetic field is given. This solution admits a nonzero initial current density, and predicts a sequence of events associated with the evolution of a current sheet in a plasma subjected to an initial hyperbolic magnetic field configuration. This is confirmed by laboratory experiments. Next, the calculation is extended to include the density variations in the plasma. The corresponding solution predicts that the current sheet at the neutral point evolves more rapidly when the plasma density builds up locally around the magnetic neutral point.
Resistive ballooning modes driven by anomalous transport effects
Authors: Sundaram A. K.
Published: July 2002

Using Braginskii’s two fluid equations, the stability of resistive ballooning modes is examined in the presence of parallel thermal conduction, anomalous electron viscosity, and radial thermal conductivity. A generalized set of coupled second-order differential equations in φ and ψ is derived in ballooning space and is solved to obtain analytical solutions in two interesting frequency regimes, SCs/ qR ≪ ‖ω‖ ≪ Cs/  qR and ‖ω‖ ≫ Cs/qR. It is shown that the anomalous thermal transport term excites the new m=1 resistive ballooning mode (‖ω‖ ≫ Cs/qR) with a large growth rate. The excitation of the m=2 type (or Δ′ driven) mode, on the other hand, is found to be strongly influenced by both anomalous electron viscosity and radial thermal conduction. Finally, the additional effect of parallel electron thermal conduction is shown to give new resistive ballooning modes with significantly large growth rates varying as fractional powers of anomalous electron viscosity and classical thermal conductivity.
Modeling the viscous wall region
Authors: Azab Karam Anwar , McLaughlin John B.
Published: July 2002

A model is used to study the viscous wall region of turbulent shear flows over rigid flat surfaces. Periodic boundary conditions are imposed in the horizontal directions with periodicity lengths that are several times larger than the experimental streak spacing. In order to sustain the turbulence in the viscous wall region, the averaged x component of the velocity is set equal to a fixed profile outside the viscous wall region. Pseudospectral methods are used to solve the governing equations with the Marcus time splitting scheme. It is shown that a model of the viscous wall region can reproduce much of the behavior seen in direct simulations of turbulence that place greater demands on computer resources. The model is used to investigate the flow of energy in the viscous wall region and the relationship between low-speed streaks and vortices in the viscous wall region.
Role of impurity dynamics in resistivity-gradient-driven turbulence and tokamak edge plasma phenomena
Authors: Hahm T. S. , Diamond P. H. , Terry P. W. , Garcia L. , Carreras B. A.
Published: July 2002

The role of impurity dynamics in resistivity-gradient-driven turbulence is investigated in the context of modeling tokamak edge plasma phenomena. The effects of impurity concentration fluctuations and gradients on the linear behavior of rippling instabilities and on the nonlinear evolution and saturation of resistivity-gradient-driven turbulence are studied both analytically and computationally. At saturation, fluctuation levels and particle and thermal diffusivities are calculated. In particular, the mean-square turbulent radial velocity is given by 〈v̂2r〉 =(E0Ls/Bz)2 (L−1η+L−1z)2. Thus edged peaked impurity concentrations tend to enhance the turbulence, while axially peaked concentrations tend to quench it. The theoretical predictions are in semiquantitative agreement with experimental results from the TEXT [Bull. Am. Phys. Soc. 30, 1443 (1985)], Caltech [Phys. Fluids 29, 309 (1986)], and Tosca [in the Proceedings of the 12th European Conference on Controlled Fusion and Plasma Physics (European Physical Society, Budapest, 1985), Vol. I, p. 311] tokamaks. Finally, a theory of the density clamp observed during CO-NBI on the ISX-B tokamak [in Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1981), Vol. I, p. 377] is proposed.
Large-scale structure generation by anisotropic small-scale flows
Authors: Yakhot Victor , Pelz Richard
Published: July 2002

Direct numerical simulation techniques are used to study the effect of spontaneous symmetry breaking leading to the phenomenon of large-scale secondary flow generation by anisotropic small-scale flow. It is shown that anisotropy is a major factor that determines the ability of the small-scale flow to generate the inverse energy cascade, that the large-scale secondary flow is strongly anisotropic—almost unidirectional, and that the helical property of the primary flow is irrelevent. The pairing instability and long-wave modulation of the subharmonic are important in the process of generation of the large-scale structure.
Onset of convection in variable viscosity fluids: Assessment of approximate viscosity–temperature relations
Authors: Chen Yen-Ming , Pearlstein Arne J.
Published: July 2002

The effect of the viscosity–temperature relation, μ(T), on the onset of convection in a horizontal fluid layer is discussed. Linear analysis shows that, for aqueous glycerol solutions, the critical Rayleigh numbers (Racrit) obtained using the Arrhenius approximation, μA(T), are in excellent agreement with those employing the actual μ(T) data. The results for the exponential approximation μe(T) differ to an extent that depends on the glycerol mass fraction and the temperature difference (ΔT) between the plates. The error associated with use of μe(T), while small, is of the same order as, or larger than, the uncertainty in careful experiments. For the broad class of liquids for which μA(T) is an excellent approximation to μ, we have assessed the errors in Racrit associated with the widely used μe(T). As ΔT and the viscosity contrast increase, the values of Racrit deviate increasingly from those predicted using μA(T). Also, the relative error in Racrit is much smaller than the maximum relative error in the coefficients [involving μ(T) and its derivatives with respect to T] of the linear disturbance equations.
Renormalized perturbation theory: Vlasov–Poisson system, weak turbulence limit, and gyrokinetics
Authors: Zhang Y. Z. , Mahajan S. M.
Published: July 2002

The self-consistency of the renormalized perturbation theory of Zhang and Mahajan [Phys. Rev. 132, 1759 (1985)] is demonstrated by applying it to the Vlasov–Poisson system and showing that the theory has the correct weak turbulence limit. Energy conservation is proved to arbitrary high order for the electrostatic drift waves. The theory is applied to derive renormalized equations for a low-beta gyrokinetic system. Comparison of this theory with other current theories is presented.
Oscillatory buoyant thermocapillary flow
Authors: Mundrane M. , Zebib A.
Published: July 2002

A computational study of the character and stability of two-dimensional buoyant thermocapillary flows, valid to leading order in capillary number (Ca), is conducted in the Grashof number (Gr), Reynolds number (Re), aspect ratio, and Prandtl number (Pr) parameter space. Calculations of thermocapillary convection for low Pr fluids have generally produced steady results. Calculations of pure buoyant convection (Re=0) exhibit a Hopf bifurcation at Grcr (no thermocapillarity) that is well understood. Thus, the combined thermocapillary buoyant problem is studied to investigate the onset of oscillatory convection in the limit Gr→0. The unsteady natural convection pattern at fixed Gr≳Grcr is modified only slightly for low values of Re. When thermocapillarity acts in conjunction with buoyancy (Re≳0) it is stabilizing, in that the transition to unsteady flow occurs at Gr≳Grcr, as defined for the strictly buoyant problem. When thermocapillarity acts in opposition to buoyancy (Re<0), it is destabilizing for relatively small values of ‖Re‖, but thermocapillarity ultimately dominates the convective pattern for larger ‖Re‖, and the resulting flow is steady for the range of parameter values considered. Stability boundaries for the onset of oscillatory convection in the Gr–Re plane are given for representative values of the cavity aspect ratio and Pr.
Vortical motion contributions to stress transport in turbulent boundary layers
Authors: Klewicki J. C. , Murray J. A. , Falco R. E.
Published: July 2002

Four-wire hot-wire probe measurements are used to examine the relationships between the motions bearing spanwise vorticity, ωz, and the mechanisms responsible for turbulent stress transport. The measurements were carried out in thick zero pressure gradient turbulent boundary layers over the Reynolds number range, 1010<Rθ<4850. Because of the scale of the flow, the spatial resolution of the probe was, in general, very good. The capabilities of the probe allowed all of the terms in the balance equation for 〈u2〉, except the pressure strain correlation, to be directly measured. Regarding wall region vorticity dynamics, velocity–vorticity correlation measurements are used to investigate ωz motion contributions to the gradients of the turbulent stresses. In particular, the measured positive correlation between v and ωz for y+<15 is shown to be consistent with the large ∂〈−uv〉/∂y gradient in this region, and physically, with the outward motion of sublayer streaks. Relationships between the motions bearing ωz and the sweep and ejection bursting events are examined, and the results are discussed in connection with the turbulent diffusion term in the budget for 〈u2〉. The present results indicate that in the near-wall region (but outside the sublayer) approximately two-thirds of the contributions to the turbulent diffusion term come from the correlation between the uv shear product and ωz fluctuations. The overall results are discussed relative to coherent motion interactions and the known properties of the inner region vorticity field.
Improved Fokker–Planck model for the joint scalar, scalar gradient PDF
Authors: Fox R. O.
Published: July 2002

The joint scalar, scalar gradient probability density function (PDF) of an inert nonpremixed scalar diffusing in a one-dimensional system of random-sized lamellas is investigated by numerical simulation. The form of the scalar PDF, at a given RMS value, is nearly identical to that predicted by direct numerical simulation (DNS) of scalar mixing in isotropic turbulence and the mapping closure, and the moments of both the scalar and the scalar gradient suggest that their limiting marginal PDF are Gaussian. The joint scalar, scalar gradient PDF is found to be restricted to a bounded region in the scalar–scalar gradient plane, whose form is independent of the initial mixing ratio. These results are incorporated into the Fokker–Planck (FP) model for the joint scalar, scalar gradient PDF, and the improved model shows good agreement with numerical simulation data. An extension of the FP model that includes random stretching of the scalar gradient in isotropic turbulence is formulated.
Spin-up in a rectangular tank with low angular velocity
Authors: van de Konijnenberg J. A. , Andersson H. I. , Billdal J. T. , van Heijst G. J. F.
Published: July 2002

A comparison is made between numerical and experimental results for spin-up from rest in a rectangular container. The numerical results were obtained by using a three-dimensional finite volume method on a supercomputer. The experiments were performed with water, using tracer particles floating at the free surface in order to visualize the flow field. The numerical and experimental results are in good agreement. They show the formation of a stable three-cell pattern. In contrast to similar experiments performed at higher angular velocities, the center cell of this pattern appears to be anticyclonic. Initially, the relation between vorticity ω and streamfunction ψ of this organized flow is linear, but it is seen to evolve slowly into a relation with ∂2ω/∂ψ2<0.
Statistical mechanics renormalization group calculations for inhomogeneous turbulence
Authors: Giles M. J.
Published: July 2002

The use of the turbulence renormalization group (RG) to calculate the constants occurring in the standard k-ε equations has yielded a low value for von Kármán’s constant. A derivation of the turbulence transport equations is presented which addresses this problem from a new perspective based on a statistical mechanical RG. Different fixed points are used to describe the qualitatively different degrees of freedom associated with the various moment closures required. Initiation of the iteration of a particular moment in the correct domain of attraction is controlled by its effective initial value, the definition of which is embodied in the statistical mechanical RG. The conjectured singular contributions to the turbulence production and destruction of dissipation terms are calculated and their cancellation demonstrated. The finite residue yields the coefficient of the destruction of dissipation term. Only the ‘‘mixed’’ term contributes to the coefficient of the production of dissipation term. For the logarithmic region of a turbulent boundary layer, the present approach yields 0.39 for von Kármán’s constant and 3.2 for the shear parameter.
Locally isotropic pressure Hessian in a high-symmetry flow
Authors: Boratav Oluş N. , Pelz Richard B.
Published: July 2002

Regions in a high-symmetry flow [J. Phys. Soc. Jpn. 54, 2132 (1985); Phys. Fluids 6, 2757 (1994)] where the pressure Hessian term remains diagonal for all times are identified. It is found that vorticity also vanishes in such regions. The components of the pressure Hessian tensor are equal only at the origin, toward which the vortices approach. For the case of isotropic pressure Hessian with no vorticity, and in the absence of viscosity, the resulting equations for the evolution of the eigenvalues and the Q invariant of the strain rate tensor are integrated numerically and analytically respectively. It is found that all the eigenvalues and the Q invariant diverge to infinity in finite time. In a recent simulation of a high-symmetry flow [Phys. Fluids 6, 2757 (1994)], it is found that the two (positive) eigenvalues of the strain rate tensor become equal as all the eigenvalues and the Q invariant show trends of divergence and as the vortices approach to the origin.
Solitary waves on water of finite depth with a surface or bottom shear layer
Authors: Sha Huyun , Vanden-Broeck J.-M.
Published: July 2002

Two-dimensional, gravity solitary waves on water of finite depth with a surface layer of uniform vorticity are considered. Accurate numerical solutions are computed by a boundary integral equation method. It is found that the waves have a limiting configuration with a 120° angle at the surface crest and that the shapes of the limiting profiles near the surface crest are different for positive and negative vorticity. The effects of the shear layer strength and thickness on the wave profiles are discussed. In addition, a related configuration when the shear layer is near the bottom is also considered. It is shown that some of the branches of solutions have a limiting configuration with a 120° angle at the surface crest and that others ultimately approach a solitary wave without gravity. This is to be contrasted with the case of a surface shear layer for which all the corresponding branches approach a limiting configuration with a 120° angle at the surface crest.
Scaling of streamwise vortices in wakes
Authors: Williamson C. H. K. , Wu J. , Sheridan J.
Published: July 2002

In this Letter, we demonstrate the coexistence of two distinct systems of streamwise vortices in a bluff body wake. It appears that there exist conditions to amplify streamwise vorticity in bluff body wakes, by vortex stretching, in both the separating shear layers from the sides of the body and also in the vortex street wake. The length scale governing the streamwise vortices in the shear layer has a 1/√Re dependence, whereas the scale of such structures in the wake is independent of Reynolds number, Re (over a large range of Re). The proposition that there should exist two distinct, and possibly disparate, spanwise length scales in the cylinder wake is well supported by compiled measurements, particularly those of Williams and co-workers (Mansy et al. [J. Fluid Mech. 270, 277 (1994)]), as well as those from Chyu and Rockwell (submitted to J. Fluid Mech.).
Dispersion in a quasi-two-dimensional-turbulent flow: An experimental study
Authors: Cardoso O. , Gluckmann B. , Parcollet O. , Tabeling P.
Published: July 2002

The dispersion of a passive tracer in a quasi-two-dimensional turbulent flow and the geometry of corresponding isoconcentration lines are investigated experimentally. The flow consists in an array of 900 vortices, forced in a thin layer and driven in a turbulent regime. Both the instantaneous velocity field and the concentration field are measured. A remarkable regime of anomalous diffusion—characterized by a dispersive front moving like t0.32±0.04—is observed. Examining the trajectories of individual neutral particles, we reveal the presence of ‘‘traps’’ that control most of the characteristics of this hypodiffusive regime. The fractal dimension of isoconcentration profiles and the exponents of the structure functions of both the velocity and the concentration fields are established. The corresponding values are consistent with mathematical inequalities, recently discovered, but show some disagreements with recent conjectured equalities proposed by Constantin et al. [Nonlinearity 7, 1045 (1994)].
Internal waves in xenon near the critical point
Authors: Berg Robert F. , Lyell M. J. , McFadden G. B. , Rehm Ronald G.
Published: July 2002

Just above the liquid-vapor critical point, a fluid’s large compressibility causes a stable stratification in which the density varies by as much as 10% in 1 cm. This stratification supports internal gravity waves which we observed with an oscillator immersed in a near-critical xenon sample. We found the number and frequencies of the observable modes depended on the sample cell’s orientation, with only two modes seen in the horizontal cell. The frequencies of the two modes had different temperature dependences: with decreasing temperature, the higher frequency increased monotonically from 0.7 to 2.8 Hz, but the lower frequency varied nonmonotonically, with a maximum of 1.0 Hz at 20 mK above the critical temperature. These temperature dependences continued to 20 mK below the critical temperature, where the xenon was separated into liquid and vapor phases. We calculated these two frequencies by solving the eigenvalue problem of internal waves in a box containing a stratified fluid. The fluid’s density profile was obtained from xenon’s equation of state. The calculated and measured frequencies agree to within 15%. Analytical calculations based on simple approximations of the density profile provide insight into the observed temperature dependences.
The three-dimensional development of the shearing instability of convection
Authors: Matthews P. C. , Rucklidge A. M. , Weiss N. O. , Proctor M. R. E.
Published: July 2002

Two-dimensional convection can become unstable to a mean shear flow. In three dimensions, with periodic boundary conditions in the two horizontal directions, this instability can cause the alignment of convection rolls to alternate between the x and y axes. Rolls with their axes in the y-direction become unstable to a shear flow in the x-direction that tilts and suppresses the rolls, but this flow does not affect rolls whose axes are aligned with it. New rolls, orthogonal to the original rolls, can grow, until they in turn become unstable to a shear flow. This behavior is illustrated through numerical simulations and low-order models, and the sequence of local and global bifurcations is determined.
A free surface flow with compositional-dependent interfacial properties
Authors: Giavedoni María D. , Saita Fernando A.
Published: July 2002

The effect of adsorbed surfactants on the flow that takes place in the film forming zone of the slot coater is examined. The numerical technique employed in this work, that is based on the finite element method, can suitably handle viscous free surfaces with locally varying interfacial properties. The complete information produced by the computational code allows to relate the interfacial dynamics to the mechanism involved in the mass transport process: convection and adsorption/desorption. The results presented show that the effect produced by both interfacial viscosity and interfacial elasticity are rather similar; however, the operating conditions that make them more noticeable are different.
Comments on ‘‘Existence of kinetic theory solutions to the shock structure problem’’ [Phys. Fluids 7, 911 (1964)]
Authors: Weiss Wolf
Published: July 2002

H. Holway presented a proof, based on the Boltzmann equation, in which he shows that for the moment method there exists a critical Mach number beyond which no continuous shock solution is possible. In this paper, the results of Holway’s proof are reinterpreted. From this reinterpretation, it follows that no upper bound for a critical Mach number exists.
The universal scaling exponents of anisotropy in turbulence and their measurement
Authors: L’vov Victor , Procaccia Itamar
Published: July 2002

Correlation functions of non-scalar fields in isotropic hydrodynamic turbulence are characterized by a set of universal exponents. These exponents also characterize the rate of decay of the effects of anisotropic forcing in developed turbulence. These exponents are important for the general theory of turbulence, and for modeling anisotropic flows. We propose methods for measuring these exponents by designing new laboratory experiments.
Steady spatial oscillations in a curved duct of square cross-section
Authors: Mees Philip A. J. , Nandakumar K. , Masliyah J. H.
Published: July 2002

Pressure driven flow of an incompressible Newtonian fluid in a spiral duct of square cross-section was studied both experimentally and numerically. The duct has a curvature ratio (Rc=R/a, where R is the radius of curvature and a is the duct dimension) of 15.1 at the inlet and spirals inwards for nine turns at a uniform rate. A one-component laser-Doppler anemometer was used to measure streamwise velocities. The flow development was determined for Dean number, Dn, of 100, 125, 150, 180 and 250, based on the radius at the flow inlet [Dn=Re/(Rc)1/2, where Re is the Reynolds number, vθ′a/ν]. Steady oscillations in the streamwise direction between 2-cell and 4-cell states, first predicted by Sankar et al. [Phys. Fluids 31, 1348 (1988)], were observed for Dean numbers between 139 and 240. No time dependent flow phenomena were observed. The experimental data are in very good agreement with the numerical simulations, which were based on the parabolized steady three-dimensional Navier–Stokes equations. The results are consistent with calculations by Winters [J. Fluid Mech. 180, 343 (1987)] that predict the existence of a region where no stable two-dimensional solutions exist.
Kinetic theory analysis for temperature and density fields of a slightly rarefied binary gas mixture over a solid wall
Authors: Onishi Yoshimoto
Published: July 2002

Temperature and number density fields of a binary gas mixture over a plane solid wall kept at a constant temperature have been studied analytically on the basis of the linearized version of the Boltzmann equation of BGK type subject to the boundary condition of Maxwell’s type (specular-diffusive reflection). An analysis within the Knudsen layer in the vicinity of the wall has been carried out by solving the set of equations accurately, which has enabled us to obtain the distributions of the temperature and number density explicitly over the entire flow field. Fictitious gas mixtures have been taken up, in addition to the mixtures of real gases such as helium–neon, helium–argon, neon–argon and so on, in order to see the effects of the molecular mass ratio, the concentration ratio and the accommodation coefficients of the component gases on the temperature and number density fields by suppressing the effects associated with the transport coefficients. The macroscopic jump coefficients in temperature at the wall have also been given for making a comparison with the other results available. The comparison with the theoretical results by other authors for a helium–argon mixture case shows a reasonably good agreement. The experimental data, however, seem to be too large compared with the present results, which may partly be attributable to some ambiguities in the definitions of some quantities involved in the experiment.
Wave patterns in a thin layer of sand within a rotating horizontal cylinder
Authors: Fried Eliot , Shen Amy Q. , Thoroddsen S. T.
Published: July 2002

A variety of wave patterns are found to form in a thin layer of sand inside a cylinder rotated about its horizontal axis of symmetry at constant angular velocity. In particular, we observe a spanwise instability characterized by serrated frontal shapes remarkably similar to those seen in Newtonian fluids. Within a certain parameter range, an accompanying spatial pattern forms on the rising side of the cylinder and travels along the cylinder span. The associated phase velocity is relatively constant, whereas the relevant wavelength increases quadratically with angular rotation speed. Standing waves appear at a critical rotation rate. Further, in some cases, a propagating cellular pattern forms on the surface of the medium.
Inertial range structures in decaying compressible turbulent flows
Authors: Porter David H. , Woodward Paul R. , Pouquet Annick
Published: July 2002

Simulations of decaying compressible turbulent flows have been performed using the PPM algorithm on grids of 5123 and 10243 computational cells. Although the run on the finer grid has not yet been carried out to a time large enough for the spectra to relax fully, it adds significantly to the results on the coarser grid by lengthening the range of wave numbers in which the flow exhibits a self-similar character. There is an inertial range of scales in the decaying flow on the finer mesh that is free from direct effects of dissipation, forcing, boundary conditions, or initial conditions. Favre averaging of the high resolution data is performed on different scales from which the vorticity structures in the inertial range may be visualized and characterized without confusion from the smaller-scale features of the near dissipation range. We find that the vorticity structures of the inertial range are filamentary as well, but qualitatively different—shorter and more curved—than those of the dissipation range. Quantitative evidence of the action of vortex stretching in developed turbulence is also presented.
Coupling between anomalous velocity and passive scalar increments in turbulence
Authors: Boratav Oluş N. , Pelz Richard B.
Published: July 2002

Given (and confirmed numerically) that the exponents α and β in the passive scalar and velocity structure functions 〈(ΔT3)a〉∼rα, and 〈(Δu3)a〉∼rβ are anomalous, the scaling of γ in 〈(u(x+r)−u(x))a(T(x+r)−T(x))2a〉∼rγ is investigated. Analytical estimates show that γ cannot be as anomalous as α or β. Numerical computations (Pr=1, Reλ=141) show that γ is closer to β than to α. In addition, the statistical dependence of the velocity and passive scalar differences leads to an enhanced anomaly in γ.
The effect of interfacial instabilities in a stratified resuspension flow on the pressure loss
Authors: Loimer Thomas , Schaflinger Uwe
Published: July 2002

This study investigates the stability of a laminar, cocurrent flow of a concentrated suspension below a clear fluid layer in a plane, horizontal channel. The suspension is treated as a Newtonian fluid with effective density and viscosity dependent on the particle concentration. In such cases, the flow problem resembles the stratified flow of two different superposed fluids, which is well known to be unstable to long interfacial waves. The evolution equation for long interfacial waves is derived by employing a method of multiple time scales and a regular perturbation technique. In this study, the particle concentration within the suspension layer is a function of the local height of the perturbed interface. A wall slip boundary condition for the suspension is employed at the bottom wall of the channel. The evolution equation is Burgers’ equation, which predicts the behavior of an initial disturbance. The variable particle concentration affects the stability of the flow. For a small ratio of clear fluid to suspension layer thickness, an unstable region exists if the Froude number is below a critical value. Favorable density stratification stabilizes the flow. Finally, it is shown that interfacial waves modify the pressure loss in the channel, which is in agreement with an earlier experimental observation.
Two-dimensional steady free surface flow into a semi-infinite mat sink
Authors: Koerber A. J. , Forbes L. K.
Published: July 2002

The steady, potential flow of a fluid into a semi-infinite “mat” sink in two dimensions is examined, the mat sink being a region along the flat bottom, where the vertical outflow velocity is specified by −V(x). The fluid possesses a free surface that is drawn right down into the sink. An integral equation technique is employed and solved numerically. Solutions are found for the supercritical case, where the Froude number F>1, and free surface profiles are presented for two different forms of the outflow velocity profile V(x).
On the interaction between two oppositely signed, shielded, monopolar vortices
Authors: Schmidt M. R. , Beckers M. , Nielsen A. H. , Rasmussen J. Juul , van Heijst G. J. F.
Published: July 2002

The formation two-dimensional dipolar vortices by the interaction between two shielded monopolar vortices with opposite vorticity, as shown in a numerical study by Couder and Basdevant,Reference 1 is investigated in detail, both experimentally, in a nonrotating stratified fluid and numerically by direct solutions of the two-dimensional Navier–Stokes equations. A comparative study between the laboratory experiments and numerical simulations is performed. The vorticity distribution measured in the early stage of the evolution in the laboratory is used as initial data for the simulations, and an additional damping term in the Navier–Stokes equations, that accounts for the vertical diffusion in the laboratory experiments, is used. The results show that, depending on the initial separation between the vortices, the shields of the monopoles are peeled off and indeed a compact dipole with a linear (ω,ψ)-relationship is formed, or when the monopoles are further apart the shields of the monopoles are perturbed and two tripoles are formed. The characteristics of the emerged dipole are analyzed and a dye visualization of the dipole formation is performed. A second, more general numerical study yields a relationship between the formation time of the dipole and the initial separation distance between the monopoles and it shows that the deshielding process can be explained by the domination of strain over vorticity.
The velocity of a circular disk moving edgewise in quasi-steady Stokes flow toward a plane boundary
Authors: Trahan Jeffrey F. , Hussey R. G. , Roger R. P.
Published: July 2002

Measurements are presented for the velocity U of a circular disk as it moves edgewise in quasi-steady Stokes flow toward a fixed plane boundary. The results are compared with the idealized case of a disk of zero thickness. After empirical extrapolation to zero thickness, the experimental results are in good agreement with the theoretical expression of Davis [J. Eng. Math. 27, 209 (1993)]. When the experimental values are extrapolated to a fluid of infinite extent, the dimensionless drag for a disk of nonzero thickness agrees well with the previous beads-on-a-shell calculations of Roger [Phys. Fluids 27, 787 (1984)] and with additional values presented here. An empirical thickness correction is found; when this correction is added to the zero thickness expression of Davis, the results in the far field agree with experiment for thickness to diameter ratios as large as 0.77. When the disk thickness is equal to its radius, the far-field velocity, made dimensionless in a particular way, is very close to that of a sphere of the same radius. A squeeze film lubrication region is observed when the disk is close to the plane boundary. In this region, the dimensionless velocity varies as (h/t)3/2, where t is the disk thickness and h is the distance from the boundary to the nearest point on the disk. The lubrication region extends up to x=h/t=0.15. In the transition region between the lubrication regime and the far field, the dimensionless velocity is well represented by U/US=(0.605x−0.029)/(x+1), where US is the Stokes velocity; this relation is valid for 0.125<x<2.
Multiplicity of equilibrium states in laterally heated thermosolutal systems with equal diffusivity coefficients
Authors: Tsitverblit N.
Published: July 2002

This work uncovers the instabilities arising in laterally heated stably stratified systems when the diffusivities of the two involved components are equal. These instabilities are demonstrated to be the result of the differential diffusion caused by the unequal lateral diffusion gradients of the components. Such gradients form in the perturbed state due to the different side-wall boundary conditions. Examination of the bifurcation phenomena in the finite enclosures with equal diffusivities exhibited most qualitative features established by Tsitverblit and Kit [Phys. Fluids A 5, 1062 (1993)] and Tsitverblit [Phys. Fluids 7, 718 (1995)] for such phenomena in the heat-salt problem. In the behavior of singularities and steady flows, a number of the regularities that are not distinct in the heat-salt case were distinguished. Additional results obtained with the solute sidewall boundary conditions being of the same (fixed-value) type as the temperature conditions were also discussed.
Analyzing mean transport equations of turbulence and linear disturbances in decaying flows
Authors: Thacker W. D. , Gatski T. B. , Grosch C. E.
Published: July 2002

The decay of laminar disturbances and turbulence in mean shear-free flows is studied. In laminar flows, such disturbances are linear superpositions of modes governed by the Orr–Sommerfeld equation. In turbulent flows, disturbances are described through transport equations for representative mean quantities. The link between a description based on a deterministic evolution equation and a probability-based mean transport equation is established. Because an uncertainty in initial conditions exists in the laminar as well as the turbulent regime, a probability distribution must be defined even in the laminar case. Using this probability distribution, it is shown that the exponential decay of the linear modes in the laminar regime can be related to a power law decay of both the (ensemble) mean disturbance kinetic energy and the dissipation rate. The evolution of these mean disturbance quantities is then described by transport equations similar to those for the corresponding turbulent decaying flow.
Wall-boundary conditions in probability density function methods and application to a turbulent channel flow
Authors: Minier Jean-Pierre , Pozorski Jacek
Published: July 2002

An application of a probability density function (PDF), or Lagrangian stochastic, approach to the case of high-Reynolds number wall-bounded turbulent flows is presented. The model simulates the instantaneous velocity and dissipation rate attached to a large number of particles and the wall-boundary conditions are formulated directly in terms of the particle properties. The present conditions aim at reproducing statistical results of the logarithmic region and are therefore in the spirit of wall functions. A new derivation of these boundary conditions and a discussion of the resulting behavior for different mean variables, such as the Reynolds stress components, is proposed. Thus, the present paper complements the work of Dreeben and Pope [Phys. Fluids 9, 2692 (1997)] who proposed similar wall-boundary particle conditions. Numerical implementation of these conditions in a standalone two-dimensional PDF code and a pressure-correction algorithm are detailed. Moments up to the fourth order are presented for a high-Reynolds number channel flow and are analyzed. This case helps to clarify how the method works in practice, to validate the boundary conditions and to assess the model and the code performance.
Influence of compressibility on propagation of curved flames
Authors: Travnikov O. Yu. , Bychkov V. V. , Liberman M. A.
Published: July 2002

The nonlinear problem of propagation of a curved stationary flame in a compressible flow is studied by means of two-dimensional numerical simulations of the complete set of equations of flame dynamics including chemical kinetics, thermal conduction, and fuel diffusion. It is shown that curved shape of a flame in a compressible fuel mixture leads to stronger increase of the flame velocity than in the case of isobaric flames. It is found that acceleration of a flame due to the development of the curved shape generates a shock of noticeable intensity ahead of the flame front. The shock compresses the fresh fuel and, in turn, changes parameters of the flame. As a result, strongly curved flames in compressible flows can be observed in tubes much narrower than in the case of isobaric flows. Additional amplification of the flame velocity is obtained due to the development of asymmetrical structures at the flame fronts in wide tubes.
Sand waves in unidirectional flows: Scaling and intermittency
Authors: Nikora Vladimir I. , Goring Derek G.
Published: July 2002

A simple model of sand wave dynamics in terms of physically sound phenomenology which may lead to either ordinary scaling or multiscaling is suggested. The extended self-similarity (ESS) analysis of measurements strongly supports the latter, suggesting complex dynamics that possibly involves intermittency in the wave energy dissipation. Both ESS and generalized ESS of sand waves appeared to be remarkably similar to those of turbulence.
Eulerian space–time correlations in turbulent shear flows
Authors: Phillips W. R. C.
Published: July 2002

This paper is concerned with the generic form of space–time correlations of instantaneous velocity fluctuations in turbulent shear flows. The study has as its basis the Kovasznay–Corrsin conjecture modified to account for inhomogeneities. Details of the modifications were dictated by comparison with direct numerical simulations of turbulent channel flow. For example, analysis of the simulations shows that the space–time correlations at optimal delay depict, when appropriately normalized, a form independent of turbulence component. It is also evident that the half width of the correlation grows, in the outer region of the layer, like Vn+1, while the Lagrangian time scale grows like Vn, where 2<n<3 and V is the mean convection velocity. The resulting generic form for the space–time correlation captures these effects well and brings to light a Reynolds number effect that is most evident in the tail of the correlations at nonoptimal delay.
The velocity distribution function in an infinitely strong shock wave
Authors: Takata Shigeru , Aoki Kazuo , Cercignani Carlo
Published: July 2002

The structure of an infinitely strong shock wave (i.e., a shock wave with infinitely large upstream Mach number) is investigated on the basis of the Boltzmann equation for hard-sphere molecules. The velocity distribution function is expressed as a sum of a multiple of the Dirac delta function, centered at the upstream bulk velocity, and the remainder. The equation for the latter, which contains the linear collision term linearized around the delta function and the nonlinear collision term, is solved numerically by an accurate finite-difference method after the nonlinear collision term is replaced by the BGK collision model. The result not only confirms the singularity in the remainder observed in the previous Monte Carlo simulation [Cercignani et al., Phys. Fluids 11, 2757 (1999)] but also provides more detailed information about the structure of the singularity.
Free surface flow into a horizontal slot with zero gravity
Authors: McCue S. W.
Published: July 2002

The two-dimensional free surface flow of a finite-depth fluid into a horizontal slot is considered. For this study, the effects of viscosity and gravity are ignored. A generalized Schwarz–Christoffel mapping is used to formulate the problem in terms of a linear integral equation, which is solved exactly with the use of a Fourier transform. The resulting free surface profile is given explicitly in closed form.
Small scale magnetic flux-averaged magnetohydrodynamics
Authors: Pfirsch D. , Sudan R. N.
Published: July 2002

By relaxing exact magnetic flux conservation below a scale λ a system of flux-averaged magnetohydrodynamic equations are derived from Hamilton’s principle with modified constraints. An energy principle can be derived from the linearized averaged system because the total system energy is conserved. This energy principle is employed to treat the resistive tearing instability and the exact growth rate is recovered when λ is identified with the resistive skin depth. A necessary and sufficient stability criteria of the tearing instability with line tying at the ends for solar coronal loops is also obtained. The method is extended to both spatial and temporal averaging in Hamilton’s principle. The resulting system of equations not only allows flux reconnection but introduces irreversibility for appropriate choice of the averaging function. Except for boundary contributions which are modified by the time averaging process total energy and momentum are conserved over times much longer than the averaging time τ but not for less than τ. These modified boundary contributions correspond to the existence, also, of damped waves and shock waves in this theory. Time and space averaging is applied to electron magnetohydrodynamics and in one-dimensional geometry predicts solitons and shocks in different limits.
The nonlinear saturation of beam-driven instabilities: Irregular bursting in the DIII-D tokamak
Authors: Heidbrink W. W. , Danielson J. R.
Published: July 2002

Intense fast-ion populations created by neutral-beam injection into a tokamak can destabilize fishbone modes and other instabilities. Regular, periodic bursts of fishbones often occur but, when another magnetohydrodynamic (MHD) mode is also unstable, the burst cycle is irregular. The complexity of the burst cycle over a long time scale correlates with the purity of the Fourier spectrum during a single burst (a short time scale). The data are consistent with a simple predator–prey model in which the second MHD mode introduces periodic perturbations into the evolution equations.