bluuebunny/crossref_metadata_2025 huggingface dataset:
Lagrangian turbulence and spatial complexity in a Stokes flow
Authors: Chaiken J. , Chu C. K. , Tabor M. , Tan Q. M.
Published: July 2002

A simple Stokes flow problem, corresponding to an incompressible flow between two eccentric cylinders rotating alternately, is investigated numerically. It is demonstrated that for a wide range of system parameters the fluid particles can evolve along highly chaotic orbits, thereby providing an example of so called ‘‘Lagrangian turbulence.’’ Passive scalar distributions can rapidly evolve into structures of remarkable spatial complexity that can be characterized in terms of the underlying phase space dynamics. An investigation is made of the ability of simple area preserving mappings, deduced from the physical problem, to reproduce the dynamics obtained from the exact solution.
Poloidal flux loss and axial dynamics during the formation of a field-reversed configuration
Authors: Milroy R. D. , Slough J. T.
Published: July 2002

A method has been developed that uses the observed strength of the axial implosion during field-reversed configuration (FRC) formation to infer the trapped poloidal flux level in the time interval after the radial implosion, but before the axial implosion. The method uses a 2-D magnetohydrodynamic (MHD) model to characterize the implosion strength as a function of trapped flux. An inferred flux loss time history prior to the axial implosion exhibits a rather short 9 μsec lifetime until the axial implosion reaches the midplane, which causes field gradients to relax and the flux loss rate to be reduced. By comparing the experimental flux loss time histories with numerical calculations, a plasma resistivity time history has been inferred. An additional flux loss that often occurs after the axial implosion, but before 2-D equilibrium is achieved, has also been identified. It was found necessary to include the effects of classical viscosity in the model to accurately represent axial dynamics. The effects of viscosity in current experiments has been studied, and it is found that if the ion temperature is sufficiently high, the parallel component of classical ion viscosity can significantly damp the strength of the axial contraction.
Pressure gradient alignment with strain rate and scalar gradient in simulated Navier–Stokes turbulence
Authors: Ashurst Wm. T. , Chen J.-Y. , Rogers M. M.
Published: July 2002

In a simulated turbulent shear flow the pressure gradient caused by velocity fluctuations alone has increased probability for alignment with the most compressive strain direction, which is similar to passive scalar-gradient behavior. The pressure-gradient component depending on the mean shear indicates no correlation with the strain directions.
Failure of the Fokker–Planck approximation to the Boltzmann integral for (1/r) potentials
Authors: Shoub Edward C.
Published: July 2002

It is shown that the widely used Landau–RMJ collision term provides an inadequate description of collisional relaxation caused by Coulomb or gravitational interactions because of its inability to correctly describe large angle scattering events. This is established by extending the Taylor series expansion of the Boltzmann integral to fourth order thereby obtaining an approximation of the form JB[ fa, fb]ΔΩχ =ln(xmax/xmin)L2[ fa, fb] +(x2max−x2min)L4[ fa,  fb] +O(x4max), where xmax=sin(χmax/2), xmin=sin(χmin/2), and χ is the scattering angle in the center of mass frame. For χmax =180°, the first term in the series is the familiar Landau–RMJ collision term. The higher-order collision term L4 is derived and its properties are discussed. In particular it is shown that for like-particle and light–heavy particle collision, L4 can exceed L2 ln Λ over large regions of velocity space whenever the particle distribution functions fa, fb differ significantly from common equilibrium distributions. The conclusion drawn from this result is that large angle scattering events play a more significant role in the evolution of such distributions than currently believed.
The role of initial conditions in flow stability with an application to modons
Authors: Carnevale G. F. , Vallis G. K. , Purini R. , Briscolini M.
Published: July 2002

Lyapunov stability arguments may be used to show that an otherwise unstable flow can be stabilized by restriction of the class of possible perturbations. It is shown that, in general, such a restriction applied only to the initial perturbation does not imply stability for dynamics on the entire phase space nor does it necessarily imply a delay of the onset of instability. As a result, proofs of linear stability based on a restriction of the initial perturbation actually are not valid. In particular, certain criteria for the stability of modons given by Pierini [Dyn. Atmos. Oceans 9, 273 (1985)] and Swaters [Phys. Fluids 29, 1419 (1986)] and synthesized by Flierl [Annu. Rev. Fluid Mech. 19, 493 (1987)] do not, in fact, ensure stability. A model is used to demonstrate that these stability criteria do not preclude instantaneous onset of linear instability. The model also demonstrates that, although conservation of energy and enstrophy implies that the transfer of energy in an instability must be to scales both larger and smaller than the modon scale, the principal direction of transfer remains undetermined.
Electrical circuit modeling of reversed field pinches
Authors: Sprott J. C.
Published: July 2002

Equations are proposed to describe the radial variation of the magnetic field and current density in a circular, cylindrical reversed field pinch (RFP). These equations are used to derive the electrical circuit parameters (inductance, resistance, and coupling coefficient) for a RFP discharge. The circuit parameters are used to evaluate the flux and energy consumption for various start-up modes and for steady-state operation using oscillating field current drive. The results are applied to the MST device [Bull. Am. Phys. Soc. 32, 1830 (1987)].
Quasilinear and toroidal effects on current drive by electron cyclotron waves
Authors: Giruzzi G.
Published: July 2002

Current drive by electron cyclotron waves in toroidal geometry is investigated by means of a bounce-averaged Fokker–Planck code. The case of the extraordinary mode at a frequency lower than the electron gyrofrequency is studied in detail for a wave packet of finite width, carrying a power in the megawatt range, which is absorbed away from the plasma center. It is shown that in this case, because of the interplay of quasilinear and trapping effects (i) the current drive efficiency is strongly power dependent and (ii) wave absorption at the inboard part of the magnetic surfaces does not maximize the efficiency, in contrast to the results of linear theory.
Variational formulation for a multifluid flowing plasma with application to the internal tilt mode of a field-reversed configuration
Authors: Ishida A. , Momota H. , Steinhauer L. C.
Published: July 2002

Standard magnetohydrodynamic (MHD) equations are extended to include arbitrary equilibrium flows and multiple fluids and an equivalent variational form is developed. This system is appropriate for the study of stability in any multifluid flowing plasma, e.g., allowing for arbitrary poloidal and toroidal equilibrium flows and accounting for the Hall terms. The variational formalism is applied to the particular case of the internal tilting instability in a field-reversed configuration (FRC). A solution by means of the Rayleigh–Ritz technique leads to the dispersion relation, from which the growth rate and marginal stability conditions are determined. A new stability regime is found for sufficiently elongated FRC’s, arising as a consequence of the Hall effect. These results are compared with experiment and related theory.
On the decay of a turbulent vortex ring
Authors: Weigand Alexander , Gharib Morteza
Published: July 2002

The spatiotemporal evolution of a turbulent vortex ring with an initial Reynolds number of 7500 is experimentally investigated using the technique of digital particle image velocimetry. The flow is initially characterized by the laminar/turbulent transition via azimuthal bending instabilities. After transition, the shedding of vorticity from peripheral regions of the ring is found to be responsible for the formation of a wake region. This shedding process results in the staircase-like decay of the circulation and propagation speed of the vortex ring.
Nonlinear stability and rupture of ultrathin free films
Authors: Sharma Ashutosh , Kishore C. S. , Salaniwal S. , Ruckenstein Eli
Published: July 2002

The nonlinear long-wave stability and lifetimes of thin free films subjected to the excess Lifshitz–van der Waals (LW) forces are studied based on numerical solutions, and a weakly nonlinear theory (WNT), which neglects mode interactions. The WNT works best for the fastest growing (dominant) disturbances of small initial amplitudes, and also for relatively thick films. For such cases, the nonlinear viscous effects (stabilizing) and inertia (destabilizing) are usually less significant than the LW force (destabilizing), surface tension force, and the unsteady effects (both stabilizing). For large initial amplitudes, linearly stable disturbances can engender strong subcritical instabilities and film rupture due to the greatly enhanced LW forces, inertia and mode interactions.
On Bénard–Marangoni instability in the presence of a magnetic field
Authors: Thess A. , Nitschke K.
Published: July 2002

Explicit asymptotic expressions are derived for the first unstable mode of surface tension driven instability in an electrically conducting fluid subjected to a strong magnetic field. The spatial structure of the velocity, temperature, and electric current density is characterized in terms of Hartmann boundary layers—a concept that permits a physical explanation of the role of the magnetic field and an understanding of scaling laws derived in previous work.
Flow structure from an oscillating cylinder with a localized nonuniformity: Patterns of coherent vorticity concentrations
Authors: Gu W. , Rockwell D.
Published: July 2002

Forced oscillation of a uniform cylinder with a localized, fluid-induced nonuniformity at its midspan, in the form of either blowing or suction, generates well-defined patterns of vorticity concentrations. The spanwise extent of these patterns abruptly grows to an order of magnitude larger than the initially induced nonuniformity. Such patterns exhibit ordered changes in the number, arrangement, and circulation of the vorticity concentrations as the magnitude of the nonuniformity is altered.
On the onset of three-dimensionality in mixing layers
Authors: Mallier Roland
Published: July 2002

Using a nonlinear critical layer analysis, a set of nonlinear integrodifferential evolution equations is derived, governing the temporal growth of a disturbance consisting of both a two-dimensional wave and a pair of oblique waves with the same streamwise wave number as the two-dimensional wave superimposed on a tanh y mixing layer [a so-called Benney–Lin (BL) triad]. This is a model of so-called K-type transition. Numerical solutions to these equations develop a singularity at a finite time, which is confirmed by asymptotic analysis. The relevance of this analysis to the mixing layer experiments of Lasheras and Choi [J. Fluid Mech. 189, 53 (1988)] and numerical simulations of Ashurt and Meiburg [J. Fluid Mech. 189, 87 (1988)] and Rogers and Moser [J. Fluid Mech. 243, 183 (1992); NASA TM No. 103856, 1991] are discussed. As with similar equations derived for related problems, these equations are shown to have solutions which become singular after a finite time.
PDFs for velocity and velocity gradients in Burgers’ turbulence
Authors: Avellaneda M. , Ryan R. , Weinan E.
Published: July 2002

We characterize the tails of the probability distribution functions for the solution of Burgers’ equation with Gaussian initial data and its derivatives ∂kv(x,t)/∂xk, k=0,1,2,... . The tails are ‘‘stretched exponentials’’ of the form P(θ)∝exp[−(Re)−ptqθr], where Re is the Reynolds number. The exponents p, q, and r depend on the initial spectrum as well as on the order of differentiation, k. These exact results are compared with those obtained using the mapping closure technique.
Interaction between longitudinal convection rolls and transverse waves in unstably stratified plane Poiseuille flow
Authors: Fujimura K. , Kelly R. E.
Published: July 2002

Nonlinear interaction between a Tollmien–Schlichting wave and longitudinal rolls resulting from Rayleigh–Bénard instability has been investigated in an unstably stratified plane Poiseuille flow of infinite extent. Cubic order amplitude equations for the interacting modes are derived on a weakly nonlinear basis in the neighborhood of a crossover point at which both modes become unstable on a linear basis simultaneously. A bifurcation analysis based on use of the actual numerical coefficients obtained from the governing equations and evaluated for various values of the Prandtl number is performed, and the results, such as the effect of longitudinal rolls on the subcritical instability characteristic of a Tollmien–Schlichting wave, are discussed.
Collision rates of spherical drops or particles in a shear flow at arbitrary Péclet numbers
Authors: Zinchenko Alexander Z. , Davis Robert H.
Published: July 2002

Collision rates of two nondeformable, freely suspended drops (or particles) subject to Brownian motion in a simple shear at low Reynolds number are calculated from the solution of the full Fokker–Plank equation for the pair distribution function. Unlike previous studies on shear-induced collisions, the solution is presented for arbitrary Péclet number (Pe), thus covering a broad range of drop sizes. An efficient numerical technique includes a mixed Galerkin/finite-difference approximation and the ideas of analytical continuation, to represent the solution of the discrete problem as a convergent series for all real Pe. The mobility functions are provided from exact two-drop hydrodynamics and near-contact asymptotics. Extensive calculations are presented for the collision efficiency as a function of the size ratio, drop-to-medium viscosity ratio (μ̂), and Pe≤O(102), for the case of no interdroplet forces. For μ̂≳0, the correction to the collision efficiency for Pe≫1 is O(Pe−1/2). For bubbles (μ̂=0), there is also an O(Pe−2/3) correction of opposite sign, resulting in a local minimum for the collision efficiency. The asymptotic analysis for the opposite limit of Pe≪1 is in excellent agreement with the numerical calculations. For intermediate Pe, the exact numerical solution is compared with different ‘‘additive approximations.’’ The simple two-term additivity approximation is generally unsuccessful, whereas a modified, three-term approximation provides reasonable results except at small size ratios and large viscosity ratios. The effect of the van der Waals attractions on the collision efficiency for typical emulsion drops of 1–10 micron size with μ̂=O(1) is relatively small, of the order 10% in the Brownian regime. As a limiting case of drops, the collision efficiency for equal-sized solid spheres with van der Waals attractions is calculated for Pe≤200; this limit shows a stronger dependence on the Hamaker constant and the retardation parameter. The solution for solid spheres is in excellent agreement with reported experimental data on flocculation dynamics for suspensions with moderate Péclet numbers.
Melting driven thermohaline convection
Authors: Bénard C. , Bénard R. , Bennacer R. , Gobin D.
Published: July 2002

This study is concerned with the experimental and numerical analysis of thermohaline natural convection in an aqueous solution, driven by melting of a block of pure ice into the liquid mixture. Experimentally, the flow structure evolution and the heat transfer characteristics are studied for a binary H2O–Na2CO3 mixture in the domain of negative buoyancy ratios and for a wide range of solutal and thermal Rayleigh numbers. The observations are analyzed with the help of the classical results about cell formation in a stratified fluid due to sideways heating. The comparison with the numerical results shows that the mechanisms that define the flow structure are essentially due to thermohaline convection and not to the melting process. Finally, the fusion kinetics is analyzed, and the melting rate is correlated to the governing parameters of natural convection in the liquid.
EDQNM model of a passive scalar with a uniform mean gradient
Authors: Herr Stacy , Wang Lian-Ping , Collins Lance R.
Published: July 2002

Dynamic equations for the scalar autocorrelation and scalar-velocity cross correlation spectra have been derived for a passive scalar with a uniform mean gradient using the Eddy Damped Quasi Normal Markovian (EDQNM) theory. The presence of a mean gradient in the scalar field makes all correlations involving the scalar axisymmetric with respect to the axis pointing in the direction of the mean gradient. Equivalently, all scalar spectra will be functions of the wave number k and the cosine of the azimuthal angle designated as μ. In spite of this complication, it is shown that the cross correlation vector can be completely characterized by a single scalar function Q(k). The scalar autocorrelation spectrum, in contrast, has an unknown dependence on μ. However, this dependency can be expressed as an infinite sum of Legendre polynomials of μ, as first suggested by Herring [Phys. Fluids 17, 859 (1974)]. Furthermore, since the scalar field is initially zero, terms beyond the second order of the Legendre expansion are shown to be exactly zero. The energy, scalar autocorrelation, and scalar-velocity cross correlation were solved numerically from the EDQNM equations and compared to results from direct numerical simulations. The results show that the EDQNM theory is effective in describing single-point and spectral statistics of a passive scalar in the presence of a mean gradient.
The stability of compressible mixing layers in binary gases
Authors: Kozusko F. , Lasseigne D. G. , Grosch C. E. , Jackson T. L.
Published: July 2002

We present the results of a study of the inviscid two-dimensional spatial stability of a parallel compressible mixing layer in a binary gas. The parameters of this study are the Mach number of the fast stream, the ratio of the velocity of the slow stream to that of the fast stream, the ratio of the temperatures, the composition of the gas in the slow stream and in the fast stream, and the frequency of the disturbance wave. The ratio of the molecular weight of the slow stream to that of the fast stream is found to be an important quantity and is used as an independent variable in presenting the stability characteristics of the flow. It is shown that differing molecular weights have a significant effect on the neutral-mode phase speeds, the phase speeds of the unstable modes, the maximum growth rates, and the unstable frequency range of the disturbances. The molecular weight ratio is a reasonable predictor of the stability trends. We have further demonstrated that the normalized growth rate as a function of the convective Mach number is relatively insensitive (≊25%) to changes in the composition of the mixing layer. Thus, the normalized growth rate is a key element when considering the stability of compressible mixing layers, since once the basic stability characteristics for a particular combination of gases is known at zero Mach number, the decrease in growth rates due to compressibility effects at the larger convective Mach numbers is somewhat predictable.
Intermittency of vorticity in a turbulent shear flow
Authors: Shafi H. S. , Zhu Y. , Antonia R. A.
Published: July 2002

Autocorrelations of squared velocity derivatives and squared vorticity fluctuation components have been measured at the centerline in the wake of a circular cylinder. Near the start of the inertial range, all the correlations exhibit similar power-law behaviors and yield essentially the same estimate of the intermittency exponent μ. The results imply that (∂u/∂x)2 may be a reasonable substitute for the instantaneous dissipation rate of turbulent kinetic energy, for determining the value of μ.
On the decay of two-dimensional homogeneous turbulence
Authors: Chasnov J. R.
Published: July 2002

Direct numerical simulations of decaying two-dimensional turbulence in a fluid of large extent are performed primarily to ascertain the asymptotic decay laws of the energy and enstrophy. It is determined that a critical Reynolds number Rc exists such that for initial Reynolds numbers with R(0)Rc the flow field evolves with increasing Reynolds number. Exactly at R(0)=Rc, the turbulence evolves with constant Reynolds number and the energy decays as t−1 and the enstrophy as t−2. A t−2 decay law for the enstrophy was originally predicted by Batchelor for large Reynolds numbers [Phys. Fluids Suppl. II, 12, 233 (1969)]. Numerical simulations are then performed for a wide range of initial Reynolds numbers with R(0)>Rc to study whether a universal power-law decay for the energy and enstrophy exist as t→∞. Different scaling laws are observed for R(0) moderately larger than Rc. When R(0) becomes sufficiently large so that the energy remains essentially constant, the enstrophy decays at large times as approximately t−0.8.
Ship waves on a viscous fluid of finite depth
Authors: Chan Andy T. , Chwang Allen T.
Published: July 2002

In this paper we are concerned with the wave generation by a singular forcelet in a viscous fluid of finite depth, where the singularity is located far from the bottom and not very near the free surface. In the first part of this work, the image system of an Oseenlet bounded by a no-slip wall, is considered. It is found that the resultant velocity field can be described by a planar distribution of vertical Oseen doublets and a negative Oseenlet located at the mirror point of the singularity with respect to the plane wall. In the second part of the work we deal with the generation of waves by these solutions. By imposing the linearized free-surface conditions on the solutions obtained from the first part, the wave generated is shown to exhibit the Kelvin ship wave pattern that agrees with observation. The effects of water depth and of submergence on the wave amplitude are also investigated.
The role of nonunique axisymmetric solutions in 3-D vortex breakdown
Authors: Tromp J. C. , Beran P. S.
Published: July 2002

The three-dimensional, compressible Navier–Stokes equations in primitive variables are solved numerically to simulate vortex breakdown in a constricted tube. Time integration is performed with an implicit Beam-Warming algorithm using fourth-order compact operators to discretize spatial derivatives. Initial conditions are obtained by solving the steady, compressible, and axisymmetric form of the Navier–Stokes equations with Newton’s method. The effects of three-dimensionality on flows that are initially axisymmetric and stable to 2-D disturbances are examined. Stability of the axisymmetric base flow is assessed through 3-D time integration. Axisymmetric solutions at a Mach number of 0.3 and a Reynolds number of 1000 contain a region of nonuniqueness. Within this region, 3-D time integration reveals only unique solutions, with nonunique axisymmetric initial conditions converging to a unique solution that is steady and axisymmetric. Past the primary limit point, which approximately identifies the appearance of critical flow (a flow that can support an axisymmetric standing wave), the solutions bifurcate into 3-D time-periodic flows. Thus this numerical study shows that the vortex strength associated with the loss of stability to 3-D disturbances and that of the primary limit point are in close proximity. Additional numerical and theoretical studies of 3-D swirling flows are needed to determine the impact of various parameters on dynamic behavior. For example, it is possible that a different flow behavior, leading to a nearly axisymmetric vortex breakdown state, may develop with other inlet profiles and tube geometries.
PDF modeling for inhomogeneous turbulence with exact representation of rapid distortions
Authors: Van Slooten P. R. , Pope S. B.
Published: July 2002

A model for inhomogeneous turbulence is constructed that provides an exact representation of rapidly distorted homogeneous turbulence (RDT). The fundamental quantity modeled is the joint PDF of the velocity and wave vector which is related to the unit wavenumber vector. This joint PDF provides a model equation for the evolution of the directional spectrum, the integral over the wavenumber magnitude of the velocity spectrum. At this level the rapid pressure–rate-of-strain correlation is closed yielding exact equations in RDT. For decaying turbulence, the return-to-isotropy terms are modeled by stochastic diffusion equations for the velocity and wave vector. A general model of this type is constructed along with four simplified versions. The decay models are combined with the RDT model to give complete models for homogeneous turbulence, which are tested for several flows. The homogeneous models are then extended in a general manner to inhomogeneous turbulence.
Coarsening of solid-liquid mixtures in a random acceleration field
Authors: Thomson J. Ross , Casademunt Jaume , Drolet François , Viñals Jorge
Published: July 2002

The effects of flow induced by a random acceleration field (g-jitter) are considered in two related situations that are of interest for microgravity fluid experiments: the random motion of isolated buoyant particles, and diffusion driven coarsening of a solid-liquid mixture. We start by analyzing in detail actual accelerometer data gathered during a recent microgravity mission, and obtain the values of the parameters defining a previously introduced stochastic model of this acceleration field. The diffusive motion of a single solid particle suspended in an incompressible fluid that is subjected to such random accelerations is considered, and mean squared velocities and effective diffusion coefficients are explicitly given. We next study the flow induced by an ensemble of such particles, and show the existence of a hydrodynamically induced attraction between pairs of particles at distances large compared with their radii, and repulsion at short distances. Finally, a mean field analysis is used to estimate the effect of g-jitter on diffusion controlled coarsening of a solid-liquid mixture. Corrections to classical coarsening rates due to the induced fluid motion are calculated, and estimates are given for coarsening of Sn-rich particles in a Sn-Pb eutectic fluid, an experiment to be conducted in microgravity in the near future.
Blasius boundary layer flow over an irregular leading edge
Authors: Weidman P. D.
Published: July 2002

Uniform flow over a flat plate with an irregular leading edge is investigated. A similarity reduction to Blasius’s equation for the three-dimensional flow is obtained in the context of boundary layer theory. Now, however, the similarity variable is y/Δ(x,z), where x is the streamwise coordinate, y is the plate-normal coordinate, z is the spanwise coordinate, and Δ(x,z) is the planform distribution function which takes into account the position of the irregular leading edge. The wall shear stress and also the boundary layer, displacement, and momentum thicknesses are proportional to this common distribution function.
The effect of slight viscosity on a near-critical swirling flow in a pipe
Authors: Wang S. , Rusak Z.
Published: July 2002

The effect of slight viscosity on a near-critical axisymmetric incompressible swirling flow in a straight pipe is studied. We demonstrate the singular behavior of a regular-expansion solution in terms of the slight viscosity around the critical swirl. This singularity infers that large-amplitude disturbances may be induced by the small viscosity when the incoming flow to the pipe has a swirl level around the critical swirl. It also provides a theoretical understanding of Hall’s boundary layer separation analogy to the vortex breakdown phenomenon. In order to understand the nature of flows in this swirl range, we develop a small-disturbance analysis. It shows that a small but finite viscosity breaks the transcritical bifurcation of solutions of the Euler equations at the critical swirl into two branches of solutions of the Navier–Stokes equations. These branches fold at limit points near the critical swirl with a finite gap between the two branches. This means that no near-columnar equilibrium state can exist for an incoming flow with swirl close to the critical level and the flow must develop large disturbances in this swirl range. Beyond this range, two equilibrium states may exist under the same inlet/outlet conditions. When the flow Reynolds number is decreased this special behavior uniformly changes into a branch of a single equilibrium state for each incoming swirl. We also derive a weakly nonlinear approach to study the effect of slight viscosity on standing waves in a long pipe. This special behavior of viscous solutions shows good agreement with the numerical simulations of the axisymmetric Navier–Stokes equations by Beran and Culick and provides a theoretical understanding of these computations. The relevance of the results to the axisymmetric vortex breakdown in a pipe is also discussed.
Mixing of a passive scalar in magnetically forced two-dimensional turbulence
Authors: Williams Benjamin S. , Marteau D. , Gollub J. P.
Published: July 2002

More than 35 years ago, Batchelor discussed from a theoretical point of view the spatial power spectrum Eθ(k) of a weakly diffusing impurity mixed by a turbulent fluid flow. Under plausible assumptions including the random straining of fluid elements, Eθ(k) is expected to scale as k−1 for a range of wave numbers k beyond the cutoff of the energy spectrum, followed by a diffusive tail at a wave number determined by the rate of strain and the diffusivity. Some experiments over the years appear to support this conclusion, while others do not. We have investigated this issue experimentally in a quasi-two-dimensional turbulent flow, established in a thin buoyant layer that is electromagnetically forced by an array of permanent magnets beneath the cell. The wave number cutoff of the velocity field is established by particle image velocimetry, and the fluctuations are determined to be homogeneous and isotropic. To study mixing, a dye solution is introduced steadily at one side of the buoyant layer, and mixed fluid is extracted at the other until the fluctuations become steady. The time-averaged spatial power spectrum of the dye concentration distribution is measured for several distinct forcing configurations, including both regular and random magnet arrays; the latter produces convincingly isotropic concentration fluctuations. We find that Eθ(k) falls strongly below k−1 at wave numbers lower than expected from theory. The results do not appear to depend significantly on the scalar injection parameters or on the magnet arrangement. Periodic forcing at higher viscosity leads to chaotic rather than turbulent flows, with little change in Eθ(k). The observations can be explained in part by the intermittency characteristic of these two-dimensional flows, where the stretching of fluid elements is localized in space and time.
Monte Carlo simulation of nonequilibrium flow in a low-power hydrogen arcjet
Authors: Boyd Iain D.
Published: July 2002

A particle-based Monte Carlo numerical method is developed for computation of flow in a low-thrust hydrogen arcjet. The method employs the direct simulation Monte Carlo technique to compute the nonequilibrium fluid mechanics and thermochemical relaxation. Simulation of plasma effects is included at a simple level that ensures charge neutrality. A new model is developed to include Ohmic heating in the simulation. Results are presented for a flow condition that has been studied experimentally with a number of different diagnostic techniques. A strong degree of thermal nonequilibrium is found in the flow. It is demonstrated that Ohmic heating is important, and that the Monte Carlo model captures the important physics very well. The predicted results are in very good agreement with most of the experimental data.
The flow of a liquid film on the inside of a rotating cylinder, and some related problems
Authors: Wilson S. D. R. , Williams J.
Published: July 2002

A liquid film flows on the inner surface of a rotating horizontal cylinder. The simplest lubrication model assumes a force balance between viscosity and the streamwise component of gravity, and the equation for the film thickness admits a continuous solution only when the average thickness is less than a certain critical value. Above this value, a discontinuous solution is possible but the details are not accessible by means of the simple theory. This behavior can be traced to the gradual periodic variation of the streamwise component of gravity in the streamwise direction. We consider also two related problems in which this variation occurs more or less abruptly: (i) when the moving wall comprises two straight segments inclined at different angles, and (ii) when the dragged film emerges through the free surface of a second, overlying liquid. These problems are approached by introducing a smoothing parameter, namely surface tension, and solving a suitable initial value problem. We use the method of lines for this purpose because of the availability of robust ODE software which can exploit the structure of the problem; however, the periodic conditions of the cylinder problem necessitate a special approach to the discretization.
Magnetic damping of buoyant convection during semiconductor crystal growth in microgravity: Spikes of residual acceleration
Authors: Ma Nancy , Walker John S.
Published: July 2002

This paper treats the decay of the buoyant convection in a circular cylinder after a brief spike of large acceleration. There is a steady, uniform, axial magnetic field which is sufficiently strong that nonlinear inertial effects and convective heat transfer are negligible. Since the governing equations are linear, the solution for a spike at any angle to the cylinder’s axis is given by the superposition of two solutions for an axial spike and a transverse spike. The flows are axisymmetric and three-dimensional for the axial and transverse spikes, respectively. With the transverse spike, the axial temperature gradient drives a single cell of circulation with transverse vorticity, and the radial temperature gradient drives two opposite cells of circulation with axial vorticity on opposite sides of the diameter parallel to the acceleration. Although the axial temperature gradient is larger than the radial one in the Bridgman crystal-growth process, the damping of transverse vorticity with an axial magnetic field is much stronger than the magnetic damping of the axial vorticity, so that the two-cell axial-vorticity circulation dominates. For a typical Bridgman process with a 0.2 T magnetic field and with silicon, the buoyant convections driven by the axial and transverse spikes of acceleration decay to one percent of their magnitudes immediately after the spikes in 3 and 14 s, respectively.
Symmetry and reversibility in mixing fluids
Authors: Flekko/y Eirik G.
Published: July 2002

A notion of reversibility in miscible fluid flow, that does not depend on the amount of molecular diffusion, is introduced. This notion relies on a reciprocity relation for hydrodynamic dispersion which is derived and discussed. Using these results, an experimental technique for the measurement of hydrodynamic reversibility is investigated by means of numerical simulations employing a lattice Boltzmann model. Results demonstrate the sensitivity of the technique as well as potential biological applications.
Experimental and numerical investigations of the interface profile close to a moving contact line
Authors: Shen Chonghui , Ruth Douglas W.
Published: July 2002

For the problem of one fluid displacing another on a solid surface, Dussan V. et al. (1991) proposed a one-parameter analytical solution (the DRG solution) to describe the dynamic interface shape in the overlap region of the intermediate and the outer regions, for small capillary numbers. In the present study we examined the validity of the DRG solution with both experimental and numerical approaches. Our experiments consisted of displacing air with paraffin oil in parallel (Hele–Shaw) glass cells. The slope of the air–oil interface was measured at distances from the contact line, ranging between 5 and 200 μm. The displacement speeds corresponded to capillary numbers ranging between 4.7×10−6 and 2.6×10−4. Excellent agreement was obtained among the DRG solution, the numerical, and the experimental results in the region >10 μm from the contact line, but systematic deviation was observed in the region close to the contact line. This deviation was confirmed by the numerical simulations that used the finite element method. The measured dynamic contact angle increases with the displacing speed and can be correlated with a power law in Ca, which is similar to Tanner’s law.
Direct numerical simulations of low Reynolds number turbulent channel flow with EMHD control
Authors: O’Sullivan Peter L. , Biringen Sedat
Published: July 2002

We present results of numerical simulations of turbulence control in saltwater channel flows using electromagnetic (EM) forces. The control actuators are millimeter-sized micro-tiles flush mounted in the lower channel wall. This arrangement closely models one of the experimental designs proposed and developed by Bandyopadhyay at NUWC. We have studied two main secondary flow patterns which we denote by UV and WV (i.e., predominantly streamwise/normal and spanwise/normal) induced by both static and pulsed EM forcing. We have observed low net drag reduction, with a maximum of approximately 1%. This may be within the uncertainty of our computations. However, we have also found regions of localized reduction/increase in wall shear stress as high as ±11% versus the uncontrolled flow. Also, in every simulation with control we have observed a consistent (albeit small) reduction in skin friction which increases confidence in the results. The method of pulsing the EM force did not result in any observable resonance effects, at the low Reynolds numbers of this study. The mean turbulence intensities appear to be only weakly correlated with the reduction in viscous drag. The change in net drag does not appear to scale linearly on the magnitude of the EM forcing in the cases we have considered. Flow visualizations in the both the UV and WV cases indicate that the mean secondary flow above the actuators consists of a pair of near-wall oppositely oriented streamwise vortices which induce a flow where the normal velocity is wall-ward and is accompanied by strong spanwise wall jets.
The effects of thin films on the hydrodynamics near moving contact lines
Authors: Stoev K. , Ramé E. , Leonhardt T. , Garoff S.
Published: July 2002

We explore the effects of thin films on the hydrodynamics of macroscopic fluid bodies spreading over solid surfaces. To examine these effects, we measure the interface shape within microns of moving contact lines and compare those measurements to two asymptotic models in the limit of small capillary number, Ca. One model requires that the films affect the hydrodynamics only in a microscopic region near the contact line and allows the macroscopic meniscus to exhibit a nonzero effective contact angle. The other model describes the film as containing mobile fluid and specifically models the flow as fluid moves into or out of the film as the contact line moves. We examine fluids advancing and receding on wetting and nonwetting surfaces with spontaneously forming (molecular scale) and pre-existing (micron scale) films. Our results emphasize the importance of the mobility of the molecules in these very thin films in determining the hydrodynamics governing the moving contact line. The first model, which describes fluids advancing over dry surfaces, also accounts for the hydrodynamics of liquids advancing over very thin, immobile films. Surprisingly, the same model fails when fluid recedes on a nonwetting surface and no film is present. For mobile pre-existing films, the second model, based on Landau and Levich’s theory, accounts for the hydrodynamics in the limit of small Ca.
The scaling of pressure in isotropic turbulence
Authors: Nelkin Mark , Chen Shiyi
Published: July 2002

We study the scaling behavior of the pressure structure function for isotropic turbulence. This function is given exactly by Hill and Wilczak [J. Fluid Mech. 296, 247 (1995)] in terms of the three independent fourth order velocity structure functions, L(r)=〈Δu4(r)〉, T(r)=〈Δv4(r)〉, and M(r)=〈Δu2(r)Δv2(r)〉. We show from direct numerical simulation (DNS) that the cancellation between the positive terms proportional to L(r) and T(r) and the negative terms proportional to M(r) is almost complete. This suggests that the pressure structure function is extremely sensitive to recently observed small differences in scaling among the three quantities L(r), T(r), and M(r). We illustrate this sensitivity by calculating the pressure structure function in the atmospheric boundary layer using the recent data of B. Dhruva, Y. Tsuji, and K. R. Sreenivasan [Phys. Rev. E 56, R4928 (1997)]. The cancellation among the three terms persists, and gives an effective scaling exponent for the pressure structure function, 〈(Δp(r))2〉∝r1.17, which is smaller than the scaling exponent for any of the three velocity structure functions.
Marangoni instability of two liquids mixing at a free surface
Authors: Tan E. , Thoroddsen S. T.
Published: July 2002

The impact of a water drop on a thin layer of glycerin leads to the formation of an intricate flower-like pattern. We show that these leaf-like forms are generated by a surface-tension instability at the air–liquid interface along which there exists variable concentration of glycerin and water. Spatial variations of surface tension drive intense vortices inside the water layer, which interact with the glycerin–water concentration at the surface. Horizontal bending of these vortices is reinforced by the resulting enhancement of the surface-tension gradients.
Three-dimensional stability of a vortex pair
Authors: Billant Paul , Brancher Pierre , Chomaz Jean-Marc
Published: July 2002

This paper investigates the three-dimensional stability of the Lamb–Chaplygin vortex pair. Short-wavelength instabilities, both symmetric and antisymmetric, are found. The antisymmetric mode possesses the largest growth rate and is indeed the one reported in a recent experimental study [J. Fluid Mech. 360, 85 (1998)]. The growth rates, wave numbers of maximum amplification, and spatial eigenmodes of these short-wavelength instabilities are in good agreement with the predictions from elliptic instability theory. A long-wavelength symmetric instability similar to the Crow instability of a pair of vortex filaments is also recovered. Oscillatory bulging instabilities, both symmetric and antisymmetric, are identified albeit their growth rates are lower than for the short-wavelength instabilities. Their behavior and eigenmodes resemble those of the oscillatory bulging instability occurring in the mixing layer.
Taylor expansions in powers of time of Lagrangian and Eulerian two-point two-time velocity correlations in turbulence
Authors: Kaneda Yukio , Ishihara Takashi , Gotoh Koji
Published: July 2002

A method is developed for generating the Taylor expansions in powers of the time difference of the Lagrangian and Eulerian two-point two-time velocity correlations in turbulence. The expansions are based on the Taylor series of the Eulerian and Lagrangian velocity fields subject to given dynamics along with initial and boundary conditions. The lowest few coefficients in the expansions enable us to construct approximations to the correlations. An application of the method to turbulence obeying the Navier-Stokes dynamics yields approximations, particularly Padé approximations that agree well with direct numerical simulations of homogeneous isotropic turbulence at moderate Reynolds numbers. The ratios of the second-order to the zeroth-order coefficients of the Taylor series of the Lagrangian and Eulerian correlations give, respectively, the estimates for the Lagrangian and Eulerian micro time scales τL and τE. An analysis of a high resolution (5123 grid points) direct numerical simulation database at large Reynolds number suggests the scalings τL∝k−2/3 and τE∝k−1 for wave numbers k in the inertial subrange. The role of flow structures in turbulence in determining the time scales is also discussed.
Multiscale velocity correlation in turbulence: Experiments, numerical simulations, synthetic signals
Authors: Benzi R. , Biferale L. , Ruiz-Chavarria G. , Ciliberto S. , Toschi F.
Published: July 2002

Multiscale correlation functions in high Reynolds number experimental turbulence, numerical simulations, and synthetic signals are investigated. Fusion Rules predictions as they arise from multiplicative, almost uncorrelated, random processes for the energy cascade are tested. Leading and subleading contribution, in the inertial range, can be explained as arising from a multiplicative random process for the energy transfer mechanisms. Two different predictions for correlations involving dissipative observable are also briefly discussed.
Bounds for second order structure functions and energy spectrum in turbulence
Authors: Constantin P. , Nie Q. , Tanveer S.
Published: July 2002

In this paper we derive upper bounds for the second order structure function as well as for the Littlewood–Paley energy spectrum — an average of the usual energy spectrum E(k). While the upper bound results are consistent with a Kolmogorov type dependence on wave number k, the bounds do not involve the usual dissipation rate ε. Instead the bounds involve a dissipative quantity ε̂ similar to ε but based on the L3 average of ∇u. Numerical computations for a highly symmetric flows with Taylor microscale Reynolds numbers up to Rλ=155 are found to be consistent with the proposition that a relation in the inertial regime of the type E(k)∼Ĉε̂2/3k−5/3 holds with constant Ĉ.
On orientation averages for vortex models of turbulence
Authors: Yongnian Huang , Xiongping Luo
Published: July 2002

About 40 years ago Professor Zhou and Professor Tsai suggested a statistical theory of the axisymmetric vortex structures of homogeneous isotropic turbulence. Now we generalize it to the nonaxisymmetric vortices case. In this paper a spherical averaging method is used to study the statistical average rules. An exact general calculating formula of the orientation average is given. It can greatly simplify the calculations of high order correlation functions and moments.
Subgrid-scale model for the temperature fluctuations in reacting hypersonic turbulent flows
Authors: Martı́n M. Pino , Candler Graham V.
Published: July 2002

A direct numerical simulation (DNS) database is used to develop a model of subgrid-scale temperature fluctuations for use in large-eddy simulations of turbulent, reacting hypersonic flows. The proposed model uses a probability density representation of the temperature fluctuations. The DNS database reveals a physically consistent relation between the resolved-scale flow conditions that may be used to predict the standard deviation of the Gaussian probability density function (PDF). The model is calibrated and tested by comparison to simulations of decaying isotropic turbulence. The conditional single-variable PDF model is found to capture the fluctuations in temperature and product formation.
Dynamics of vapor bubbles with nonequilibrium phase transitions in isotropic acoustic fields
Authors: Gumerov Nail A.
Published: July 2002

Based on a multiscale asymptotic technique, a weakly nonlinear theory of rectified heat transfer to vapor bubbles is developed. The theory takes into account effects of internal and external heat transfer near the bubbles including memory terms, viscosity and slight compressibility of the liquid, surface tension, and nonequilibrium phase transitions. It is shown that the combination of these effects strongly influences bubble dynamics in high frequency acoustic fields. Results of calculations of bubble dynamics in water and liquid helium are presented. The role of kinetics of phase transitions is analyzed.