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Notes: The axisymmetric creeping motion of multiple composite spheres is analyzed to investigate the hydrodynamic interactions among these particles. A composite particle referred to in this paper is a spherical solid core covered with a permeable shell, whose thickness can be arbitrary. The Stokes equation and the Brinkman equation are used to describe the flow fields outside and inside the particle, respectively. For two identical composite spheres with thin porous layers in near contact, a lubrication analysis is employed to examine their relative motion. Analytic expressions for the pressure and the drag force are obtained for the layers having high permeability. For general cases, a boundary collocation method is applied to numerically solve for the unknown coefficients in the series solutions for the flow behavior of the multiple particles. The resulting drag forces are in good agreement with the predictions from the lubrication analysis and the reflection method. In general, the strength of hydrodynamic interaction among composite particles lies between the values among permeable particles with the same permeabilities and among solid particles. The hydrodynamic behavior for composite spheres may be approximated by that for permeable spheres when the porous layer is sufficiently thick, depending on the permeability. When the particles undergo relative motion, the drag increases with decreasing distance between them. However, the drag on the particle with larger size or lower permeability may reach a minimum at a certain distance for a chain of dissimilar particles, rather than in contact, when they translate at the same velocity. © 1998 American Institute of Physics.

Notes: The transition from two-dimensional thermoconvective steady flow to a time-dependent flow is considered for a liquid with a high Prandtl number (Pr=105) in a liquid bridge with a curved free surface. Both thermocapillary and buoyancy mechanisms of convection are taken into account. The computer program developed for this simulation transforms the original nonrectangular physical domain into a rectangular computational domain. To solve the problem in body-fitted curvilinear coordinates, the time-dependent Navier–Stokes equations were approximated by central differences on a stretched mesh. For liquid bridges with a flat interface, the instability corresponding to an azimuthal wave number of m=0 is not found for the investigated range of Marangoni numbers. The instability corresponding to an m=0 is found for relatively low Marangoni numbers only in liquid bridges with a nonflat, free surface, and nonzero Rayleigh number. The steady state becomes unstable to axially running waves. It is shown that the onset of instability depends strongly upon the volume of the liquid. The stability boundary is reported for the aspect ratio Γ=height/radius=4/3 and for a wide range of liquid bridge volumes. The physical mechanism of the oscillations is based on the temporal interaction of the temperature sensitive free surface with the small local disturbances, created by temperature distribution inside the liquid bridge. © 1998 American Institute of Physics.

Notes: Experiments on the onset of buoyant instabilities leading to periodic formation of vortical structures in planar buoyant plumes of helium and helium/air mixtures injected into quiescent air are reported for a range of nozzle widths (w=20–70 mm), plume fluid densities (pure helium to that approaching air), and velocities at the nozzle exit. First, the plume parameters corresponding to the onset of the oscillatory instability were experimentally determined by varying the nozzle exit velocity for different nozzle widths and plume fluid densities in two different nozzle configurations. These configurations corresponded to a freestanding rectangular nozzle and a rectangular nozzle surrounded by a flat plate in the plane of the nozzle exit. The observed plume behavior in the near field was characterized as nonoscillatory, transitional, or pulsatile. The onset of pulsations in the near field of these buoyant plumes (within a height of two nozzle widths) was best correlated in terms of the plume source Reynolds number and the plume fluid to ambient density ratio. It was also found that the boundary conditions surrounding the nozzle exit had an influence on the onset of plume instability in the near field. Specifically, at a given plume to the ambient density ratio, the plumes with flat plate surround were found to transition to the oscillatory state at a lower value of the threshold velocity and therefore are less stable than the plumes originating from freestanding nozzles. Subsequently, the plume oscillation frequencies were measured as a function of plume width, plume source velocity, and the density ratio for a range of these parameters. The plume oscillation frequency was found to correlate well in terms of the nondimensional parameters, Strouhal number, S=(fw)/Vp, and Richardson number, Ri=[(ρ∞−ρp)gw]/ρ∞Vp2, yielding a correlation S=0.55Ri0.45 determined for 1〈Ri〈102. This correlation is somewhat different from that of the axisymmetric buoyant plumes, which can be attributed to the differences in mixing rates and the strength of the local buoyancy flux in planar and axisymmetric plumes. The vortical structures formed in the unstable plumes also exhibit several distinct vortex pair modes. The centers of the formed vortex pairs, in general, do not remain colinear and distort with respect to each other when compared with the axisymmetric plume vortex rings, which are toroidal. The convection speeds of the vortex pair centers were also measured and reported in this study. © 1998 American Institute of Physics.

Notes: The similarity form of the scalar-variance spectrum at high Schmidt numbers is investigated for nonstationary turbulence. Theoretical arguments show that Batchelor scaling may apply only at high Reynolds numbers. At low Reynolds numbers, Batchlor scaling is not possible unless the turbulence is stationary or the enstrophy decays asymptotically as t−2. When this latter condition is satisfied, it is shown from an analysis using both the Batchelor and Kraichnan models for the scalar-variance transfer spectrum that the k−1 power law in the viscous-convective subrange is modified. Results of direct numerical simulations of high Schmidt number passive scalar transport in stationary and decaying two-dimensional turbulence are compared to the theoretical analysis. For stationary turbulence, Batchelor scaling is shown to collapse the spectra at different Schmidt numbers and a k−1 viscous-convective subrange is observed. The Kraichnan model is shown to accurately predict the simulation spectrum. For nonstationary turbulence decaying at constant Reynolds number for which the enstrophy decays as t−2, scalar fields for different Schmidt numbers are simulated in situations with and without a uniform mean scalar gradient. The Kraichnan model is again shown to predict the spectra in these cases with different anomalous exponents in the viscous-convective subrange. © 1998 American Institute of Physics.

Notes: The spreading of surfactant coated thin liquid films is often accompanied by an instability producing significant film corrugation, fingering and branching. Marangoni stresses, responsible for the rapid and spontaneous spreading, are suspected as the main cause of unstable flow. Traditional eigenvalue analysis of a self-similar solution describing Marangoni driven spreading has predicted only stable modes. We present results of a transient growth study which reveals enormous amplification of initially infinitesimal disturbances in the film thickness. This analysis provides, for the first time, evidence of an instability resembling experimental patterns. © 1998 American Institute of Physics.

Notes: The classical result of Smoluchowski [Z. Phys. Chem. 92, 129 (1917)] for the collision rate of monodisperse particles in a laminar shear flow is shown to be inaccurate due to the inclusion of the self-collision. In the present work we extend Smoluchowski's result by excluding the self-collision in the counting of collision pairs. A numerical simulation for particle collisions in a laminar shear flow at very low concentration is carried out to validate the extended result of Smoluchowski. Good agreement for the collision rate between the numerical simulation and the prediction based on the extended expression is obtained. © 1998 American Institute of Physics.

Notes: A power series mathematical solution is advanced for the problem of instability of an inviscid liquid sheet of parabolic velocity profile emanated from a nozzle into an inviscid gas. A comparison of the instability of a sheet of parabolic velocity profile with one of a uniform velocity profile is performed in order to deduce the effects of velocity profile relaxation on instability. The results show that for both antisymmetrical and symmetrical disturbances departure from uniformity of the velocity profile causes the instability to be reduced. The physical interpretation and practical implications of the present findings are discussed. © 1998 American Institute of Physics.

Notes: We consider the propagation of chemical fronts in a Hele-Shaw flow where the front is assumed to propagate with a curvature dependent velocity. The motivation is to model some recent experiments that employ aqueous autocatalytic chemical reactions in such a device. The density change across the front in such experiments is quite small so the Boussinesq approximation can be used, and the flow field generated is exclusively due to buoyancy effects. We derive a free boundary formulation based on Darcy's law and potential theory, and describe the evolution in terms of the θ−L formulation, in which the tangent angle and the perimeter of the closed front are followed in time. Numerical solutions are obtained for this formulation with a rising and expanding bubble. As observed in the experiments, a fingering phenomenon which is different from the surface tension associated phenomenon appears in our calculations. The mechanisms that control the wavelength selection of the fingers, and a comparison with the result of a linear stability analysis for flat fronts are discussed. © 1998 American Institute of Physics.

Notes: 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. © 1998 American Institute of Physics.

Notes: We examine non-linear spiral flow in the Taylor–Couette problem for a wide gap with axially periodic conditions. We present a highly efficient computational method adapted to this problem, based on continuation methods applied to a pseudospectral discretization of the Navier–Stokes equations in a rotating frame of reference. The spiral flow is computed in a wide range of parameters, and different features are explored in detail: domain of existence of the flow, behavior for high Reynolds number, appearance of axial flows, dependency on parameters, and stability against helical disturbances. A first integral is obtained and used to describe the particle trajectories in the fluid. This description shows that the axial and radial motion of the particles is mainly confined within an internal boundary layer. © 1998 American Institute of Physics.

Notes: A recent analysis of the stability of spherical bubble oscillations shows that the high order shape modes are parametrically unstable with respect to small but finite perturbations [Z. C. Feng and L. G. Leal, J. Fluid Mech. 266, 209 (1994)]. Using a heuristic approach it is shown here that the acoustic radiation due to the liquid compressibility plays an important role in stabilization of the high frequency modes and overall stability of the bubble spherical shape. © 1998 American Institute of Physics.

Notes: Asymptotic solutions in the Lagrangian variables that describe a peaking surface standing weakly nonlinear dispersive wave are reported. This wave can be considered as a standing wave of greatest height. The waves are excited parametrically in a vertically oscillating vessel and have the frequency equal to that of the excitation. © 1998 American Institute of Physics.

Notes: Combination modes appear in the spectrum of the surface pressure signals when a circular cylinder is forced to oscillate at a frequency different from the von Karman vortex shedding frequency. The spatial symmetry of the sum and difference modes depends on the direction of cylinder oscillation, and is predictable with a simple set of symmetry relations. As a result of the symmetry relations, cross-flow oscillations of the cylinder aimed at enhancing fluctuating lift also channel energy into the fluctuating drag component through the combination modes. © 1998 American Institute of Physics.

Notes: We report laboratory measurements of nonlinear parasitic capillary waves generated by longer waves in a channel. The experiments are conducted for three frequencies of longer waves (4, 5, and 6 Hz), corresponding to wavelengths of approximately 11, 7, and 5 cm. For these wavelengths we apply a model developed recently by Fedorov and Melville [J. Fluid Mech. 354, 1 (1998)] to predict the wave profile. Based on a viscous boundary layer approximation near the surface, the model enables us to efficiently calculate gravity-capillary waves. We present direct comparisons that show good agreement between the measurements and numerical predictions over a range of parameters. Finally, we give some simple estimates for a sharp cutoff in the wave number spectra observed in both the numerical solutions and the laboratory measurements of short gravity-capillary waves. © 1998 American Institute of Physics.

Notes: A temperature gradient is applied along a fluid filled slot. A basic state is considered where the slot is subject to thermocapillary forces and vertical mean gravity, each of which produces a parallel flow and a vertical advected temperature gradient, and is also subject to streamwise mean gravity, which will make the applied temperature stratification either stable or unstable. When this basic state is perturbed by jitter imposed in the spanwise direction, normal to the plane of the basic flow, the resulting fluid motion is three dimensional. The flow and temperature fields are found to have a simple functional dependence on streamwise and spanwise coordinates, but retain a complicated dependence on vertical coordinate. Perturbation equations describing the vertical variation of these fields are derived when the jitter is weak. At first order in the spanwise jitter, there is a time periodic spanwise-streamwise circulation around the slot. As this circulation also advects heat, it produces spanwise temperature gradients, enabling thermocapillarity and vertical gravity to generate subsidiary spanwise flows. At next order in the weak spanwise jitter, parallel streamwise flows are encountered, along with streamwise and vertical temperature gradients. In most parameter regimes these are opposed to the flow and temperature fields in the basic state. A thorough parametric investigation is performed where the weak spanwise jitter equations are solved, assuming for simplicity that streamwise gravity is absent. This leads to comparatively simple polynomial solutions in vertical coordinate for the various fields. A large number of parameters can still affect the solutions, however, and a detailed parametric investigation is performed. Interesting behavior is found at small Biot number, with trapping of heat producing large temperatures in the slot and large subsidiary flows. The spanwise to streamwise aspect ratio is another influential parameter, since geometric constraints encountered at extreme values of this ratio suppress certain velocity components of the flow and enhance others, thereby suppressing or enhancing temperature advection. These advected temperature fields themselves produce subsidiary velocities and subsidiary temperatures, which can exhibit a subtle and often counterintuitive dependence on the spanwise-streamwise aspect ratio. © 1998 American Institute of Physics.

Notes: The treatment of chemical reactions and nonequilibrium energy exchange in Direct Simulation Monte Carlo calculations is examined. Details of a Maximum Entropy chemical reaction model are presented that is based on the classical scheme devised by Levine and Bernstein. Data are given for all of the significant reactions that occur in hypersonic reentry flight into the atmospheres of the Earth, Mars, and Venus. The method is an extension of that described and used previously by the authors (Gallis and Harvey [J. Fluid Mech. 312, 149 (1996); AIAA J. 34(7), 1378 (1996)]) and now includes carbon dioxide/nitrogen and ionic reactions. The model allows an appropriate dependence of each reaction on its controlling energy mode and avoids inappropriate use of equilibrium distributions to determine the reaction probabilities and post-collision energy reallocation. Sample flow solutions are given and comparisons are made with results obtained using continuum solvers. © 1998 American Institute of Physics.

Notes: In the context of coaxial swirl injectors used in liquid bipropellant rockets, a detailed experimental study has been made on the mutual interaction between thin coaxial, conical liquid sheets. As the flow rates are increased, the sheets move close to each other and merge at a definite flow condition. The presence of the inner jet influences the behavior of the outer jet, even before merging. The merging and separation processes exhibit hysteresis. This leads to drastic variations in spray characteristics depending on the approach to the hysteresis regime. Many of these features as well as those on the movement of the contact point can be traced to changes occurring in the static pressure in the cavity between the two sheets. © 1998 American Institute of Physics.

Notes: Localized disturbances in laminar boundary-layers at Reynolds number Reδ*=950 were studied using direct numerical simulation. Instability mechanisms in both an adverse and zero pressure gradient were investigated by introducing three different three-dimensional disturbances. The first disturbance was centered around a pair of oblique waves in Fourier space, the second around a plane wave, while the third was axisymmetric. For small amplitudes, the first disturbance developed into a wave-packet of oblique waves in adverse pressure gradient and into a streaky structure with a trailing wave-packet in a zero pressure gradient. The second disturbance developed into a wave-packet centered around plane waves in both pressure gradients. The third disturbance developed into a wave-packet of plane waves in adverse pressure gradient and, due to the transient growth mechanism, into a streaky structure in a zero pressure gradient. For finite-amplitude plane wave-packets in a zero pressure gradient, a subharmonic secondary instability was observed which subsequently developed into an elongated Λ structure. The secondary instability was less significant in adverse pressure gradient due to the large growth rate of the primary instability. Breakdown was observed as high-frequency oscillations on the spike over the head of the Λ vortices. Providing the initial amplitude was sufficiently large, the vortex pair yielded the fastest route to turbulence. The main growth mechanism in this scenario, in addition to the exponential growth in the adverse pressure gradient case, was the nonlinear excitation of transient growth of streaks by interacting oblique modes. Disturbances dominated by streaks needed substantially larger amplitudes before secondary instability or breakdown occurred. In that case, breakdown was shifted from the spike to an instability of the rear part of the streaks. © 1998 American Institute of Physics.

Notes: A novel numerical technique for simulating interfacial gravity waves is considered. The model comprises an immiscible, binary fluid lattice Boltzmann model incorporating a gravitational interaction and simulates two immiscible, viscous fluids of different densities with a sharp interface between them. The model is described and the accuracy of the technique is considered. Simulation results are presented and the wave velocities, the oscillation frequency and the damping rate are found and compared to theory. A good comparison is found suggesting that the lattice Boltzmann approach is indeed accurately mimicking the wave dynamics. © 1998 American Institute of Physics.

Notes: Flows in a rotating annular tank [J. Sommeria, S. D. Meyers, and H. L. Swinney, Nonlinear Topics in Ocean Physics, edited by A. Osborne (North Holland, Amsterdam, 1991); Nature (London) 337, 58 (1989); T. H. Solomon, W. J. Holloway, and H. L. Swinney, Phys. Fluids A 5, 1971 (1993); J. Sommeria, S. D. Meyers, and H. L. Swinney, Nature (London) 331, 689 (1989)] with a sloping bottom (that simulates a barotropic atmosphere's Coriolis force with a topographic β-effect [J. Pedlosky, Geophysical Fluid Dynamics, 2nd ed. (Springer, Berlin, 1986)]) produce eastward and westward jets, i.e., azimuthal flows moving in the same or opposite direction as the annulus' rotation. Flows are forced by pumping fluid in and out of two concentric slits in the bottom boundary, and the direction of the jets depends on the direction of the pumping. The eastward and westward jets differ, with the former narrow, strong, and wavy. The jets of Jupiter and Saturn have the same east–west asymmetry [P. S. Marcus, Ann. Rev. Astron. Astro. 431, 523 (1993)]. Numerical simulations show that the azimuthally-averaged flow differs substantially from the non-averaged flow which has sharp gradients in the potential vorticity q. They also show that the maxima of the eastward jets and Rossby waves are located where the gradients of q are large, and the maxima of the westward jets and vortex chains are located where they are weak. As the forcing is increased the drift velocities of the two chains of vortices of the eastward jet lock together; whereas the two chains of the westward jet do not. Inspired by a previously published, [P. S. Marcus, Ann. Rev. Astron. Astro. 431, 523 (1993)] piece-wise constant-q model of the Jovian jets and based on numerical simulations, a new model of the experimental flow that is characterized by regions of undisturbed flow and bands of nearly uniform q separated by sharp gradients is presented. It explains the asymmetry of the laboratory jets and quantitatively describes all of the wave and vortex behavior in the experiments including the locking of the vortex chains of the eastward jet. The simulations and new model contradict the predictions of a competing, older model of the laboratory flow that is based on a Bickley jet; this raises concerns about previous calculations of Lagrangian mixing in the laboratory experiments that used the Bickley model for the fluid velocity. The new model, simulations and laboratory experiments all show that jets can be formed by the mixing and homogenization of q. The relevance of this to the jets of Jupiter is discussed. © 1998 American Institute of Physics.

Notes: A vapor in a gap between two parallel plane surfaces of its condensed phase, on which evaporation or condensation may take place, is considered in the case where another gas that neither evaporates nor condenses on the surfaces (say, a noncondensable gas) is also contained in the gap. The steady flow of the vapor caused by evaporation on one surface and condensation on the other and the behavior of the noncondensable gas are investigated on the basis of kinetic theory. First, fundamental features of the flow field are clarified for small values of the Knudsen number (associated with vapor–vapor collisions) by a systematic asymptotic analysis of the Boltzmann equation. Then, the problem is analyzed numerically by means of the direct simulation Monte Carlo method, and the steady behavior of the vapor and of the noncondensable gas (e.g., the spatial distributions of the macroscopic quantities) is clarified for a wide range of the Knudsen number. In particular, it is shown that, in the limit as the Knudsen number tends to zero (the continuum limit with respect to the vapor), there are two different types of the limiting behavior depending on the amount of the noncondensable gas, and evaporation and condensation can take place only when the average density of the noncondensable gas is vanishingly small in comparison with that of the vapor. © 1998 American Institute of Physics.

Notes: Using direct numerical simulations of turbulent channel flow, we present a new method for skin friction reduction, enabling large-scale flow forcing without requiring instantaneous flow information. As proof-of-principle, x-independent forcing, with a z wavelength of 400 wall units and an amplitude of only 6% of the centerline velocity, produces a significant sustained drag reduction: 20% for imposed counterrotating streamwise vortices and 50% for colliding, z-directed wall jets. The drag reduction results from weakened longitudinal vortices near the wall, due to forcing-induced suppression of an underlying streak instability mechanism. In particular, the forcing significantly weakens the wall-normal vorticity ωy flanking lifted low-speed streaks, thereby arresting the streaks' sinuous instability which directly generates new streamwise vortices in uncontrolled flows. These results suggest promising new drag reduction techniques, e.g., passive vortex generators or colliding spanwise jets from x-aligned slots, involving durable actuators and no wall sensors or control logic. © 1998 American Institute of Physics.

Notes: Nonlinear oscillations of viscous liquid drops with and without initial internal circulation are investigated. The full Navier–Stokes equations are solved for a liquid drop surrounded by a dynamically inactive ambient gas. The Galerkin/finite element technique along with the spine-flux method for the advection of the free boundaries are used. Internal circulations are generated by imposing a constant velocity at the surface of the drop and obtaining the steady state velocity field for a fixed drop shape. Oscillations of drops subject to small to large amplitude, and for the second-, third-, fourth-, and fifth-mode disturbances are considered. New data on the period and the decay factor of the oscillations are reported. The internal circulation in a drop released from an even-mode shape results in the transfer of energy mainly between the even modes. The internal circulation in a drop released from an odd-mode shape results in the transfer of energy between both odd and even modes. In general, the internal circulations generated by a constant surface velocity tend to transfer energy from any mode of drop oscillations to the second mode. This tendency increases as the strength of the internal circulation increases. © 1998 American Institute of Physics.

Notes: Numerical stability analysis and general flow characterization were performed for the flow induced by transverse rotating magnetic fields in cylindrical containers. Starting from Richardson's theoretical critical value for the generation of Taylor vortices in infinite cylinders, overstability in finite cylinders with different aspect ratios was investigated. Decreasing aspect ratio leads to a more stable configuration. For small cylinders and reasonable frequencies of the magnetic field, instabilities arise at low magnetic inductions, e.g., Bc(approximate)0.5 mT [gallium as model liquid, with radius of the cylinder R=12.5 mm, aspect ratio (h/d)=2 and frequency f=50 Hz]. As a source of instabilities Taylor vortices have been identified. They are transported by the secondary flow, emerging in finite cylinders due to the imbalance of pressure gradient and centrifugal force close to the top and bottom, thus generating time-dependent flow. Their generation is statistical and manifests itself in, e.g., nonperiodic temperature oscillations with small amplitudes in a classical Bénard configuration. Furthermore the intensity of the secondary flow was investigated for the isothermal case to give hints on its general influence on the overall mass transport. © 1998 American Institute of Physics.

Notes: An experimental study of turbulent primary breakup at the free surface of plane liquid wall jets along smooth walls in still air at normal temperature and pressure is described. The study seeks a better understanding of spray formation processes in marine environments, such as in bow sheets. The measurements involved initially nonturbulent annular liquid wall jets, to approximate plane liquid wall jets, with the growth of a turbulent boundary layer along the wall initiated by a trip wire. Pulsed shadowgraphy and holography were used to observe liquid surface properties as well as drop sizes and velocities after turbulent primary breakup. Test conditions included several liquids (water, glycerol mixtures and ethyl alcohol), liquid/gas density ratios of 680–980, wall jet Reynolds numbers of 17 000–840 000 and Weber numbers of 6 100–57 000, at conditions where direct effects of liquid viscosity were small. Measurements included the following: location of the onset of surface roughness, drop size and velocity distributions after breakup, flow properties at the onset of breakup, and mean drop sizes and velocities after breakup. In general, the measurements were correlated successfully based on phenomenological theories. © 1998 American Institute of Physics.

Notes: In this paper we examine how the flow in the wall region can be predicted from realistic (partial) measurements. The underlying motivation of this study is the improvement of control schemes for near-wall flows. We propose a method based on the proper orthogonal decomposition which provides estimated amplitudes for the coherent structures (i.e., the large scales) of the flow from wall measurements. The method is tested for the direct numerical simulation of a minimal flow unit. The large scales obtained by reconstruction from wall data are compared to those of the velocity field in the wall layer. The dominant structures—the streamwise streaks—are well recovered, the cross-stream motions less so since they are associated with higher-order structures unaccounted for in our truncation. We defined "rescaled" eigenfunctions to try to improve the representation of the cross-stream components of the flow. Aliasing effects due to realistic (large) sensor spacings were examined. We find that the spanwise spacing is the limiting factor for the estimation, so that a realistic grid will affect the reconstruction by at least 20% compared to full wall information. © 1998 American Institute of Physics.

Notes: Numerical experiments have been performed to study the geometric collision rate of heavy particles with finite inertia. The turbulent flow was generated by direct numerical integration of the full Navier-Stokes equations. The collision kernel peaked at a particle response time between the Kolmogorov and the large-eddy turnover times, implying that both the large-scale and small-scale fluid motions contribute, although in very different manners, to the collision rate. Both numerical results for frozen turbulent fields and a stochastic theory show that the collision kernel approaches the kinetic theory of Abrahamson [Chem. Eng. Sci. 30, 1371 (1975)] only at very large τp/Te, where τp is the particle response time and Te is the flow integral time scale. Our results agree with those of Sundaram and Collins [J. Fluid Mech. 335, 75 (1997)] for an evolving flow. A rapid increase of the collision kernel with the particle response time was observed for small τp/τk, where τk is the flow Kolmogorov time scale. A small inertia of τp/τk=0.5 can lead to an order of magnitude increase in the collision kernel relative to the zero-inertia particles. A scaling law for the collision kernel at small τp/τk was proposed and confirmed numerically by varying the particle size, inertial response time, and flow Reynolds number. A leading-order theory for small τp/τk was developed, showing that the enhanced collision is mainly a result of the nonuniform particle concentration that results from the interaction of heavy particles with local flow microstructures. © 1998 American Institute of Physics.

Notes: Vorticity is deposited baroclinically by shock waves on density inhomogeneities. In two dimensions, for a planar "slow–fast" interface, we present analytical results for σ, the circulation deposited per unit unshocked interface length, within the regular refraction regime. The parameters that describe the interaction are the Mach number (M), the density ratio of the two gases (η, η〈1), the local angle between the shock and the interface (α), and the ratio of specific heats of the two gases (γ0,γb). For weak shocks σ scales as σ∝(1−η−1/2)ξ(M)sin α and for strong shocks σ→K(η,α,γ)/(1−ξ(M)). For scaling purposes, the gases are assumed to have the same γ. K(η,α,γ) is a function of the density ratio, the interface angle, and the ratio of specific heats γ [Eq. (4.6)] and ξ(M) is the normalized pressure gradient across the shock. The planar interface approach is used to find formulas to calculate the total circulation deposited on sinusoidal interfaces. To validate the formulas, numerical simulations of the compressible Euler equations were made using a second-order Godunov code. Simulations were done for 1.05≤M≤3.0 and η=0.14, 0.33 and 0.65. © 1998 American Institute of Physics.

Notes: Mixing enhancement results are presented for compressible (convective Mach number 0.63) planar shear layers perturbed by 2D and 3D disturbances located within the supersonic-side splitter tip boundary layer. The disturbances were parametrically varied in shape, spacing, and thickness, and for each geometry time-resolved end-, side-, and plan-view visualizations of mixed fluid were obtained. The mixing layer thickness and growth rate are measured directly from the averaged images. As an indicator of the pressure loss induced by each disturbance geometry, the streamwise static pressure distribution is also recorded. The visualizations reveal that discrete 3D disturbances induce appreciable spanwise convolution, streamwise structure, and thickening of the mixing layer with disturbances as thin as 5% of the boundary layer displacement thickness. The optimal disturbance appears to have an angle of 30° to the streamwise direction and be located at the splitter tip, rather than upstream. Panoramic side-views show that the far-field growth rate increases (45% in one case) for certain discrete 3D disturbances but not 2D disturbances, despite equivalent area blockage. For the most promising geometry, quantitative measurements of the mixing layer thickness, probability of mixed fluid, and mixing efficiency were made using cold chemistry planar laser-induced fluorescence. The perturbed layer shows a slight improvement (7%) in mixing efficiency and a large increase (48%) in layer thickness, indicating that gains in the total amount of mixed fluid occur primarily by layer thickening. © 1998 American Institute of Physics.

Notes: In rimming flow, a thin film of viscous liquid is entrained on the inside of a horizontally rotating cylinder. We give an explicit criterion for determining whether or not shock solutions occur and show that the location and height of these shocks can be determined using a simple lubrication theory. © 1998 American Institute of Physics.

Notes: We study the dynamics of a compound liquid drop which is comprised of an outer membrane surface, a shell layer, and a core. The deformation due to an imposed extensional flow and the subsequent recovery are investigated computationally employing a combined Eulerian–Lagrangian technique. The numerical method allows for large viscosity and capillarity differences between layers. The present study reports several findings which provide direct insight into developing a dynamic model for leukocytes. A compound drop behaves like a homogeneous, simple liquid drop if the core is sufficiently deformed and the time scale of the core, related to the combination of its viscosity and capillarity, is comparable to that of the shell layer. Disparate time scales between the core and shell layer result in a rapid initial recoil of the drop during which the shell fluid is the primary participant in the hydrodynamics, followed by a slower relaxation period during which the core and shell layer interact with each other. Consequently, the apparent viscosity of the drop depends not only on the rheological properties of the drop, but also on the flow dynamics surrounding it. The findings obtained with the three-layer compound drop model can explain several main characteristics of leukocytes reported in the literature. Furthermore, our study suggests that unless the presence and possible deformation of the nucleus are explicitly accounted for, neither Newtonian nor non-Newtonian models for leukocytes can adequately predict the hydrodynamics of leukocytes. © 1998 American Institute of Physics.

Notes: We study the linear stability of a fluid to double-diffusive convection in the case for which the background temperature field is linear, but the mean salt distribution is a nonlinear function. A variety of idealized limits amenable to perturbative treatment are examined, and a detailed numerical study of a hyperbolic tangent profile is presented. It is shown that nonlinearity in the background salinity profile leads to pronounced competition and interaction between the linear normal modes. © 1998 American Institute of Physics.

Notes: The aim of the present paper is to study three-dimensional elliptic instability in two-dimensional flattened Taylor–Green vortices, which constitutes a model problem for the topics of wake vortex dynamics. Shortwave asymptotics and classical linear stability theory are developed. Both approaches show that the flow is unstable. In particular, the structure of the most amplified growing mode is the same as that obtained in unbounded elliptical flows. The limits of the linear regime and the effects of the nonlinear interactions are characterized by means of a spectral Direct Numerical Simulation (DNS). © 1998 American Institute of Physics.

Notes: Instantaneous velocity measurements in a gaseous mixture arising from the shock wave-induced Richtmyer–Meshkov instability are conducted for the first time in a shock tube. Laser Doppler anemometry gives us the evolution of the axial velocity fluctuations of the mixing zone, before and after its interactions with reflected shock waves from the shock tube end wall. Experimental results demonstrate that a turbulent mixing zone is generated by the incident shock wave. Afterwards, the axial variance decreases before being amplified by the first reshock interaction through a baroclinic effect. Before the second reshock arrival, we measure once again a decrease of the turbulence level which is explained by both diffusion and dissipation. © 1998 American Institute of Physics.

Notes: 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. © 1998 American Institute of Physics.

Notes: Previous long-wavelength analyses of capillary breakup of a viscous fluid thread in a perfectly inviscid environment show that the asymptotic self-similar regime immediately prior to breakup is given by a balance between surface tension, inertia, and extensional viscous stresses in the thread. In contrast, it is shown here that if viscosity in the external fluid, however small, is included then the asymptotic balance is between surface tension and viscous stresses in the two fluids while inertia is negligible. Scaling estimates for this new balance suggest that both axial and radial scales decrease linearly with time to breakup, so that the aspect ratio remains O(1) with time but scales with viscosity ratio like (μint/μext)1/2 for μint(very-much-greater-than)μext, where μint and μext are the internal and external viscosities. Numerical solutions to the full Stokes equations for μint=μext confirm the scalings with time and give self-similar behavior near pinching. However, the self-similar pinching region is embedded in a logarithmically large axial advection driven by the increasing range of scales intermediate between that of the pinching region and that of the macroscopic drop. The interfacial shape in the intermediate region is conical with angles of about 6° on one side and 78° on the other. © 1998 American Institute of Physics.

Notes: The behavior of small liquid drops, hanging from a circular disk and approaching a pool surface of the same liquid at different temperatures, is studied experimentally and numerically. The experiments show that if isothermal conditions prevail the drop is immediately engulfed by the liquid. On the contrary, if the temperature of the drop is sufficiently larger or sufficiently smaller than the temperature of the liquid surface, this engulfment is prevented even if the drop is pressed on the liquid surface and "enters" the liquid pool. A number of experiments have been carried out on silicone oils (with different viscosities). At the same time the problem was studied numerically with the assumption that a thin air film is formed between the drop and the liquid bath surface, due to the entrainment of the surrounding air caused by the Marangoni flow; the pressure in the air film balances the pressure necessary to keep the drop submerged in the liquid bath. The critical temperature differences for the drop engulfment are determined experimentally. A parametric numerical analysis is performed to determine the influence of the viscosities of the liquids. The experimental findings are correlated by computed critical temperature differences. A sufficient agreement is found between numerical and experimental results. © 1998 American Institute of Physics.

Notes: Steady-state Burgers turbulence supported by white-in-time random forcing at low wave numbers is studied analytically and by computer simulation. The peak of the probability distribution function (pdf) Q(ξ) of velocity gradient ξ is at ξ=O(ξf), where ξf is a forcing parameter. It is concluded that Q(ξ) displays four asymptotic regimes at Reynolds number R(very-much-greater-than)1: (A) Q(ξ)∼ξf−2ξexp(−ξ3/3ξf3) for ξ(very-much-greater-than)ξf (reduction of large positive ξ by stretching); (B) Q(ξ)∼ξf2|ξ|−3 for ξf(very-much-less-than)−ξ(very-much-less-than)R1/2ξf (transient inviscid steepening of negative ξ); (C) Q(ξ)∼|Rξ|−1 for R1/2ξf(very-much-less-than)−ξ(very-much-less-than)Rξf (shoulders of mature shocks); (D) very rapid decay of Q for −ξ≥O(Rξf) (interior of mature shocks). The typical shock width is O(1/Rkf). If R−1/2(very-much-greater-than)rkf(very-much-greater-than)R−1, the pdf of velocity difference across an interval r is found to be P(Δu,r)∝r−1Q(Δu/r) throughout regimes A and B and into the middle of C. © 1998 American Institute of Physics.

Notes: We consider the case of a test sphere (ball) of radius a1 rotating at constant angular velocity ω in an otherwise quiescent unbounded suspension of uniformly sized spheres of radii a2 dispersed in a Newtonian fluid of viscosity μ. To the first order in the volume fraction c of suspended spheres it is shown that when the ball is small compared with the suspended spheres the suspension does not behave as regards the hydrodynamic torque L exerted on the ball like a homogeneous Newtonian fluid characterized by the usual Einstein viscosity coefficient μs=μ(1+5/2c). Explicitly, the torque on the rotating sphere does not obey Kirchoff's law, L=8πμsa13ω for no slip. Rather, a modified form of Kirchoff's law is obtained in which the Einstein coefficient of 5/2 is multiplied by a coefficient which is less than unity in magnitude and is functionally dependent only upon the suspended-sphere/test-sphere size ratio, λ=a2/a1. In the "continuum limit," where λ tends to zero, one recovers Kirchoff's law. Accordingly, the deviation from Kirchoff's law is interpreted in terms of an apparent Knudsen-like "slip" at the rotating ball surface since this slip vanishes in the continuum limit. The existence of an apparent slip is consistent with recent experiments performed on small rotating spheres, albeit in concentrated suspensions, in which the "viscosity" of the suspension—defined via Kirchoff's law in terms of the experimentally measured torque L as L/8πa13ω—was observed to be less than the viscosity of the suspension as measured by standard viscometric methods. Similar, although quantitatively different O(c) theoretical Knudsen-like slip results were also obtained for the "inverse" case, where the torque L on the rotating ball is held constant for all time and its mean angular velocity calculated. © 1998 American Institute of Physics.

Notes: In the present work, a fine, dry powder was sheared in a Couette device: i.e., sheared between concentric vertical cylinders. The torque generated on the rough, inner cylinder was measured as this inner wall was rotated. Our experiments provided evidence that, in a column of granular material undergoing continuous shearing, normal and shear stresses increase linearly with depth. In other words, Janssen's analysis ceases to apply if granular material is continuously sheared. © 1998 American Institute of Physics.

Notes: The strong dependence of the rheology of a fluid on temperature has a great impact on the style of thermally driven convection. When the viscosity contrast is sufficiently large, the viscosity of the coldest fluid at the top of a bottom-heated box is so high that this fluid layer becomes very stiff and a so-called cold "stagnant lid" develops on top of a hot convecting layer. Studying this style of convection is relevant for planetary mantles since the rheology of mantle material is likely to be very strongly temperature dependent. In this paper, the Rayleigh number dependence of stagnant-lid convection with a viscosity contrast of 106 is studied numerically in two and three dimensions in wide Cartesian domains. Like in constant-viscosity cases, the convection in the layer underneath the stagnant lid undergoes the typical transition from steady to time-dependent with the thinning of plumes and with the appearance of boundary layer instabilities as the Rayleigh number increases. A stagnant-lid style of convection was obtained in 2D and 3D for all supercritical Rayleigh numbers considered and the interior temperature appeared not to depend on the Rayleigh number. We have compared our results with other theoretical and numerical results and we found a close agreement. © 1998 American Institute of Physics.

Notes: A typical experimental vortex generator was perturbed by inclining the exit orifice. Instantaneous velocity fields were measured with particle image velocimetry at a Reynolds number, Γ0/ν, of 2800, which falls in the laminar regime for the axisymmetric case. Despite the nearly uniform velocity of the axisymmetric piston, the velocity exiting the cylinder is spatially and temporally non-uniform. Specifically, the exit velocity and the entrainment are larger on the short cylinder side. This fluid motion leads to an initial vortex roll-up with maximum and minimum circulation at the shortest and longest cylinder locations, respectively. A highly complex vortex structure forms, consisting of a primary vortex ring with varying circulation and branched vortex tubes that initially extend from the primary ring upstream toward the cylinder. The variation of the circulation in the primary ring and the strength of the branched vortex tubes increase with incline angle. The branched vortex tubes induce a strong cross-stream sweep of fluid toward the long cylinder side. The branched tubes convect across the cylinder exit with the sweep, break free of the cylinder, and pass through the primary ring. Beyond this time, the vortex structure consists of two closed-loop branches connected on the short cylinder side. As the flow progresses, the center of momentum moves toward the short cylinder side. As the cylinder incline angle is increased, the migration away from the centerline increases, and the flow becomes increasingly disorganized. The propagation speed and penetration distance are reduced because of the loss of coherent circulation. Qualitatively similar velocity fields and flow visualization photographs are presented for a larger (nominally turbulent) Reynolds number of 23000.© 1998 American Institute of Physics.

Notes: The structural features of turbulence at the free surface of a channel flow have been experimentally investigated. The experiments were conducted in a horizontal channel of large aspect ratio in the (depth based) Reynolds number range of 2800–8800. The results indicate that the persistent structures on the free surface can be classified as upwellings, downdrafts, and spiral eddies. Upwellings are shown to be related to the bursts originating in the sheared region at the channel bottom and the eddies are seen to be generated at the edges of the upwellings. The eddies often merge if rotating in the same direction, and form "pairs" if rotating in opposite directions—though there are occasional mergers of such counter-rotating ones. The spiral eddies decay slowly and are sometimes annihilated by fresh upwellings. The population densities and the persistence times of the various structures were measured for different flow conditions. The resulting data show that the physical parameters characterizing the structures at the interface, scale with a mix of inner (wall shear stress and viscosity) and outer variables. Measurement of the streamwise and spanwise velocities at the free-surface were made by particle imaging velocimetry (PIV) and the surface normal velocity near the free-surface estimated by continuity. The results indicate that the upwellings and spiral eddy regions would be expected to dominate scalar transport rates at high Prandtl/Schmidt numbers. The one-dimensional energy spectra of the flow field at the free-surface compare well with direct numerical simulations and show a region with −5/3 slope at low wave numbers. This experimentally confirms a previous result regarding the two-dimensionality of turbulence near the free surface, based on numerical simulations by Pan and Banerjee [Phys. Fluids 7, 1649 (1995)]. © 1998 American Institute of Physics.

Notes: The turbulent regime of a Rayleigh–Bénard convective flow is studied through the analysis of temporal series and three-dimensional data fields obtained by direct numerical simulations. Numerical probes are positioned in the homogeneous (in the center) and non–homogeneous (close to the boundaries) turbulence regions of the cell and the corresponding data are obtained at low Prandtl (Pr=0.022) for a range of Rayleigh numbers 5×104≤Ra≤106. We discuss the dependence upon the Rayleigh number of some quantities characterizing the turbulence in the low and high frequency range such as length scales, dissipation and flow isotropy. The analysis of the velocity and vorticity spectra indicates that, in the center of the cell, the turbulence remains locally isotropic for the whole range of Ra considered. Furthermore, the dynamics of the large convective cell and the turbulence parameters, depend upon Ra in a manner consistent with experimental results at higher Ra. In conclusion, none of the indicators considered supports the idea of a transition in the turbulent state (often referred to as the soft–to–hard turbulence transition). © 1998 American Institute of Physics.

Notes: We investigate the stability of a straight vortex tube of constant vorticity in the presence of external shearing and straining flows orthogonal to the axis of the vortex tube. We find that the tube is unstable at degenerate wavenumbers (i.e., wavenumbers at which two Kelvin wavemodes have the same frequency). The maximum growth rate of the instability is weighted by the sum of the shear magnitude and the strain magnitude. The presence of the shear also shifts the wavenumber of the instability. © 1998 American Institute of Physics.

Notes: The dynamic procedure is applied to the problem of modeling the subgrid-scale variance and dissipation rate of a conserved scalar in large eddy simulations of turbulent reacting flows. A simple scaling relation for the subgrid-scale variance is proposed, and the coefficient of the scaling law is obtained using the dynamic procedure. The variance dissipation rate is modeled by assuming equilibrium with the local variance production rate, which is obtained using a dynamic model. Example model predictions are obtained using actual large eddy simulation data, and the subgrid variance predicted by the dynamic model is compared to results obtained using a scale similarity model. Generalization of the approach to multiple scalars and nonconserved scalars is briefly discussed. © 1998 American Institute of Physics.

Notes: The flow of two viscous liquids is investigated numerically with a volume of fluid scheme. The scheme incorporates a semi-implicit Stokes solver to enable computations at low Reynolds numbers, and a second-order velocity interpolation. The code is validated against linear theory for the stability of two-layer Couette flow, and weakly nonlinear theory for a Hopf bifurcation. Examples of long-time wave saturation are shown. The formation of fingers for relatively small initial amplitudes as well as larger amplitudes are presented in two and three dimensions as initial-value problems. Fluids of different viscosity and density are considered, with an emphasis on the effect of the viscosity difference. Results at low Reynolds numbers show elongated fingers in two dimensions that break in three dimensions to form drops, while different topological changes take place at higher Reynolds numbers. © 1998 American Institute of Physics.

Notes: Diffusion flame (DF) attachment and liftoff are examined, leading to (1) explanations of the origins of previous, successful empirical correlations; (2) the discovery of multiple lifting regimes. The latter includes a very slow flow regime, a slow-to-moderate flow regime, and a moderate-to-fast flow regime. Formulas for liftoff height (l(circumflex)g) and characteristic flame tip breadth (l(circumflex)r) are developed from a combination of the differential and integral form of the conservation equations. These formulas are compared with numerical solutions of the same equations. © 1998 American Institute of Physics.

Notes: We have studied experimentally the effects of an unstable linear density profile on the evolution of homogeneous grid-generated turbulence. The experiments were performed in a thermally stratified wind tunnel employing hot- and cold-wire anemometry. The unstably stratified air stream was passed through a biplanar grid and the down-stream evolution of the turbulence statistics were studied. Contrary to the stably stratified case, where vertical velocity fluctuations are inhibited, here the buoyancy forces feed energy into the vertical motions. This injection at the actively turbulent length scales continues up to a critical time at which large-scale overturning of the entire fluid volume occurs. This overturn is due to the Rayleigh–Benard-type instability, which is manifest in the mean temperature field by a large plume rising up from the tunnel floor at the centerline. During the viscous decay, downstream of the grid, the r.m.s. vertical velocity fluctuations are relatively enhanced becoming 1.45 times the stream-wise fluctuations, before this overturn. The normalized buoyancy flux is also enhanced by the destabilizing buoyancy forces, reaching values as large as 0.88, significantly larger than those observed in the passively stratified case. Spectral ratios identify the length scales most affected. Results for different grid mesh-sizes show that the statistics are Reynolds number independent over the range of values studied here, i.e., Reλ between 21 and 66. The probability density functions of temperature and velocity remain Gaussian in the homogeneous region. As the large-scale overturn takes over the flow, the scalar and velocity fluctuations are enhanced dramatically and qualitative changes are observed in the pdf of the temperature fluctuations. © 1998 American Institute of Physics.

Notes: Flows under the influences of environmental rotation and stable density stratification often exhibit an approximate force balance and a consequently slow rate of evolution at large Reynolds number. Such flows are typically anisotropic in their velocity field. This regime is relevant to large-scale motions in the Earth's atmosphere and ocean, as well as many other planetary and astrophysical systems. The Balance Equations are usually an accurate approximate model for this regime. However, they have solvability limits associated with a change of type in their time-integration operator. In this paper we derive these limiting conditions for the conservative Balance Equations in isentropic coordinates, show that the least familiar of these conditions coincides with loss of convexity of the streamfunction for horizontal velocity in the inertial reference frame, and identify these conditions with the general conditions for symmetric loss of stability for circular and parallel flows as well as for the three-dimensional loss of stability for elliptical flows. We then conjecture that the identified limits of balance coincide generally with the boundary between the distinctive nonlinear dynamical behaviors (i.e., their turbulent cascade and dissipation rates) associated with the large- and small-scale regimes in geophysical and astrophysical flows. © 1998 American Institute of Physics.

Notes: Mixing processes in gravity current fronts have only recently been quantified due to their complex, unsteady nature. The similarity of the mixing processes in these pioneer works, however, has not been explored adequately. Experiments that explore a wide range of fronts have been performed. These experiments have used techniques that exhaustively sample the temporal (using a high-speed conductivity probe) and spatial (using planar laser-induced fluorescence) density field more thoroughly than any previous work. Both types of experiments have confirmed earlier research suggesting that low Reynolds number fronts mix differently and less than higher Reynolds number flows. Similarity appeared to be achieved for Req〉1000, where Req is a Reynolds number based upon the cube root of the buoyancy flux into the front and the height of current. It appears that certain secondary mixing processes, seen by other researchers studying stratified mixed layers, are responsible for the earlier changes seen with Reynolds number and cause significant mixing at the front. © 1998 American Institute of Physics.

Notes: We present criteria for monitoring the validity of the Navier–Stokes approximation during the simulation of a rarefied gas. Our approach is based on an underlying kinetic formulation through which one can construct nondimensional non-negative definite matrices from moments of the molecular distribution. We then identify one such 3×3 matrix that can be evaluated intrinsically in the Navier–Stokes approximation. Our criteria are based on deviations of the eigenvalues of this matrix from their equilibrium value of unity. Not being tied to a particular benchmark problem, the resulting criteria are portable and may be applied to any Navier–Stokes simulation. We study its utility here by comparing stationary planar shock profiles computed using the Navier–Stokes equations with those computed using Monte Carlo simulations. © 1998 American Institute of Physics.

Notes: The departure from Kolmogorov (1941) scaling of high-order moments of longitudinal velocity increments in a fully developed turbulent channel flow is investigated using data obtained with hot wire anemometry (HWA), laser Doppler velocimetry (LDV) and direct numerical simulation (DNS). The magnitude of the departure increases towards the wall, reaching a local maximum at a distance of about 20 wall units. © 1998 American Institute of Physics.

Notes: The granular flow through an open silo is investigated experimentally. A mechanism based both on the dilation of the granular medium and an interaction with the interstitial gas causes the flow to stop at regular intervals. The experiments are carried out at different surrounding pressures P0, and it is found that the intermittent flow becomes continuous at sufficiently low P0, showing that the intermittency is linked to the interaction the gas. The scaling of the average flow rate with particle size further supports our view of the gas-grain interaction. © 1998 American Institute of Physics.

Notes: We consider small disturbances to the steady viscous flow between concentric rotating circular cylinders. It is shown that as the dimensionless gap width δ approaches zero the terms from ∂/∂θ in the governing equations are O(δ1/2) and so do not appear in the first approximation. This is in contrast to the classical small-gap approximation, in which terms from ∂/∂θ do appear in the first approximation. Here θ is the usual azimuthal angle. Let ε be a measure of the size of the small perturbation. In Sec. III it is argued that the asymptotic relation ε∼δ2 is needed to obtain a correct approximation to weakly nonlinear axisymmetric (Taylor-vortex) equilibrium flow for small values of δ. We use this relation between ε and δ to obtain a unified amplitude equation to describe both axisymmetric modes and those with a general dependence on the azimuthal angle, taking into account weakly nonlinear effects. This allows a description of single-mode equilibrium states and of their stability. Some unexpected results are obtained about the stability of these modes. The mode with m=0 is shown to be stable for all relevant values of the Taylor number T. This is to be expected under the particular limiting process used. However the modes with m=1, 2, and 3 are shown to become stable for successively higher values of T. It is also shown that these nonaxisymmetric equilibrium states may be obtained by the solution of some initial value problems, thus leaving open the possibility of attaining wavy disturbances by a different method than the usual one of instability of Taylor vortices. © 1998 American Institute of Physics.

Notes: We present a numerical investigation of the linear response of a turbulent flow to a perturbation at large scale. In the incompressible case, we show that part of the small scale action corresponds to the standard turbulent viscosity, but that there are also other terms which are important for the system dynamics and which do not reduce to a simple turbulent viscous effect. In the compressible case, we show that the small scales of the turbulent flow create a turbulent pressure force which resists compression. An adiabatic index is estimated for this pressure and is found to decrease with time scale, from a strongly adiabatic behavior down to a subisothermal behavior. © 1998 American Institute of Physics.

Notes: An extensive experimental study of the two-dimensional inverse energy cascade is presented. The experiments are performed in electromagnetically driven flows, using thin, stably-stratified layers. Complete instantaneous velocity fields are measured using particle imaging velocimetry techniques. Depending on the bottom-wall friction, two different regimes are observed: when the friction is low, the energy transferred from the forcing scale towards large scales accumulates in the lowest accessible mode, leading to a mean rotation of the flow and to an energy spectrum displaying a sharp peak at the minimum wave-number. This condensation is accompanied by the emergence of a very strong vortex around which the rotation is organized. At higher frictions, the inverse energy cascade conjectured by Kraichnan [Phys. Fluids 10, 1417 (1967)] is observed and is found to be stationary, homogeneous and isotropic, with a Kolmogorov constant consistent with numerical estimates. This inverse cascade does not appear to be characterized by the presence of strong coherent vortices. The characteristic size of the latter is of the order of the injection scale. Their statistical properties tend to show that the cascade is rather driven by a clustering mechanism involving same sign vortices rather than a sequence of merging events producing larger and larger vortices. Intermittency effects are also investigated for the inverse cascade range. It is found that, within experimental errors, there is no intermittency in the inverse cascade range of two-dimensional turbulence and that the statistics of velocity increments, either longitudinal or transverse, are close to Gaussian. These results constitute the first experimental study of intermittency in two-dimensional turbulence as well as the first observation of normal scaling in a field of research which has been increasingly concerned with anomalous exponents. © 1998 American Institute of Physics.

Notes: Standing and propagating plane waves in a rigidly rotating stably stratified fluid are considered. Based on a WKB analysis, it is shown numerically that almost all of them are unstable with respect to three-dimensional short-wavelength perturbations. The waves whose wavenumber vector is parallel to the axis of rotation and stratification are stabilized as the Brunt-Väisälä frequency N (normalized by the angular velocity of rigid rotation) increases, whereas the inclined waves are unstable at any N. These instabilities are caused by parametric resonances of low order (first and second) and the instability growth rate is determined theoretically, when the wave amplitude is small. © 1998 American Institute of Physics.

Notes: The rarefied gas flow between two coaxial cylinders caused by the evaporation and condensation on their surfaces is investigated on the basis of the kinetic and hydrodynamical equations. It is assumed that the cylinders may rotate with equal angular velocity. The equilibrium is perturbed by the small density difference of evaporated particles on the inner cylinder. The hydrodynamical equation has been solved analytically and the kinetic equation has been solved by the discrete velocity method modified for the discontinuous distribution function. The fields of the density, the velocity and the temperature are presented for a wide range of the Knudsen number. An analysis of the influence of the rotation of the cylinders on the flow field is given. © 1998 American Institute of Physics.

Notes: Recent experimental results [J. Fluid Mech. 345, 45 (1997)] for long-wavelength surface-tension-driven rupture of thin liquid layers (∼0.01 cm) found the onset for significantly smaller imposed temperature gradients than predicted by linear stability analyses that assume an initially flat interface with periodic boundary conditions. The presence of sidewalls and other aspects of the experiment, however, led to deformed interfaces even with no imposed temperature gradient. These sidewall effects were not due to a small system size since experiments with aspect ratios as large as 450 were significantly affected. The stability analysis presented here takes into account the effects of the deformed interface profile and shows that these effects account for some of the disagreement between experiment and theory. In addition, deviations from standard linear stability theory caused by these effects have the same qualitative behavior as the deviations seen in the experiments. © 1998 American Institute of Physics.

Notes: In this Brief Communication, we report a new finding on a Taylor–Couette flow in which the outer cylinder is stationary and the inner cylinder is accelerated linearly from rest to a desired speed. The results show that when the acceleration (dRe/dt) is higher than a critical value of about 2.2 s−1, there exists a new flow regime in which the flow pattern shows remarkable resemblance to regular Taylor vortex flow but is of shorter wavelength. However, when the acceleration is lower than 2.2 s−1, a wavy flow is found to occur for the same Reynolds number range. To our knowledge, this is probably the first time that such a phenomenon has been observed. For completeness, the case of a decelerating cylinder is also investigated, and the results are found to be almost the same. © 1998 American Institute of Physics.

Notes: In the publication by Hu and Mei [Phys. Fluids 10, 1028 (1998)] a correction to the collision formula is described for like particles within a given size category. Here we show that the formula derived by Sundaram and Collins (1997) is already consistent with Hu and Mei (1998) and so their correction does not apply. © 1998 American Institute of Physics.

Notes: A mechanism by which smooth initial conditions evolve towards a topological reconfiguration of fluid interfaces is studied in the context of Darcy's law. In the case of thin fluid layers, nonlinear PDEs for the local thickness are derived from an asymptotic limit of the vortex sheet representation. A particular example considered is the Rayleigh–Taylor instability of stratified fluid layers, where the instability of the system is controlled by a Bond number B. It is proved that, for a range of B and initial data "subharmonic" to it, interface pinching must occur in at least infinite time. Numerical simulations suggest that "pinching" singularities occur generically when the system is unstable, and in particular immediately above a bifurcation point to instability. Near this bifurcation point an approximate analytical method describing the approach to a finite-time singularity is developed. The method exploits the separation of time scales that exists close to the first instability in a system of finite extent, with a discrete spectrum of modes. In this limit, slowly growing long-wavelength modes entrain faster short-wavelength modes, and thereby, allow the derivation of a nonlinear evolution equation for the amplitudes of the slow modes. The initial-value problem is solved in this slaved dynamics, yielding the time and analytical structure of a singularity that is associated with the motion of zeros in the complex plane, suggesting a general mechanism of singularity formation in this system. The discussion emphasizes the significance of several variational principles, and comparisons are made between the numerical simulations and the approximate theory. © 1998 American Institute of Physics.

Notes: The stability of a two-fluid boundary layer is investigated. A boundary layer shears a second fluid that is bounded by the wall and the shearing fluid. The eigenvalue problem governing the linear stability of the configuration is solved using an efficient shooting-search method. Besides the Tollmien-Schlichting mode (hard mode) found in the classical hydrodynamical stability theory an additional Yih-mode (interfacial mode) exists due to the two-fluid interface. Effects of viscosity and density stratifications, thickness of the bounded fluid, gravity, surface tension as well as the non-Newtonian character of the lower fluid on the stability characteristics are determined. The interfacial mode is found to be very sensitive against viscosity stratification. However, with a highly viscous liquid layer, the system approaches a single-layer behavior. The shear-thinning non-Newtonian liquid layer is observed to have a stabilizing effect for both of the modes. Surface tension is stabilizing for short waves for the interfacial mode but a more complex effect was observed for the hard mode. Gravity is stabilizing with a favorable density stratification. Density stratification alone is destabilizing for low and moderate values of this parameter but becomes stabilizing for higher values. When the external boundary layer profile is turbulent, the interfacial mode is more likely to be observed in an experiment. Agreement of the obtained results with experimental, theoretical and numerical results reported in the literature is good. This is encouraging as the study is intended for solving the stability characteristics of de/anti-icing fluid-air systems and comparing the results with the experimental data when they become available. © 1998 American Institute of Physics.

Notes: It is known that streaming can be generated in a liquid bridge by vibrating an end wall. This phenomenon has been used in an attempt to minimize thermocapillary flow during crystal growth in a floating zone, by inducing such a streaming running in the opposite direction to it [Grugel et al., J. Cryst. Growth 142, 209 (1994)]. In the present theoretical study, the nature of this streaming and its effects on the average flow and temperature fields in a floating zone are investigated. It is noticed that in the experiment, the applied frequencies were high enough such that the corresponding wavelengths of the capillary ripples were much smaller than the dimensions of the zone. It is believed that the ripples were a traveling wave that generated the streaming in the direction of the wave propagation as a result of Stokes drift. For such a wave to be traveling, it must be dissipated sufficiently by viscosity upon reaching the other wall to guarantee negligible reflection there. Accordingly, a model is formulated to study the reduction of thermocapillary flow in a floating zone by means of streaming. It is found that for a half zone, streaming can minimize the thermocapillary flow near the vibrating wall and make the temperature uniform across the zone there. For a full zone, streaming can minimize the flow but cannot make the temperature uniform near the wall. For a long full zone, streaming can similarly minimize the flow. But in addition, the temperature near each wall is uniform with or without streaming. © 1998 American Institute of Physics.

Notes: The problem of the rotatory oscillation of an axi-symmetric body in an axi-symmetric, viscous, incompressible flow at low Reynolds number has been studied. In contrast to the steady rotation of a body, which involves solving the Laplace equation, the study of an oscillating body requires solution of the Helmholtz equation which results from the simplification of the unsteady Stokes equations. In the present work, we have numerically evaluated the local stresses and torques on a selection of free, oscillating, axi-symmetric bodies in the continuum regime in an axi-symmetric viscous incompressible flow. The Helmholtz equation was solved by a Green's function technique. The accuracy of the technique is tested against known solutions for a sphere, a prolate spheroid, a thin disk, and an infinitely long cylinder. Good agreements have been obtained. Finite cylinders have been studied and the edge correction factors for the circular disk geometry, that are basic to oscillating disk viscometers, have been calculated. It has been found that the calculated edge correction factors, based on the ratios of the real parts of the actual torques (calculated from this work) to the ideal torques, agree to within 1% to 10% with the reported values obtained by Clark et al. [Physica A 89, 539 (1977)] using the theory of Kestin and Wang [J. Appl. Mech. 24, 197 (1957)]. However, since the ratios of the real parts and the ratios of the imaginary parts of the torques do not coincide, the edge correction factors depend upon which ratio is used. © 1998 American Institute of Physics.

Notes: The advection of a passive scalar field by a rapidly decorrelating random velocity field with power-law scaling is computed by simulations in a cyclic square at resolutions of 40962 and 81922 grid points. Structure functions of the scalar field are measured and inertial-range scaling exponents are determined. The conditional mean of the scalar-field dissipation term and its moments are found. The results are compared with theoretical predictions and with other recent simulations. © 1998 American Institute of Physics.

Notes: Direct numerical simulations at 2563 resolution have been carried out to study the response of isotropic turbulence to the concurrent effects of solid-body rotation and stochastic, isotropic forcing at the large scales. Because spectral transfer to the smaller scales is weakened by rotation, energy input from forcing gradually builds up at the large scales, causing the overall kinetic energy to increase. At intermediate wave numbers the energy spectrum undergoes a transition from a limited k−5/3 inertial range to k−2 scaling recently predicted in the literature. Although the Reynolds stress tensor remains approximately isotropic and three-component, evidence for anisotropy and quasi-two-dimensionality in length scales and spectra in different velocity components and directions is strong. The small scales are found to deviate from local isotropy, primarily as a result of anisotropic transfer from the large scales. To understand the spectral dynamics of this flow, we study the detailed behavior of nonlinear triadic interactions in wave number space. Spectral transfer in the velocity component parallel to the axis of rotation is qualitatively similar to that in nonrotating turbulence; however, the perpendicular component is characterized by a much weakened energy cascade at high wave numbers and a local reverse transfer at the largest scales. The broader implications of this work are briefly addressed. © 1998 American Institute of Physics.

Notes: This work numerically investigates laminar plane twin-jet flows with side-wall confinement. Time-dependent computations on the full physical domain are performed in light of the possible emergence of flow unsteadiness and an asymmetric pattern. Of particular concern is how wall-confinement and jet momentum influence the transition of flow patterns. Results presented herein provide further insight into the complexities involving issues such as the variety of flow structure and the related bifurcations, jet–jet and jet–wall interactions, and flow instability involved in the confined twin-jet flow field. © 1998 American Institute of Physics.

Notes: In the present study we use two- and three-dimensional large-eddy simulations to examine the role of small-scale turbulence within a transitional separation bubble studied experimentally by Gaster (AGARD Conference Proceedings No. 4, 1966, pp. 813–854). In addition, several large-eddy simulation parameters and models are studied to show their effect on the computations. The inclusion of a small-scale turbulence model in the two-dimensional computations leads to an increase in the time-averaged separation bubble length and a slight reduction in the peak of the pressure coefficient distribution near reattachment. Increasing the filter width or increasing the Smagorinsky coefficient reduces the peak in the pressure coefficient distribution but also decreases the pressure coefficient within the pressure plateau. The two-dimensional LES accurately predicts the time-averaged bubble length of Gaster but does not accurately describe the experimental wall pressure distribution within the bubble. Three-dimensional LES computations allow the generation of vortex shedding and Görtler vortices within the separated region. A computation without a subgrid scale model allows the Görtler vortices to grow in strength and eliminate the boundary layer separation. The application of a subgrid scale model reduces the strength of Görtler vortices and spanwise vortex shedding. This produces a bubble size and time-averaged wall pressure distribution which compare favorably with experiment. Little difference is seen between the results using the constant coefficient and dynamic coefficient models. © 1998 American Institute of Physics.

Notes: Numerical modeling of the nonreactive mixing processes associated with a lobed fuel injector in a coflowing air stream is presented. The lobed fuel injector is a device which generates strong streamwise vorticity, producing locally high strain rates which can enhance the molecular mixing of reactants while delaying ignition in a controlled manner. Vortex element modeling is used to simulate flow field evolution and fuel element mixing characteristics for this lobed fuel injector. Quantitative predictions for vorticity generation and qualitative results for streamwise rollup compare well qualitatively with recent experimental investigations of this flow field [Smith et al., Phys. Fluids 9, 667 (1997)]. Parametric studies of the effects of lobe amplitude-to-wavelength ratio, lobe angle, and lobe shape for given flow conditions suggest that geometrical features may be optimized to enhance mixing and control reaction processes. © 1998 American Institute of Physics.

Notes: Direct Monte Carlo simulation is used to investigate the stability of a dilute freely evolving granular gas of hard disks. The boundary between stability and instability in the plane (α,L), where α is the restitution coefficient and L the size of the system, has been delineated. Instability is associated with the buildup of spatial correlations, which describes the formation of velocity vortices in the system. The simulation results are compared with theoretical predictions presented recently, and a good agreement is found. © 1998 American Institute of Physics.

Notes: We address direct simulation Monte Carlo (DSMC) implementation of phenomenological models of the rotational relaxation process suitable for an arbitrary gas mixture composed of atomic and quantized diatomic species. The macroscopic relaxation process is parametrized by a constant or temperature-dependent collision number Zr such as that of Parker [Phys. Fluids 2, 449 (1959)]. The energy redistribution properties predicted by such a model at the collision level are compared with a recent quasiclassical state-to-state model. Modified forms of the constant collision number, and thus constant relaxation probability, serial quantized Borgnakke–Larsen algorithm [Phys. Fluids A 5, 2278 (1993)] and the null collision SICS-D algorithm [Phys. Fluids A 4, 1782 (1992)] are shown to be equivalent. The generalization to an energy-dependent relaxation probability [Phys. Fluids 6, 4042 (1994)] leads to a systematic bias toward delayed relaxation, due to approximations inherent in the analytical formulation. The error induced in the predicted relaxation behavior as a function of temperature is approximately equivalent in magnitude to a previously proposed, but unrelated, correction factor [Phys. Fluids 6, 2191 (1994)], and also to the variation in the temperature-dependent Parker collision number over a wide range of conditions. Comparisons between DSMC and state-to-state calculations of the rotational distribution function in a relaxing bath quantify the microscopic limitations of the phenomenological model. Finally, a direct comparison of DSMC results with experimental shock layer measurements demonstrates that the energy-dependent relaxation model has a negligible advantage over the constant probability model when the collision number is chosen judiciously. © 1998 American Institute of Physics.

Notes: The convective flow field in a vessel is investigated by laser Doppler Anemometry (LDA) and Particle Image Velocimetry (PIV, namely Particle Tracking Velocimetry—PTV). The vessel is heated from below along a linear element at a temperature higher than that of the fluid. Hot fluid raises up and generates two counterrotating vortices. For a given aspect ratio, the two vortices become unstable and start to oscillate on a vertical plane (orthogonal to the heating element). This regime is investigated for increasing Rayleigh numbers to analyze the transition from regular to irregular conditions. The main transition mechanism is observed to be mostly connected to type II intermittency, a mechanism not frequently observed in experiments. However, at some Rayleigh numbers the present data does not definitely rule out type III intermittency. The phenomenon is analyzed by looking at the main frequencies in the spectrum of the horizontal velocity component and their changes with the Rayleigh number at a point above the heating element. Modifications in the local energy spectrum are analyzed by using the Wavelet Transform (WT) tool. Data obtained by PTV measurements make it possible to point out the spatial configuration of the flow and to determine the two velocity components on the measurement plane. These data are used to clarify the fundamental mechanisms of the transition. Instabilities are observed as sudden changes between two regimes of oscillations of the two counterrotating vortices: the first is characterized by oscillations centered on the vertical axis and the second by nonsymmetrical oscillations. © 1998 American Institute of Physics.

Notes: Forced advection of passive scalar by a smooth d-dimensional incompressible velocity in the presence of linear damping is studied. Acting separately advection and damping do not lead to an essential intermittency of the steady scalar statistics, while being mixed together produce a very strong non-Gaussianity in the convective range: 2n-th moment of scalar difference, 〈[θ(t;r)−θ(t;0)]2n〉 is proportional to rξ2n, ξ2n=min{2n,d2/4+2αdn/[(d−1)D]−d/2}, where α/D measures the rate of the damping in the units of the stretching rate. The probability density function (PDF) of the scalar difference is also found. © 1998 American Institute of Physics.

Notes: This Brief Communication presents a simple second-order differential equation extracted from experimental data, which can mimic the velocity fluctuations that are typical of bursting. The starting time series concerns the longitudinal component of turbulent velocity measured near the wall in a hydraulically smooth pipe flow. By means of standard conditional sampling techniques, we found the typical behavior of velocity fluctuations during the bursting events, to which we then applied the trajectory method in order to extract the equation of motion. The resulting equation, containing quadratic and cubic nonlinearities, follows the original time series very well, and may represent a useful starting point for the construction of more complex models of this phenomenon.© 1998 American Institute of Physics.

Notes: An analytical model for predicting the universal time scale for formation of vortex rings generated through impulsively started jets is considered. The model is based on two assumptions, namely the validity of the slug model in simulating the discharge process of the fluid out of the cylinder and the approximation of the vortex at the pinch off moment by a vortex in the Norbury family. The nondimensional stroke length L/D (referred to as "formation number," following Gharib et al. [J. Fluid Mech. 360, 121 (1998)]) predicted by the model satisfactorily matches the experimental observation of Gharib et al. The model introduces two nondimensional parameters that govern the limiting formation number: nondimensional energy End and circulation Γnd. The predicted value of End matches very well with the experimental data. It is also predicted that there is a limiting value for the nondimensional circulation in the range 1.77(approximately-less-than)Γnd(approximately-less-than)2.07. © 1998 American Institute of Physics.

Notes: Experiments on flow stability and pattern formation in Couette flow between two cylinders with highly elastic polymer solutions are reported. It is found that the flow instabilities are determined by the elastic Deborah number, De, and the polymer concentration only, while the Reynolds number becomes completely irrelevant. A mechanism of such "purely elastic" instability was suggested a few years ago by Larson, Shaqfeh, and Muller [J. Fluid Mech. 218, 573 (1990)], referred to as LMS. It is based on the Oldroyd-B rheological model and implies a certain functional relation between De at the instability threshold and the polymer contribution to the solution viscosity, ηp/η, that depends on the polymer concentration. The elastic force driving the instability arises when perturbative elongational flow in radial direction is coupled to the strong primary azimuthal shear. This force is provided by the "hoop stress" that develops due to stretching of the polymer molecules along the curved streamlines. It is found experimentally that the elastic instability leads to a strongly nonlinear flow transition. Therefore, the linear consideration by LMS is expanded to include finite amplitude velocity perturbations. It is shown that the nature of the elastic force implies major asymmetry between inflow and outflow in finite amplitude secondary flows. This special feature is indeed exhibited by the experimentally observed flow patterns. For one of the flow patterns it is also shown that the suggested elastic force should be quite efficient in driving it, which is important evidence for the validity of the mechanism proposed by LMS. Further, the predicted relation between De and ηp/η is tested. At fixed ηp/η the elastic instability is found to occur at constant Deborah number in a broad range of the solution relaxation times in full agreement with the theoretical prediction. The experimentally found dependence of the Deborah number on ηp/η also agrees with the theoretical prediction rather well if a proper correction for the shear thinning is made. This provides further support to the proposed instability mechanism. © 1998 American Institute of Physics.

Notes: In this paper numerical simulations of the irrotational fluid flow associated with the entry of circular disks of a given mass into a semi-infinite fluid domain in the limits of very low to moderate Froude numbers are reported. This work is motivated by an experimental study performed by Glasheen and McMahon who investigated the low-Froude-number water entry of circular disks and found a linear relationship between the cavity seal depth and the Froude number and also showed that a single value of a modified drag coefficient is sufficient to predict the drag force on the disk. The numerical calculations performed in this paper confirm these experimental findings for steady cavity regimes and identify the ranges of Froude number and dimensionless mass values for which these results hold. Excellent agreement between the numerical computations and analytical velocity predictions, as well as the experimental cavity seal depth measurements, are obtained although the agreement between the measured and the computed drag coefficient values is not as good. The cavity seal depth and the drag coefficient are also found to depend on the disk mass and the numerical results in this paper show that for any disk of dimensionless mass M there exists a value of the Froude number for which the cavity dynamics are steady. Also, a very low-Froude-number regime in which gravitational forces are dominant and for which the cavity dynamics are qualitatively different than for low-to-moderate-Froude-number cases is also numerically explored in this paper. Finally, a bifurcation in the cavity seal mechanism from deep seal to surface seal was found at a Froude number F=105. © 1998 American Institute of Physics.

Notes: The stability of an axisymmetric liquid bridge between unequal circular disks in an axial gravity field is examined for all possible values of the liquid volume and disk separation. The parameter defining the disk inequality is K, the ratio between the radii of the smaller and larger disks. Both axisymmetric and nonaxisymmetric perturbations are considered. The parameter space chosen to delimit the stability regions is the Λ-V plane. Here, Λ is the slenderness (ratio of the disk separation to the mean diameter, 2r0, of the two support disks), and V is the relative volume (ratio of the actual liquid volume to the volume of a cylinder with a radius equal to r0). Wide ranges of the Bond number and the ratio K are considered. Emphasis is given to previously unexplored parts of the stability boundaries. In particular, we examine the maximum volume stability limit for bridges of arbitrary Λ and the minimum volume stability limit for small Λ bridges. The maximum volume stability limit was found to have two distinct properties: large values of the critical relative volume at small Λ, and the possibility that stability is lost to axisymmetric perturbations at small values of K. For a set of K, the maximum Bond number beyond which stability of the bridge is no longer possible for any combination of V and Λ is determined. In addition, the maximum value of the actual liquid volume of a stable bridge that can be held between given disks for all possible disk separations was examined for fixed Bond number. It is found that this volume decreases as K decreases and (depending on the sign of the Bond number) tends to the critical volume of a sessile or pendant drop attached to the larger disk. © 1998 American Institute of Physics.

Notes: This paper presents a method for calculating the external inductance and mutual inductance coefficients of tokamak plasma configurations in a consistent way. The method actually solves the external equilibrium problem, linking the poloidal equilibrium fields with the value of the total plasma current and the geometric parameters that describe the plasma cross section. This link imposes constraints upon the values of the inductance for superconducting tori obtained by a previous method described by S. P. Hirshman and G. H. Neilson [Phys. Fluids 29, 790 (1986)]. Only if these constraints are properly taken into account do their results correspond to real tokamak equilibrium configurations. The present method is illustrated by calculating the external equilibrium parameters for a wide range of values of the tokamak aspect ratio. Of particular interest are the results for the external inductance, the elongation, and the vertical equilibrium field in the low aspect-ratio range A〈1.5. © 1998 American Institute of Physics.

Notes: Alfvén resonances, where the local flow speed relative to the boundary is equal to the local Alfvén speed, introduce novel dynamical features in a differentially rotating plasma. The spatial structure and dynamics of current sheets in such plasmas is investigated analytically as well as numerically. The current sheets at Alfvén resonances tend to power-law singularities. The growth of current sheets is algebraic in time in the linear regime and saturates in the presence of dissipation without the intervention of nonlinear effects. These results have significant implications for forced reconnection and Alfvén wave dissipation in laboratory and space plasmas. © 1998 American Institute of Physics.

Notes: In this paper a time evolution equation for internal kink oscillations is derived. It is valid for both stable and unstable plasma regimes, and incorporates the response of an energetic particle population. A linear analysis reveals a parallel between (i) the time evolution of the spatial derivative of the internal kink radial displacement and (ii) the time evolution of the perturbed particle distribution function in the field of an electrostatic wave (Landau problem). It is shown that diamagnetic drift effects make the asymptotic decay of internal kink perturbations in a stable plasma algebraic rather than exponential. However, under certain conditions the stable root of the dispersion relation can dominate the response of the on-axis displacement for a significant period of time. The form of the evolution equation naturally allows one to include a nonlinear, fully toroidal treatment of energetic particles into the theory of internal kink oscillations. © 1998 American Institute of Physics.

Notes: A formalism is developed for optimizing the design of feedback coils placed around a tokamak plasma in order to control the resistive shell mode. It is found that feedback schemes for controlling the resistive shell mode fail whenever the distortion of the mode structure by the currents circulating in the feedback coils becomes too strong, in which case the mode escapes through the gaps between the coils, or through the centers of the coils. The main aim of the optimization process is to reduce this distortion by minimizing the coupling of different Fourier harmonics due to the feedback currents. It is possible to define a quantity α0 which parametrizes the strength of the coupling. Feedback fails for α0≥1. The optimization procedure consists of minimizing α0 subject to practical constraints. If there are very many evenly spaced feedback coils surrounding the plasma in the poloidal direction then the optimization can be performed analytically. Otherwise, the optimization must be performed numerically. The optimal configuration is to have many, large, overlapping coils in the poloidal direction. © 1998 American Institute of Physics.

Notes: The dynamics of relativistic runaway electrons in tokamak plasmas is analyzed using a test particle description that includes acceleration in the toroidal electric field, collisions with the plasma particles, and deceleration due to synchrotron radiation losses. The region of momentum space in which electron runaway takes place is determined. It is found that relativistic and synchrotron radiation effects lead to a critical electric field ER〉(kTe/mec2)ED, below which no runaways are generated. In addition, the trajectories of the test electrons in momentum space show a stable equilibrium point that sets a limit on the energy that the runaway electrons can reach. Analytical expressions are given for this energy limit as a function of the toroidal electric field and plasma parameters. The dominant radiative mechanisms limiting the runaway electron energy are identified in the whole range of electric field values. © 1998 American Institute of Physics.

Notes: A simple equation for Stringer spin up due to anomalous transport valid in arbitrary toroidal symmetric geometry is derived. Additional terms are found compared with previous work that can be traced to a different ordering of the parallel velocity. The influence of elongation and Shafranov shift is shown to be small. Neoclassical viscosity is included and the case of both small and large viscosity are discussed.© 1998 American Institute of Physics.

Notes: A study on preheating effects in laser-driven shock waves is presented. Two different diagnostics were used: the color temperature measurement deduced by recording the target rear side emissivity in two spectral bands, and the rear surface reflectivity measurement by using a probe beam. In order to test the response of the two diagnostics to the preheating, three types of targets characterized by different radiative properties were used. The greater sensitivity of the second diagnostic compared with the first was demonstrated. A model which calculates the reflectivity using a one-dimensional hydrodynamic code data was developed. In this model, the wave propagation equations in the expanding plasma using an appropriate model for the electron–ion collision frequency applicable to the cold solid-hot plasma transition were solved. The comparison between the calculated and measured reflectivities allows us to estimate the preheating process. © 1998 American Institute of Physics.

Notes: The effect of plasma on backward wave oscillator (BWO) emission in a 12–18 GHz frequency range is given. It is shown that the Ku band emission corresponds to the cylindrically symmetric transverse magnetic TM01 and not the higher mode. Due to the slowing down of waves with the increase in plasma density there occurs a BWO mode switching, i.e., BWO switches from a bounded mode to an unbounded one. Here the analysis for the switched BWO in the unbounded mode is given. The expressions for the temporal and spatial growth rates in the presence of plasma are obtained. The efficiency calculations are also given. Comparison of the results with that of a previous experiment [IEEE Trans. Plasma Sci. 18, 497 (1990)] has been carried out. © 1998 American Institute of Physics.

Notes: The steady state of the driven oscillations of the system consisting of N oscillators coupled by friction is considered. It is shown that for large values of N this state is asymptotically described by the F-function previously introduced in the theory of resonant magnetohydrodynamic (MHD) waves in plasmas. © 1998 American Institute of Physics.

Notes: A new expression of Δ′ and instability criterion for m≥2 tearing modes is derived for arbitrary magnetic shear configuration in the low beta and large aspect ratio limit. Local solutions of an ideal external kink equation are solved analytically by means of proper expansion and transformation. An analytic expression of the criterion parameter Δ′ results from the analytic solutions. The instability criterion obtained depends on the location of the resistive layer, and on a dimensionless parameter λ related to the ratio of the gradients of the equilibrium current density and of the rotational transform. Strauss's Δ′ formula and the previous instability criterion are recovered as a special case in the large-m limit without a conducting wall. Considering both the boundary conditions at the plasma core and the conducting wall, the expression of Δ′ is extended to include the stabilizing effect of the conducting wall. The properties of tearing instability are analyzed based on the expression of Δ′. © 1998 American Institute of Physics.

Notes: The spectrum of unstable perturbations of a simple magnetized atmosphere is studied. Magnetic field lines are straight, horizontal, and line tied to conducting walls at both ends. The temperature has horizontal variation across the field lines as well as vertical variation. The unstable spectrum close to marginal stability is found to be continuous from zero to a maximum growth rate. The structure of the unstable continuum modes is calculated in the dissipationless limit. The presence of singularities in the eigenfunction does not affect the growth rate significantly, nor does it lead to plasma heating. © 1998 American Institute of Physics.

Notes: A self-consistent set of equations for the fast space–time evolution of fluctuations and the slow space–time evolution of density and flows in a toroidal plasma, relevant for simulations using field-aligned coordinates in thin flux tubes, has been derived. The methodology for the derivation of these equations is outlined for a model set of equations for the plasma edge, specific to resistive ballooning modes but readily adaptable to other instabilities. The derivation proceeds by first writing the axisymmetric and fluctuating equations in the usual toroidal coordinate system. These are then transformed to the twisted coordinate flux-tube system. Most simulations which use twisted flux-tube computational grids transform to the field-aligned coordinate system first and then take averages to obtain the slow evolution. They however miss some terms since the two operations, namely, multiscale separation and coordinate transformation, do not necessarily commute, because of subsidiary assumptions on the box size. In the present formulation, all the relevant neoclassical effects such as the Pfirsch–Schlüter current and the Stringer spin-up as well as the toroidal Reynolds stress are properly included. This set of multiscale equations is appropriate for the study of the formation and evolution of transport barriers. © 1998 American Institute of Physics.

Notes: In this paper we describe a new theory of like particle collisional transport for a non-neutral plasma confined in a Penning trap. The theory is valid in the regime ωb〉ωE, ωb〉νc, and rc〈λD where ωb is the axial bounce frequency, ωE is the E×B rotation frequency, νc is the collision frequency, rc is the cyclotron radius, and λD is the Debye length. In this regime each particle can be bounce averaged into a long rod and the transport understood as arising from the E×B drift motion of the rods due to long-range mutual interactions. This is a very different mechanism than is considered in the classical theory of transport, where a particle guiding center undergoes a step of order rc as a result of a velocity scattering collision. For the parameter range considered, the new theory predicts transport rates that are orders of magnitude larger than those predicted by classical theory and that scale with magnetic field strength like 1/B rather than 1/B4. The new theory differs from a previous analysis of transport due to E×B drift interactions of charged rods, in that the finite length of the rods is taken into account. This enables transport to occur even for the case of an E×B drift rotation frequency that is a monotonic decreasing function of radius (as was the case in recent experiments). © 1998 American Institute of Physics.

Notes: On the China Tokamak (CT-6B) [Nucl. Fusion 36, 1669 (1996)], application of negative limiter bias resulted in enhanced Er shear in the naturally occurring Er shear layer near the fixed limiter radius with negligible change of plasma density, electron temperature, the parallel plasma flow, and the impurity ion radiation power. In the layer, decreased turbulent fluctuation, reduced poloidal correlation and increased nonlinear coupling of the turbulence were observed to be very possibly correlated with enhanced Er shear. The results suggest that there exists interaction of Er shear with turbulence, and an Er shear-induced shift in the phase angle between density and poloidal electric field fluctuations and nonlinear three-wave coupling may play an important role in suppressing edge turbulence. © 1998 American Institute of Physics.