摘要:

It is shown that the renormalization group theory of turbulence leads to the relation Ba=CKPtbetween the turbulent Prandtl numberPt, the Kolmogorov constantCK, and the Batchelor constant Ba.

ISSN:0031-9171    

DOI:10.1063/1.866057

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The existence of unstable resistive drift‐Alfve´n modes is shown in a cylindrical geometry. The modes, driven by nonuniformities in the diamagnetic drift frequency, are unstable even when the associated purely resistive mode is stable. The growth rate has a weak, &eegr;1/4, dependence on resistivity. Because of their large growth rates, they may play an important role in tokamak confinement.

ISSN:0031-9171    

DOI:10.1063/1.866058

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

In the steady laminar flow past a sudden expansion at large Reynolds numberR, the equations of motion reduce to the boundary‐layer equations asR→∞ if the longitudinal length scale of the separated eddy increases linearly and indefinitely withR. In part I of this series [Phys. Fluids29, 1353 (1986)], several sudden expansion geometries were considered, and in each case, when the inflow was uniform, steady solutions to the boundary‐layer equations were found to exist provided that the expansion ratio remained above a critical value where the pressure gradient became singular near the reattachment point of the eddy. These results suggested that for uniform inflows and smaller values of the expansion ratio, the eddy length could not continue to increase linearly withRif the latter were sufficiently large. In the present work a global Newton method was employed to obtain finite‐difference solutions to the steady Navier–Stokes equations up toR=1000 for a uniform inflow past a cascade of sudden expansions. The calculations show that for large values of the expansion ratio, the eddy length increases linearly withR, and that the main features of the flow approach those predicted by the boundary‐layer solutions, including the existence of large pressure gradients near the reattachment point, as the expansion ratio is reduced toward the critical value. However, for smaller values of the expansion ratio where solutions to the boundary‐layer equations could not be found, the steady solutions to the Navier–Stokes equations approach, with increasingR, the limit of an inviscid eddyO(1) in length, with the main features of the flow conforming to the theoretical model of Batchelor [J. Fluid Mech.1, 388 (1956)] for an inviscid separated eddy behind a bluff body.

ISSN:0031-9171    

DOI:10.1063/1.866062

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

A description is given of the structure of the turbulent wake behind a circular cylinder that was determined using a conditional averaging technique. The structure was found for a steady flow and also for a flow in which an in‐line velocity perturbation was superimposed on the steady component. The perturbation frequency was chosen so that the frequency of vortex shedding locked‐in to the perturbation frequency. The structures of the two wakes are compared and it is found that large changes occur with lock‐in, with the strength of the vortices increasing and their lateral separation decreasing. It is estimated that the increase in the vortex strength results from an increase in the amount of vorticity shed from the cylinder and also a small change in the amount of vorticity surviving the vortex formation process. The model, which Davies [J. Fluid Mech.75, 209 (1976)] found gave a good representation of the average wake flow, was used to provide comparisons with the experimental results. In general, the agreement between the theoretical and experimental results was very satisfactory.

ISSN:0031-9171    

DOI:10.1063/1.866170

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The moderate‐amplitude axisymmetric oscillations of an inviscid liquid shell surrounding an incompressible gas bubble are calculated by a multiple‐time‐scale expansion for initial deformations composed of two‐lobed perturbations of the shell and a displacement of the bubble from the center of mass of the liquid. Two types of small‐amplitude motion are identified and lead to very different nonlinear dynamic interactions, as described by the results valid up to second order in the amplitude of the initial deformation. In the ‘‘bubble mode,’’ the oscillations of the captive bubble and the liquid shell are exactly in phase and the bubble vibrates about its initial eccentric location. The bubble moves toward the center of the drop when the shell is perturbed into a ‘‘sloshing mode’’ of oscillation where both interfaces move out of phase. These results explain the centering of liquid shells observed in several experiments.

ISSN:0031-9171    

DOI:10.1063/1.866190

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

When a vertical temperature gradient is applied to a large solid containing a spherical fluid inclusion, the temperature in the fluid is a function only of height. The stability of this fluid against convection is investigated and it is found that the principle of exchange of stabilities applies. The linear differential system governing stability is then solved; the results show that the thermal conductivity of the surrounding solid is always stabilizing and that the most unstable mode is the first asymmetric mode, for which the critical Rayleigh number is given. The energy method can be applied, with due modifications to account for heat conduction in the surrounding solid. The same mathematical governing differential system would then be obtained, giving the same number for the upper bound of the Rayleigh numbers below which the fluid is stable. This number is then truly critical: The fluid is stable or unstable according to whether the Rayleigh number is below or above it, whatever the magnitude of the disturbance. The results are discussed in the context of the movement of the spherical inclusion in a soluble solid. The greater instability of the asymmetric mode indicates that when instability occurs, the fluid inclusion will have a sidewise component, which is greater for a greater supercritical Rayleigh number. The effect of double diffusion is also discussed.

ISSN:0031-9171    

DOI:10.1063/1.866056

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The collision integrals describing the rate of exchange of momentum and tensorial energy between the components in a binary mixture of neutral gases with very different atomic masses are determined for arbitrary values of their two temperatures and velocities, for realistic intermolecular potentials, and allowing for large departures of the heavy gas from equilibrium conditions. In the range of interest where the system is perturbed within times of the order of the slow relaxation time characterizing the transfer of energy between unlike molecules, the light gas distribution function is Maxwellian to lowest order, with corrections given asymptotically in powers of the small parameterm/mpformed with the ratio of the species molecular masses. Also, provided that the ratioTp/Tbetween the temperatures of the two gases remains much smaller thanmp/m, the desired collision integrals may be evaluated asymptotically in powers ofm/mpin all generality. The computation is carried out in detail for the case when the interaction between atoms is described by a Lennard–Jones potential. A combination of numerical computations with optimal matching of analytical expressions valid for large and small slip velocities leads to a set of compact formulas which hold for the limits of high and low temperatures and to a general approximate expression for all temperatures.

ISSN:0031-9171    

DOI:10.1063/1.866511

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The propagation of a sound wave in a polyatomic gas is studied by using the Hanson and Morse polyatomic gas model [Phys. Fluids10, 345 (1967)] in the Wang‐Chang and Uhlenbeck equation, with Maxwell’s diffuse boundary conditions. The model equation and the associated boundary conditions are transformed into a system of integral equations, which is then solved numerically. The computed results for attenuation and the speed of sound for nitrogen, oxygen, and air at 300°K, and a wide range of rarefaction parameters, are compared with the experimental data of Greenspan [J. Acoust. Soc. Am.31, 155 (1959)], and of Meyer and Sessler [Z. Phys.149, 151 (1957)], and previously reported theoretical results.

ISSN:0031-9171    

DOI:10.1063/1.866059

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The thermal relaxation of a two‐dimensional (2‐D) plasma in a uniform magnetic field is investigated. Previous workers [J. Plasma Phys.12, 21 (1974)] observed that the relaxation process is anomalous in that the relaxation may occur more rapidly with a modest magnetic field than without. A simple model is presented which explains the anomalous behavior in terms of correlations between successive collisions. The model predicts the relaxation time to scale as (&ohgr;c/&ohgr;p)−1/2(n&lgr;2D)1/2&ohgr;−1pfor modest magnetic fields (&ohgr;c/&ohgr;p<1). This scaling law is tested with 2‐D electrostatic particle simulations. These simulations show the relaxation time to scale with (&ohgr;c/&ohgr;p)−1/2as predicted by the correlated collision model. For very large magnetic fields (&ohgr;c≫&ohgr;p) the simulations show the relaxation time to increase with &ohgr;cbecause of finite size particle effects as the cyclotron radius becomes comparable to the particle size. The predicted (n&lgr;2D)1/2dependence of the relaxation time was observed at early times in the simulations; however, as the distribution approached a Maxwellian, the dependence shifted toward (n&lgr;2D)1as in an unmagnetized plasma.

ISSN:0031-9171    

DOI:10.1063/1.866060

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The reflection of a planar ion‐acoustic soliton from an insulated or a biased metallic planar wall is studied. Numerical solutions of the cold‐ion fluid equations, the Boltzmann distribution for electrons, and Poisson’s equation show that the incident soliton is partially reflected and partially absorbed by the wall. The reflection is larger for wider solitons and for a more negatively biased wall. The numerical results are in reasonable agreement with the recent experiment of Nishida [Phys. Fluids27, 2176 (1984)].

ISSN:0031-9171    

DOI:10.1063/1.866061

出版商:AIP    

年代:1987

数据来源: AIP