摘要:

Time‐dependent convection for infinite Prandtl number fluids has been investigated hitherto in the physical domain. Dynamics of plumelike structures resulting from boundary‐layer instabilities can be interpreted in the spectral domain as having both direct and inverse cascades of energy taking place. In the physical domain only a small part of the spectrum is discernible. But the rest of the spectrum is needed for properly describing the nonlinear process. Only a relatively few modes, fewer than ten, are actually required for describing the essential features associated with the onset of plume dynamics.

ISSN:0031-9171    

DOI:10.1063/1.866850

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

In his discussion of contact line equilibrium for a system comprising two liquids and a solid, Gibbs [ScientificPapers(Dover, New York, 1961), Vol. 1, p. 326] used an argument that resulted in two inequalities he claimed to be applicable when the three‐phase contact line coincides with an edge on the solid surface. A simple counterexample is given that shows Gibbs’s inequalities lack universal applicability. A serious objection to Gibbs’s argument is noted and his discussion is altered to remove the objectionable feature. This leads to modified inequalities, which surprisingly are known and have been attributed to Gibbs by recent authors.

ISSN:0031-9171    

DOI:10.1063/1.866851

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The drag coefficientCD=48/Rfor a spherical bubble in a uniform streaming flow at high Reynolds number, which was first obtained via a dissipation method by Levich [Zh. Eksp. Teor. Fiz.19, 18 (1949)], is rederived here by direct integration of the normal stress over the bubble surface. The present study also shows that the drag coefficient up toO(R−1) depends only on theO(1) vorticity distribution right on the bubble surface, and is independent of the vorticity distribution in the fluid. Therefore the drag coefficient up toO(R−1) is completely determined by the irrotational flow solution, which is perfectly consistent with the dissipation method.

ISSN:0031-9171    

DOI:10.1063/1.866852

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

Experiments are reported in which long air bubbles rising in liquid‐filled vertical tubes were perturbed by coaxial wires. Distinctly different flow regimes were found to arise as the thickness of the wire was varied. The breaking of axial symmetry observed in the experiments is discussed in the light of ideas from bifurcation theory.

ISSN:0031-9171    

DOI:10.1063/1.866853

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

Post‐instability viscous fingering in rectilinear flow in a Hele–Shaw cell has been studied experimentally. Of particular interest was the characterization of the range of length scales associated with tip splitting, over a reasonably wide range of parameters. A digital imaging system was used to record the patterns as a function of time, which allowed properties such as the tip velocity, finger width, perimeter, and area to be studied as functions of time and capillary number. The tip velocity was observed to be approximately constant regardless of the occurrence of splitting events, and the average finger width decreased as the degree of supercriticality increased. Quantitative measures of the fact that there is a limit to the complexity of viscous fingers are provided, and that over the range of parameters studied, no evidence for fractal fingering exists. A discussion of the dynamics of tip splitting explains why this is so.

ISSN:0031-9171    

DOI:10.1063/1.866854

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

Measurements of the Fourier components of the axial variation of the velocity componentwin a Taylor–Couette apparatus containing ten pairs of vortices at various average wavenumbersq, as a function of &egr;≡R/Rc−1, are reported. For all values ofqstudied, excellent agreement with the perturbation expansion of Davey [J. Fluid Mech.14, 336 (1962)] for the amplitudes of the Fourier components was obtained, provided the power law dependence on &egr; was taken as a function of &egr;˜≡&egr;−&egr;m(q). Here &egr;m(q) is the marginal stability curve, below which the laminar flow state is stable against perturbations of wavenumberq. The wavenumber dependence of the leading coefficients in the expansions for the fundamental and first harmonic was also measured, and it was found that while the coefficient for the fundamental was independent ofq, the coefficient for the first harmonic monotonically decreased with increasingq, over the range studied.

ISSN:0031-9171    

DOI:10.1063/1.866855

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

Recently published experimental results [Int. J. Heat Mass Transfer,23, 738 (1980)] on thermally driven high Rayleigh number turbulent convection have shown that theN∝R2/7relation (whereNis the Nusselt number andRis the Rayleigh number), which is valid up toR≊5×108, is superceded at this point by the relationN=A&sgr;R1/3that holds at least up toR≊1011. For water (Prandtl number &sgr;=6.6), the experimental value forA&sgr;was found to beA&sgr;=0.0556±0.001. In the present work, the equations for a turbulent fluid driven by thermal convection are solved using the two‐point closure prescription of the direct interaction approximation. The theoreticalNvsRrelation at highRis found to be of the formN=A&sgr;R1/3and for &sgr;=6.6, and the predicted value of the coefficientA&sgr;is computed to beA&sgr;≲0.08, in good agreement with the experimental value. Extension of the model to situations other than convection is discussed.

ISSN:0031-9171    

DOI:10.1063/1.866856

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

When a liquid spray is injected into the upper region of a closed container, it will entrain air as it falls to the bottom under the influence of gravity. In some cases, the resulting flow field assumes the form of one or more large ring vortices. In this paper, the droplet drag mechanism by which this systematic motion is sustained in steady state is studied theoretically and numerically. It is shown that the structure of the airflow is approximately that of a solution to the inviscid fluid equations. The airflow velocity is determined by the equilibrium of energy exchanged between the air and the spray in different regions of the flow. A simple formula for estimating the order of magnitude of the flow velocity is derived. Numerical calculations that solve for the coupled flow of the gas and the interacting spray are presented for cases of practical interest. The effect of varying the droplet diameter distribution and the mass flow rate of the spray is investigated.

ISSN:0031-9171    

DOI:10.1063/1.866857

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The governing equations for stimulated Raman scattering are derived in a Lorentz frame moving with arbitrary velocity relative to the background plasma. These equations are fundamental to the study of relativistic beat‐wave solitary waves, which have recently been proposed for particle acceleration by Mimaetal. [Phys. Rev. Lett.57, 1421 (1986)]. An averaged Lagrangian density is constructed for this three‐wave interaction. This results in a natural definition for the action flux density four‐vector of each wave and the combined stress–energy tensor. It also follows from the Lagrangian structure of the system that the Manley–Rowe relations are satisfied. The covariant formalism presented here can also be used to study wave propagation in a multicomponent plasma, in which each plasma species moves with arbitrary velocity relative to the frame of observation. As a specific example, the dispersion relation for Langmuir‐wave propagation in two warm relativistic electron beams is derived for the first time.

ISSN:0031-9171    

DOI:10.1063/1.866858

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

In the beat‐wave accelerator [Phys. Rev. Lett.43, 267 (1979)], a large‐amplitude Langmuir wave is produced by the beating of two laser beams whose frequencies differ by approximately the plasma frequency. The relativistic equations governing this three‐wave interaction are shown to admit two types of solitary‐wave solutions.Temporalsolitary waves propagate at speeds greater than the speed of light and carrynoinformation.Spatialsolitary waves propagate at speeds less than the speed of light anddocarry information. Analytic expressions are obtained for the envelopes of these waves and for the relationship between their speed and maximum amplitude. For the limit in which the propagation speed of the solitary wave is equal to the speed of light, there is no distinction between a temporal solitary wave and a spatial solitary wave. However, it can be shown that the solitary wave is unstable in this limit. The potential of the spatial solitary waves for particle acceleration [Phys. Rev. Lett.57, 1421 (1986)] is studied. Although the spatial solitary waves are capable of accelerating particles to high energy, for typical beat‐wave parameters the laser–plasma coupling efficiency is too low for this scheme to be practical.

ISSN:0031-9171    

DOI:10.1063/1.866859

出版商:AIP    

年代:1988

数据来源: AIP