The effect of rotation on the Rayleigh-Bénard stability threshold

The standard method used to solve the Rayleigh-Bénard linear stability problem for a rotating fluid leads to a complex expression which can only be evaluated numerically. Here the problem is solved by a different method similar to that used in a recent paper on the non-rotating case [A. Prosperetti, “A simple analytic approximation to the Rayleigh-Bénard stability threshold,” Phys. Fluids 23, 124101 (2011)10.1063/1.3662466]. In principle the method leads to an exact result which is not simpler than the standard one. Its value lies in the fact that it is possible to obtain from it an approximate explicit analytic expression for the dependence of the Rayleigh number on the wave number of the perturbation and the rate of rotation at marginal stability conditions. Where the error can be compared with exact results in the literature, it is found not to exceed a few percent over a very broad Taylor number range. The relative simplicity of the approach permits us, among others, to account for the effects of a finite thermal conductivity of the plates, which have not been studied befor

Improved procedure for the computation of Lamb's coefficients in the Physalis method for particle simulation

The Physalis method is suitable for the simulation of flows with suspended spherical particles. It differs from standard immersed boundary methods due to the use of a local spectral representation of the solution in the neighborhood of each particle, which is used to bridge the gap between the particle surface and the underlying fixed Cartesian grid. This analytic solution involves coefficients which are determined by matching with the finite-difference solution farther away from the particle. In the original implementation of the method this step was executed by solving an over-determined linear system via the singular-value decomposition. Here a more efficient method to achieve the same end is described. The basic idea is to use scalar products of the finite-difference solutions with spherical harmonic functions taken over a spherical surface concentric with the particle. The new approach is tested on a number of examples and is found to posses a comparable accuracy to the original one, but to be significantly faster and to require less memory. An unusual test case that we describe demonstrates the accuracy with which the method conserves the fluid angular momentum in the case of a rotating particle

A numerical method for the dynamics of non-spherical cavitation bubbles

A boundary integral numerical method for the dynamics of nonspherical cavitation bubbles in inviscid incompressible liquids is described. Only surface values of the velocity potential and its first derivatives are involved. The problem of solving the Laplace equation in the entire domain occupied by the liquid is thus avoided. The collapse of a bubble in the vicinity of a solid wall and the collapse of three bubbles with collinear centers are considered

Reply to comments on "General analysis of the stability of superposed fluids"

Previous results by Plesset and Hsieh on the effects of compressibility for Rayleigh–Taylor instability are shown to be valid, and an alternative brief deduction is given

Oscillations of a gas pocket on a liquid-covered solid surface

The dynamic response of a gas bubble entrapped in a cavity on the surface of a submerged solid subject to an acoustic field is investigated in the linear approximation. We derive semi-analytical expressions for the resonance frequency, damping and interface shape of the bubble. For the liquid phase, we consider two limit cases: potential flow and unsteady Stokes flow. The oscillation frequency and interface shape are found to depend on two dimensionless parameters: the ratio of the gas stiffness to the surface tension stiffness, and the Ohnesorge number, representing the relative importance of viscous forces. We perform a parametric study and show, among others, that an increase in the gas pressure or a decrease in the surface tension leads to an increase in the resonance frequency until an asymptotic value is reached

Flow of vapour in a liquid enclosure

A solution is developed for the flow of a vapour in a liquid enclosure in which different portions of the liquid wall have different temperatures. It is shown that the vapour pressure is very nearly uniform in the enclosure, and an expression for the net vapour flux is deduced. This pressure and the net vapour flux are readily expressed in terms of the temperatures on the liquid boundary. Explicit results are given for simple liquid boundaries: two plane parallel walls at different temperatures and concentric spheres and cylinders at different temperatures. Some comments are also made regarding the effects of unsteady liquid temperatures and of motions of the boundaries. The hemispherical vapour cavity is also discussed because of its applicability to the nucleate boiling problem

A brief summary of L. van Wijngaarden's work up till his retirement

This paper attempts to provide an overview of Professor Leen van Wijngaarden's scientific work by briefly summarizing a number of his papers. The review is organized by topic and covers his work on pressure waves in bubbly liquids, bubble dynamics, two-phase flow, standing waves in resonant systems, and flow cavitation noise. A list of publications up till his retirement in March 1997 is provided in the Appendix

On the characteristics of the equations of motion for a bubbly flow and the related problem of critical flow

For the study of transients in gas-liquid flows, the equations of the so-called separated flow model are inadequate, because they possess, in the general case where gas and liquid move at different velocities, complex characteristics. This paper is concerned with the equations of motion for bubbly flow. The equations are discussed with emphasis on the aspects of relative motion and the characteristics are calculated. It is found that all characteristics are real. The results are used to establish a relation between gas velocity, liquid velocity, void fraction and sound velocity at critical flow. This relation agrees very well with experimental data for these quantities as measured by Muir and Eichhorn in the throat of a converging-diverging nozzle

The Motion of a Charge Particle in a Uniform Magnetic Field

We study the motion of a classical (nonquantal) charged particle in a uniform magnetic field by means of i) the Abraham-Lorentz equation, ii) the Dirac relativistic equation and iii) the Caldirola nonrelativistic, finite-difference equation. In cases i) and iii) closed-form solutions are obtained. For case ii) we apply for the first time the twovariable asymptotic method which enables us to obtain a uniformly valid approximate solution free of the secular terms present in the results of previous authors

The average stress in incompresible disperse flow

An analysis of the average stress in a disperse flow consisting of equal spherical particles suspended in a fluid is presented. Other than incompressibility, no assumptions are made on the rheological nature of the fluid. In particular, the Reynolds number of the particle motion relative to the fluid is arbitrary. The use of ensemble averages permits the consideration of spatially non-uniform systems, which reveals features not identified before. In particular, it is shown that, in general, the average stress is not symmetric, even when there are no external couples acting on the particles. A quantity to be identified with the mixture pressure (including the particle contribution) is identified. The structure of the momentum equations for the fluid and particle phases is systematically derived. As an example, the case of particles suspended in a locally Stokes flow is considered