Open AccessOn the stability of superposed streams of Fluids of different densities
Author(s) -
Shyke A. Goldstein
Publication year - 1931
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1931.0116
Subject(s) - turbulence , mechanics , prandtl number , stratification (seeds) , physics , thermodynamics , heat transfer , seed dormancy , germination , botany , dormancy , biology
1.1. The gliding of warm air over cold air, and of fresh water over salt water, without appreciable turbulent mixing, is a known phenomenon. Theoretically we know that, with a sudden transition in velocity and density, the laminar motion of superposed streams of fluid is unstable for any relative velocity, no matter how small, when viscosity is neglected. In reality, how ever, such sudden transitions cannot occur, or at any rate cannot be permanent, and when the width of the layer of transition is comparable with the wave length of the disturbance assumed, the analysis for an abrupt transition has no physical significance. The stability of such a system with a finite width of the layer of transition is therefore investigated below by the method of small oscillations. The investigation is a generalisation to heterogeneous stratified fluids of Rayleigh’s discussion of the homogeneous case. 1.2. The effect of a stratification of density in tending to prevent turbulence has lately been investigated by Prandtl, who, by considerations of energy, has arrived at the following criterion for the continuance of turbulence.