On the stability of the flow of stratified rotating superposed fluids

Abstract

The effect of Coriolis force on the stability of two superposed fluids is examined under the assumption of ideal (incompressible, non-viscous and zero thermal conductivity) flow. The analysis reveals only one type of instability in contrast to two types of instabilities observed by SoNTowSKI, SEIDEL, and AMES (1%9), in the absence of Coriolis force. Thus the effect of Coriolis force on the superposed flow is to make the flow more stable. In particular, the special case of upper strati fled fluid rotating and the lower non-rotating is examined in detail and we find two separate and different types of instabilities. As the velocity of the rotating fluid relative to the non-rotating one increases from zero, there first appears an instability of a selective and relatively weak nature referred to as the initial instability. This is followed, at higher velocities, by a stronger type of instability ealled the gross instability. We found that the effect of Coriolis force is to suppress the region of initial instability in the sense that the instability occurs for large velocity differences. We also found that the Coriolis force has no effect on the critieal wavenumber. These general stability results are applied to a particular problem of the Kelvin-Helmholtz instability with rotation and we find that the results are in agreement with those of CHANDRAsExHAR (1%1). We determine the rate of growth of initial instabilities, which depends on the density stratifleation and the angular velocity of the rotating gas. This growth rate, in the ease of rotation, is greater than that in the absence of rotation, which is in agreement with observations of MUNK (1947).