Interfacial instability of coupled-rotating inviscid fluids

Abstract

We consider the three-dimensional, cylindrical equivalent to the problem of instability between two inviscid fluids due to a velocity shear between them, known as Kelvin-Helmholtz instability. We begin by developing the solution to the linearized equations for a rotating fluid. While this solution is not in itself new, we carry the analysis further than previous treatments by including non-zero modes and considering the effect of the surface tension, particularly on the dispersion relation. We then consider a system of two fluids rotating at different rates and derive its dispersion relation, which is rather more complicated than that for a single rotating fluid. While a general analytic sol..