Interfacial instability of coupled-rotating inviscid fluids

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 solution is unattainable, by investigating some special cases we show that the fundamental mode is always stable, and that Kelvin–Helmholtz instability also exists for the system. We compare our results with experiments and conclude by suggesting some hypothetical links between the theory and nature.