Analytic expression for Taylor-Couette stability boundary

Abstract

We analyze the mechanism that determines the boundary of stability in Taylor-Couette flow. By simple physical argument we derive an analytic expression to approximate the stability line for all radius ratios and all speed ratios, for co- and counterrotating cylinders. The expression includes viscosity and so generalizes Rayleigh's criterion. We achieve agreement with linear stability theory and with experiments in the whole parameter space. Explicit formulae are given for limiting cases.