Evolution equations for Taylor vortices in the small-gap limit

Abstract

We consider the centrifugal instability of the viscous fluid flow between concentric circular cylinders in the small-gap limit. The amplitude of the Taylor vortex is allowed to depend on a slow time variable, a slow axial variable, and the polar angle $\theta$. It is shown that the amplitude of the vortex cannot, in general, be described by a single amplitude equation. In the absence of any slow axial variations it is shown that a Taylor vortex remains stable to wavy vortex perturbations.