Analytic expression for Taylor-Couette stability boundary

TL;DR

This paper derives a comprehensive analytic expression for the stability boundary in Taylor-Couette flow, accounting for viscosity and applicable across all parameters, aligning well with theory and experiments.

Contribution

It presents a new analytic formula for the Taylor-Couette stability boundary that generalizes Rayleigh's criterion to include viscosity and all geometric configurations.

Findings

Analytic expression matches linear stability theory.

Expression agrees with experimental data.

Provides explicit formulas for special cases.

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.