Taylor-Couette flow with temperature fluctuations: Time periodic solutions

TL;DR

This paper proves the existence of time-periodic solutions in Taylor-Couette flow with temperature variations, specifically when the cylinders' rotation ratio is rational, extending understanding of flow dynamics under thermal effects.

Contribution

It demonstrates the existence of time-periodic solutions in compressible, heat-conducting Taylor-Couette flow with non-constant cylinder temperatures, for rational rotation ratios.

Findings

Time-periodic solutions exist for rational angular velocity ratios.

The study extends flow analysis to include temperature fluctuations.

Results apply to viscous, compressible, heat-conducting fluids in cylindrical gaps.

Abstract

We consider the motion of a viscous compressible and heat conducting fluid confined in the gap between two rotating cylinders (Taylor-Couette flow). The temperature of the cylinders is fixed but not necessarily constant. We show that the problem admits a time--periodic solution as soon as the ratio of the angular velocities of the two cylinders is a rational number.