Dynamic Transition and Pattern Formation in Taylor Problem

TL;DR

This paper investigates the dynamic and structural transitions in Taylor-Couette flow, revealing how flow states change at critical points and identifying stable vortex structures using advanced transition theories.

Contribution

It applies recent dynamic transition and geometric flow theories to analyze flow pattern changes and stability in Taylor-Couette flow.

Findings

Flow undergoes continuous or jump transitions at critical Taylor number

Transition states exhibit stable Taylor vortex structures

Transition type depends on a computable nondimensional parameter R

Abstract

The main objective of this article is to study both dynamic and structural transitions of the Taylor-Couette flow, using the dynamic transition theory and geometric theory of incompressible flows developed recently by the authors. In particular we show that as the Taylor number crosses the critical number, the system undergoes either a continuous or a jump dynamic transition, dictated by the sign of a computable, nondimensional parameter $R$. In addition, we show that the new transition states have the Taylor vortex type of flow structure, which is structurally stable.