Dynamic Transition and Pattern Formation in Taylor Problem

Details Dynamic Transition and Pattern Formation in Taylor Problem Dynamic Transition and Pattern Formation in Taylor Problem

2010-05-12

arxiv.org/abs/1005.2132v1

Physics

Mathematical Physics

To appear in Chinese Annuals of Mathematics

Scientific paper

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.

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