Dynamic transition and pattern formation in Taylor problem
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- 作者：Tian Ma (1)
Shouhong Wang (2) showang@indiana.edu - 关键词：Taylor problem ; Couette flow ; Taylor vortices ; Dynamic transition theory ; Dynamic classification of phase transitions ; Continuous transition ; Jump transition ; Mixed transition ; Structural stability
- 刊名：Chinese Annals of Mathematics - Series B
- 出版时间：November 2010
- 出版年：2010
- 期刊代码：pc573_0252-9599
- 类别：mat
- 卷：31
- 期：6
- 页码：953-974
- 数据来源：sp
摘要
The main objective of this article is to study both dynamic and structural transitions of the Taylor-Couette flow, by using the dynamic transition theory and geometric theory of incompressible flows developed recently by the authors. In particular, it is shown 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, it is also shown that the new transition states have the Taylor vortex type of flow structure, which is structurally stable.