Dynamic Transition and Pattern Formation in Taylor Problem

作     者：Tian MA Shouhong WANG Tian MA Shouhong WANG Department of Mathematics, Sichuan University, Chengdu 610064, China. Department of Mathematics, Indiana University, Bloomington, IN 47405, USA.

作者机构：Department of Mathematics Sichuan University Chengdu 610064 China Department of Mathematics Indiana University Bloomington IN 47405 USA. 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2010年第31卷第6期

页      面：953-974页

核心收录：

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by the National Science Foundation  the Office of Naval Research and the National Natural Science Foundation of China 

主　　题：Taylor problem Couette flow Taylor vortices Dynamic transition theory Dynamic classification of phase transitions Continuous transition Jump transition Mixed transition Structural stability 

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.