标题： 泰勒问题中的动态转变与模式形成 显示英文标题

标题： Dynamic Transition and Pattern Formation in Taylor Problem

摘要： 本文的主要目的是利用作者最近开发的动力过渡理论和不可压缩流的几何理论，研究泰勒-库埃特流的动力和结构过渡。 特别是我们证明当泰勒数超过临界数值时，系统会发生连续或跳跃的动力过渡，这由一个可计算的无量纲参数$R$的符号决定。 此外，我们证明新的过渡状态具有泰勒涡类型的流动结构，这是结构稳定的。 显示英文摘要

摘要： 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.