旋转流动混沌行为的全局稳定性分析及数值仿真

The Analysis of Global Stability and Numerical Simulation of Chaos Behaviors of Rotating Flow

同轴圆筒间旋转流动的Couette-Taylor流问题是近一个世纪以来人们普遍关注的热点问题,由于其流动形态的可观测性以及它在湍流研究中的基础性地位及其在流体机械、石油化工等领域的广泛应用,国际上将其列为非线性科学的范例之一.为了探讨这种流动从层流到湍流过渡的方式以及流动发展到湍流之后混沌吸引子的某些特征等问题,该文采用低模分析方法研究了Couette-Taylor流的部分动力学行为及仿真问题,探讨了同轴圆筒间Couette-Taylor流三模态类Lorenz型方程组的动力学行为及仿真问题,数值模拟了系统分岔与混沌的演变历程,讨论了系统的全局稳定性.

There has been a very large number of experimental and theoretical studies of flow between concentric rotating cylinders in the century, since these pioneering works, the instability of Couette flow and Taylor vortex flow, now known as the ＂Couette-Taylor Problem＂ is a paradigm of nonlinear problem, this paper will investigate the problem of some dynamical behaviors and numerical simulation of Couette-Taylor flow between two concentric rotating cylinders. Dynamical behaviors of a three-model Lorenz-like system of Couette-Taylor flow have been discussed, such as evolutionary history of bifurcation and chaos of this low-dimensional model, as well as the analysis of global stability etc.