旋转流动的低模分析及仿真研究

为了探讨Couette-Taylor流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,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,讨论了Couette-Taylor流三模态类Lorenz型方程组的动力学行为,包括定态的失稳、极限环的出现、分岔与混沌的演变和全局稳定性分析等。通过线性稳定性分析和数值模拟等方法给出了此三维模型分岔与混沌等动力学行为及其演化历程,并借此解释了Couette-Taylor流试验中观察到的部分涡流的演化过程.基于系统的分岔图、Lyapunov指数谱、功率谱、Poincaré(庞加莱)截面和返回映射等揭示了系统混沌行为的普适特征.

Low-Dimensional Analysis and Numerical Simulation of Rotating Flow

In order to explore the transition way of the Couette-Taylor flow from laminar flow to turbulence and the characteristics of chaotic attractors in turbulence,dynamic behaviors and numerical simulation of the Couette-Taylor flow were studied by means of the low-dimensional analysis method.The dynamic properties of the 3-model Lorenz-type system of the Couette-Taylor flow were discussed,including the stability of equilibrium points,the occurence of limit cycles,the evolution of bifurcation and chaos,as well as the global stability etc.Through linear stability analysis and numerical simulation,the dynamic behavior and evolution history of bifurcation and chaos of this low-dimensional model were presented.Consequently,successive transitions of the Couette-Taylor flow from laminar flow to turbulence in the experiment were explained.The numerical simulation results of bifurcation diagrams,Lyapunov exponent spectra,Poincaré sections,power spectra and return mappings of the system reveal the general features of the system chaos behaviors.