二维不可压缩Navier-Stokes方程的七模类Lorenz方程组的动力学行为及其数值模拟

THE DYNAMICAL BEHAVIOR AND THE NUMERICAL SIMULATION OF THE SEVEN-MODE TRUNCATION SYSTEM OF THE PLANE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

本文研究了平面不可压缩的Navier-Stokes方程一个七模类Lorenz方程组的混沌行为问题.利用模式截断的方法,获得了一个七模类Lorenz方程组,证明了该方程组吸引子的存在性,并对其全局稳定性进行了分析和讨论.基于分岔图、最大李雅普诺夫指数、庞加莱截面、功率谱揭示了系统混沌行为的普适特征,仿真分析了系统动力学行为的演化过程.

The chaotic behavior of seven-mode Lorenz-like system for the plane incompressible Navier-Stokes equations is studied.By mode truncation,a seven-mode Lorenz equations is obtained.The existence of the attractor of the equations is proved,and the global stability of the equations is discussed.Based on numerical simulation results of bifurcation diagram,Lyapunov exponent spectrum,Poincare section and power spectrum of the system,general features of the system are revealed.The whole process,which shows a chaos behavior with the changing of Reynolds number,is simulated numerically.