Navier-Stokes方程九模类Lorenz方程组的动力学行为及数值仿真

The Dynamical Behavior and Numerical Simulation of a Nine-modes Lorenz Equations of Navier-Stokes Equations

为深入探讨流体流动的稳定性,本文研究了平面不可压缩Navier-Stokes方程九模类Lorenz方程组的动力学行为及数值仿真问题.对平面不可压缩Navier-Stokes方程进行傅里叶展开,采用新的截取模式得到一个九模类Lorenz系统,研究了系统的对称性、耗散性和吸引子的存在性,讨论了该方程组的定常解及其稳定性.基于分岔图与最大Lyapunov指数谱和庞加莱截面以及功率谱,文中阐述并分析了此新型混沌系统的基本动力学行为,仿真分析了系统动力学行为的演化历程,解释了随参数变化系统的不动点、周期态和混沌态等之间转变的物理过程.

In order to explore the stability of the flow, we study the nonlinear dynamical behavior and simulation problem of nine-modes Lorenz system for a two-dimensional incompressible Navier-Stokes equations. A new nine-modes truncation of Fourier series of Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is obtained. The symmetry, dissipation and existence of attractors of the system are studied, and the stationary solution and their stability properties are discussed. Based on numerical simulation results of bifurcation diagram, the Lyapunov exponent spectrum, Poincare section and power spectrum of the system, some basic dynamical behavior of the new system are investigated briefly, the physics process and evolution of the dynamical behavior from fixed point to periodic and chaotic behaviors are presented simultaneously.