Navier-Stokes方程五模类Lorenz方程组的动力学行为及数值仿真

The Dynamical Behavior and the Numerical Simulation of a Five-Modes Lorenz Equations of the Navier-Stokes Equations

本文对平面正方形区域上不可压缩的Navier-Stokes方程,进行傅立叶展开后,截断得到五模类Lorenz方程组.给出了该方程组定常解及其稳定性的讨论,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,数值模拟了雷诺数在一定范围内变化时,类Lorenz方程组的动力学行为.

We study the dynamical behavior of a five-modes Lorenz equations of the navier-stokes equations for a two-dimensional incompressible fluid on a torus.The plane incompressible Navier-Stokes equations is expanded in fourier series on a torus,then a five-modes Lorenz equations is obtained.The stationary solution and their stability properties are presented,the existence of the attractor is proved,and the global stability of the equations is disscused. The dynamical behavior is simulated numerically by computer according to the changing of Reynolds number.