用连续法计算五维对流模型的定常解和周期解

THE STEADY AND PERIODIC SOLUTIONS OFTHE 5-DIMENSIONAL CONVETION MODEL OBTAINED BY THE CONTINUATION ALGORITHM

利用连续算法(Continuation algorithm)对五维对流非线性动力系统的定常解和周期解进行了数值计算。在参数平面Ri—Re上计算出实分岔点曲线、极限点曲线、Hopf分岔点曲线,绘出了分岔图。在分岔图上的不同区域,存在性质不同的稳定解如定常吸引子、周期吸引子等。分析了定常解、周期解的分岔过程。计算结果很好地说明大气中由基本态到对流态再到波动态最后到湍流态的物理转换过程。 连续算法对研究非线性动力系统的分岔以及耗散结构是很有效的计算方法。

The continuation algorithm is applied to calculate the steady and periodic solutions of the 5 -dimensional convection nonlinear dynamical system. The real bifurcation points curve, limit points curve and Hopf bifurcation points curve of the model are drawn in the parameter plane Ri-Re. The bifurcation diagram.is obtained. The different type of stable solutions such as stationary attractor, periodic attractor and chaotic attractor and so on exist in the different blocks or regions in the bifurcation diagram. Through analysing the bifurcation course of the steady and periodic solutions curve, the physical transitions both from steady state to periodic state and from periodic state to chaotic state which happened in the atomspheric stratified layer are discussed.The numerical computation results show that the continuation algorithm is a very effective computational method for researching into the bifurcation and dissipative structure of a nonlinear-dynamical system.