两同心球间旋转流动类Lorenz方程组的静态分歧  

Bifurcation Problems of the Model System Similar to the Lorenz Equations of the Flow Between Two Concentric Rotating Spheres

作　　者：丁素珍[1] 王贺元[1] 

机构地区：[1]辽宁工学院数理科学系,辽宁锦州121001

出　　处：《数学研究》2005年第4期386-392,共7页Journal of Mathematical Study

基　　金：国家基础研究专项基金(G1999032801-07);辽宁省教育厅科研基金;辽宁工学院教师基金

摘　　要：对同心球间旋转流动的N av ier-S tokes方程谱展开后进行三模态截断,讨论了所得到的类Lorenz型方程组的分歧问题.给出了静态奇异点的条件,并计算出解分支.首先,简要介绍了Lorenz方程组以及用Lorenz截断法讨论非线性问题的意义,其次,推导同心球间旋转流动N av ier-S tokes方程的流函数-涡度形式,最后,讨论同心球间旋转流动的类Lorenz型方程组的分歧问题.Bifurcation problems of the Lorenz equations of obtained from the Navier-Stokes equations for the flow between two concentric rotating spheres is discussed, detection conditions of singular point and solution branches are given. First, we introduce Lorenz equations and meaning of this kind of nonlinear problem, second, we present velocity-stream function form of the Navier-Stokes equations for the flow between two concentric rotating spheres, third, we discuss bifurcation problems of the model system similar to the Lorenz equations obtained from the Navier-Stokes equations for the flow between two concentric rotating spheres.

关 键 词：NAVIER-STOKES方程 球Couette流 LORENZ方程 

分 类 号：O175.24[理学—数学]