两同心球间旋转流动类Lorenz方程组的分歧分析  

BIFURCATION ANALYSIS OF THE MODEL SYSTEM SIMILAR TO THE LORENZ EQUATIONS OF THE FLOW BETWEEN TWO CONCENTRIC ROTATING SPHERES

作　　者：王贺元[1] 蒋海斌[2] 

机构地区：[1]西安交通大学航空航天学院,西安710049 [2]辽宁工学院数理系,锦州121001

出　　处：《高等学校计算数学学报》2007年第3期278-288,共11页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家基础研究专项基金(G1999032801-07);中国博士后基金(2005038605);辽宁省教委科研基金资助.

摘　　要：0引言 两个同心旋转球之间的流动又称为球Couette流动．作为一个简单的模型，研究它能够为揭示流动失稳转捩至湍流这一重大理论课题的规律提供线索；同时，由于球Couette流动更象全球大气流动，研究它也能成为研究大气物理提供一个粗略的模型，为这一方面的研究提供一些理论指导．Bifurcation problems of the model system similar to the Lorenz equations of the Navier-Stokes equations for the flow between two concentric rotating spheres are discussed. Detection conditions of singular point and solution branches are given. First, we introduce some research work of spherical Couette flow and velocity-stream function form of the Navier-Stokes equations for the flow between two concentric rotating spheres. Second, we discuss bifurcation problems of the model system similar to the Lorenz equations of the Navier-Stokes equations for the flow between two concentric rotating spheres. Finally, we give a numerical example of 3-model system similar to the Lorenz equations of the Navier-Stokes equations for the flow between two concentric rotating spheres.

关 键 词：旋转流动 COUETTE流动 方程组 同心球 分歧 大气流动 大气物理 旋转球 

分 类 号：O357.1[理学—流体力学]