同轴圆柱间旋转流动类Lorenz型方程组的分歧问题

Bifurcation Problems on Model System Similar to Lorenz Equations of Flow between Two Coaxial Rotating cylinders

根据stokes算子的特征函数,利用谱方法研究了由轴对称Taylor-Couette流导出的三模态方程组。给出了三模态方程组平衡点存在的条件,讨论了所得到的三模态类Lorenz型方程组的静态分歧问题。给出了奇异点存在的条件,并计算出简单分歧点处解分支。

According to eigenfunction of Stokes operator, using spectral method 3-model system equations for axisymmetric, Taylor-Couette flows were derivated. The model system was similar to the Lorenz equation.The existence conditions of equilibrium point for 3-model system equations were given. Steady state bifurcation problems on the 3-model system similar to the Lorenz equations for the flow between two concentric rotating cylinders were discussed, with existence conditions of singular point given and solution branches of simple bifurcation point computated.