Stability analysis of a class of unsteady nonparallel incompressible flows via separation of variables
Stability analysis of a class of unsteady nonparallel incompressible flows via separation of variables
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DOI：
10.1063/1.2814296
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发表时间：
2007-11
影响因子：
4.6
通讯作者：
G. Burde;I. Nasibullayev;Alexander Zhalij
中科院分区：
文献类型：
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作者：
G. Burde;I. Nasibullayev;Alexander Zhalij
本文用分离变量法研究了某些非定常三维流动（柱坐标系下粘性不可压Navier-Stokes方程的精确解）的稳定性。本文研究了旋转多孔圆柱内的流动和同轴旋转圆柱间隙内的流动。将稳定性方程转换为新的变量允许扰动形式（对应于稳态平行流稳定性问题的正常模式），使得线性稳定性问题精确地归结为常微分方程的特征值问题。利用基于切比雪夫多项式的谱配点法对特征值问题进行了数值求解。结果显示依赖的稳定性阈值的参数的问题和空间结构的不稳定扰动模式。对于某些类的扰动，精确的解析解的特征值…
Stability of some unsteady three-dimensional flows (exact solutions of the viscous incompressible Navier–Stokes equations in cylindrical coordinates) is studied via separation of variables in the linearized equations for the flow perturbations. The flows in an expanding rotating porous cylinder and in a gap between two coaxial rotating cylinders are considered. Converting the stability equations to the new variables allows perturbation forms (counterparts of normal modes of the steady state parallel flow stability problem) such that the linear stability problems are exactly reduced to eigenvalue problems of ordinary differential equations. The eigenvalue problems are solved numerically with the help of the spectral collocation method based on Chebyshev polynomials. The results showing dependence of the stability threshold on the parameters of the problems and a spatial structure of the unstable perturbation modes are presented. For some classes of perturbations, exact analytical solutions of the eigenvalu...