共轴异向旋转筒间不可压流的临界主不稳定性

基于长隙比无穷大和Tollmien-Schilchting 行谐波假设，通过导出坐标系下不可压一阶改型边疆特征值问题，实现了异向旋转筒流动临界主不稳定性的线性分析，在稳定性方程离散中引入了一类高精度对称紧致差分格式，在特征值搜索中发展了一个高效率复矩阵双重反迭代算法。双临界点分析揭示了几何参数、、流动参数、流动参数、扰动参数相互间的变化规律。理论结果同实验测量数据基本一致。

Critical primary instabilities in incompressible flow between counter-rotating coaxial cylinders

Based on the assumptions of infinite aspect ratio and Tollmien Schlichting travelling harmonic wave, the critical primary instabilities in incompressible flow between counter rotating cylinders are investigated using linear theory. A first order modified continuous eigenvalue problem for the flow considered here is derived in cylindrical coordinate. A family of high accuracy symmetric compact difference schemes are introduced to discretize the stability equations, and then a high efficiency dual reverse iteration with complex form is improved for the eigenvalue searching. Results obtained numerically at bicritical points reveal some relations among the parameters of geometry, flow, and disturbance. Theoretical computations presented here agree well with the data from experimental measurements.