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基于抛物化稳定性方程,研究了边界层中TS波及其高阶谐波的线性和非线性演化问题。由局部法和Landau展开式导出初始条件,并计算了扰动幅值和速度型等的演化过程和特征,特别是非线性的重要作用。探讨了初始幅值、压力梯度、扰动频率对扰动演化的影响及其规律,这与边界层的稳定性和转捩研究紧密相关。算例结果与全Navier-Stokes方程的直接数值模拟结果一致。
Based on the parabolic stability equation, the linear and nonlinear evolution of the TS wave and its higher order harmonics in the boundary layer are investigated. The local conditions and the Landau expansion are used to derive the initial conditions, and the evolution process and characteristics of disturbance amplitude and velocity type, especially the important role of nonlinearity, are calculated. The effects of initial amplitude, pressure gradient and frequency of disturbance on the evolution of disturbances and their regularities are discussed, which are closely related to the study on the stability and transition of the boundary layer. The results of the example are consistent with the direct numerical simulation of the whole Navier-Stokes equation.