流动稳定性弱非线性理论中的问题及其改进

ON PROBLEMS IN THE WEAKLY NONLINEAR THEORY OF HYDRODYNAMIC STABILITY AND ITS IMPROVEMENT

流动稳定性弱非线性理论存在三个主要问题:(1)其摄动参数收敛半径太小且无具体估值;(2)其解有特定结构,一般不能满足很多实际问题的初始条件;(3)当其线性部分不是中性时,Landau系数的确定法不唯一,不知何者应是最好的方法。本文以平面Poiseuille流为例,从理论上解决了问题(1)和(2),并提出了改进办法。又通过将理论和数值模拟结果相比较的方法,澄清了问题(3)。改进了的理论,将可解决许多实际问题。

There are three main problems in the weakly nonlinear theory of hydrody-namic stability: (1) The radius of convergence with respect to the perturbation parameter is too small and there is no concrete estimation for it. (2) The solution has a special structure, thus in general, it can not satisfy the initial condition posed by many practical problems. (3) When the linear part of its solution does not correspond to a neutral case, there are more than one way in determining the Landau constants, and actually no one knows which way would yield the best result. In this paper, the problems (1) and (2) are solved theoretically, ways for its improvement have been proposed. By comparing the theoretical results with those obtained by numerical simulations, the problem in (3) has been clarified.