ON PROBLEMS IN THE WEAKLY NONLINEAR THEORY OF HYDRODYNAMIC STABILITY AND ITS IMPROVEMENT
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摘要: 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。
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关键词:
- 流动稳定性 /
- 弱非线性理论 /
- 修正的Landau方程
Abstract: 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 n... -
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