关于含有水平及垂直切变的二维流体的非线性波的稳定性

NONLINEAR WAVE STABILITY OF THE TWO-DIMENSIONAL FLUID WITH HORIZONTAL AND VERTICAL WIND SHEAR

摘要: 本文讨论了含有水平和垂直切变作用的二维流体非线性波的稳定性和解析解,其结果表明与文献1不同的是不仅决定于垂直切变,而且还决定于水平切变以及y方向的非线性作用,其稳定区域有较大的改变。这些作用均易导致扰动发生、发展。此外,据Poincare'三元变量的控制方程奇点分类法,求得了其奇点附近的解析解,其解为余弦波及椭圆余弦波的迭加,且能在一定条件下退化为谐波解,显示了二维非线性流体的某些特征,也拓广了文献1的结果。

Abstract: In this paper the effect of horizontal and vertical wind shear on the stability and the solution of nonlinear waves for a two-dimensional fluid were discussed. The results show that condition of stability is rather different from Liu Shikuo's results (1984).The stability still decided the effects of horizontal and vertical wind shear, and the nonlinear effect in Y-direction, so that some stable domain will be changed. This means that those effects even more easily lead to development of disturbances.