冷迳流的稳定性及其解析解的分析

Stability of Cold-Air Drainage and Analysis of Analytic Solution

本文利用相法讨论了y方向无限伸延的冷迳流方程.首先发现其非线性项作用由于z方向上的补偿作用而消失,即其相空间的方程是四阶线性常微分方程.利用Hurwitz方法分析其稳定时,证明了唯有中性大气符合冷迳流的稳定性条件.其解析解的趋势表明与观测结果类似.

The equations of cold-air drainage are studied using a phase angle function in this paper. The terrain is considered as an ideal two dimensional slope extending infinitely in y- direction . Firstly , it is found that nonlinear terms disappear because of some effects in z-direction . Then a linear fourth-order differential equation is obtained and its stability is analysed with Hurwitz. Its solution is obtained . Only neutral atmosphere according with stability condition of cold-air drainage .