非线性正压不稳定

本文从非线性正压涡度方程出发,考虑了行波一类的流动,并导得一个单自由度的二阶自治动力系统的常微分方程。应用常微分方程的定性理论和几何理论,在相平面的平衡点附近,对积分曲线的几何拓扑结构作了定性分析,对于两个平衡点分别导得了非线性正压不稳定的判据。还分析了整个相平面上运动的全局特征和平衡状态与参数的关系,更直观地得到与前面一致的不稳定判据。

NONLINEAR BAROTROPLC INSTABILITY

Applying the nonlinear barotropic vorticity equation to the flow of moving waves, an ordinary differential equation with single degree offreedom of the autonomous dynamic system is derived. Based on the qual-itative and geometric analyses of the differential equation, the geometrictopological structure of the integral curve is investigated in the neighbor-hood of the balance points on the phase-plane. Barotropic instability criterion is established for two balance points respectively. Overall char-acteristics of the motion on the phase-plane and the relation of balancestates to the parameters are analysed and criteria similar to the above-stated are thus found in a more intuitive way.