层结切变流体非线性惯性重力内波的稳定性

THE STABILITY OF NONLINEAR INERTIO-INTERNAL GRAVITY WAVES FOR STRATIFIED SHEAR FLOW

中文摘要:

      本文从层结切变流体的非线性惯性重力内波的方程组出发,设解为行波的形式并将非线性项在平衡点附近作Taylor展开,导得了两个变量的一阶自治动力系统的常微分方程组。应用常微分方程的稳定性理论,讨论了惯性重力内波的稳定性。分析指出:在考虑了速度垂直切变和非线性作用后,惯性重力内波的稳定性发生了变化,当L<L₀时,仍然是不稳定的,但当L₀²<0或L>L₀时是稳定的结论只是在时才是正确的,当∂u/∂z>0时,L₀²<0和L>L₀成为不稳定的条件。本文还讨论了某些条件下非线性惯性重力内波的解析解。

英文摘要:

      In this paper, starting from the equations of the nonlinear inertio-internal gravity waves in stratified shear fluid, and considering the flow about a class of the progressive waves, the autonomous dynamic systems of the first-order differential equations in two variables are derived. Using the qualitative theory of the differential equations, we analyze qualitatively the topological structure of the integral curves in the neighbourhood of the origin on a phase plane with Cartesian axes u, v.On the du/dz (the velocity shear), L²-L₀²(L is the horizontal scale, L₀ is the Rossby radius of deformation) plane, the integral curves divide the plane into some domains of different stability.