层结流体中的非线性惯性重力内波

NONLINEAR INERTIA-CRAVITY INTERNAL WAVE IN STRATIFIED FLUID

根据地球流体力学基本方程组，在密度垂直层结的情况下，引进行波坐标，研究非线性定形波在相平面上的几何拓扑结构。严格论证了不存在定形孤立波，并通过Hamilton函数及其角作用变换把行波系统化成最简形式，由此而得到非线性惯性重力内波的解析解。

Based on the fundamental equations of geophysical fluid dynamics and the consequence of vertical density stratification, this research applies travelling wave coordinate to the 3-D Boussinesq fluid to study the nonlinear permanent wave. An autonomous system of ordinary differcntial equations in two variables is obtained as follows:Rigorous study of the mathematical mechanics of the geometric topological structures in phase plane led to the conclusion that nonlinear wave is periodic in propagation direction and that solitary waves do not exist.Further researches showed the travelling wave system can be transformed into a simpler form by using the Hamilton function and 'action-angle' variables so that the complex nonlinear wave was simp1ified into a system like simple harmonic vibration.Using the transformed form of nonlinear wave and the directional angle of travelling wave, the analytic solution of nonlinear inertia-gravity internal wave can be written in the form