| 摘要: |
| 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。 |
| 关键词: 层结流体 非线性 惯性重力内波 |
| DOI： |
| 分类号: |
| 基金项目:中国科学院海洋研究所调查研究报告第2256号。国家青年基金资助，B90920106号 |
|
| NONLINEAR INERTIA-GRAVITY INTERNAL WAVE IN STRATIFIED FLUID |
|
Hou Yi jun1, Li Wei1, Wang Xinsheng2
|
|
1.Institute of Oceanology Academia Sinica, Qingdao 266071;2.Department of Pkysics, Qingdao University. Qingdao 266071
|
| Abstract: |
| 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 differential equations in two variables is obtained as follows:
(For the equations please see the PDF file.)
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 simplified 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
(For the equations please see the PDF file.) |
| Key words: Stratified fluid, Nonlinear, Inertia-gravity internal wave |
