| 摘要: |
| 从地球流体运动浅水模式的非线性方程出发，采用行波分析法给出了平面自治系统，利用相图理论，讨论了行波解的性质，提出了平面非线性系统不存在孤立波的结论；利用K-B平均法，首次获得有限振幅惯性重力波以Rossby数作为控制参量的非线性频散关系。 |
| 关键词: 非线性重力波 频散关系 |
| DOI： |
| 分类号: |
| 基金项目:国家自然科学基金!49476276;山东省重点基金!950128;中国科学院重点基金!TZ952-S1-420 |
附件 |
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| NONLINEAR GRAVITY WAVE IN GEOPHYSICAL FLUID |
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Yang Liangin, Hou Yjun, Xie Qiang, Cheng Minghua
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Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071
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| Abstract: |
| Variable transformation is used to convert the nonlinear equations governing geophysical fluid’s motion in a shallow model into a plane automous system
F (U,V) = 0
G (U,V) = 0
Phase portrait analysis on the basis of the geometric theory of ordinary differential equations was used to study the travelling wave solution properties. The result indicates that there are no solitary waves in the nonlinear system.
In order to obtain the dispersive relationship of the finite amplitude inertia-gravity wave, Taylor expansion was used in the above system at the equilibrium point (0,0). Using the K-B average method in the expansion yield, the dispersive relationship can be written as (For the equations please see the PDF file.) (Rossby number for inertia-gravity wave). Thus, the dispersive relationship includes Rossby number and the circular frequency σ increases with ε. |
| Key words: Nonlinear gravity wave, Dispersive relationship |
