周期底地形上内波的Hamilton长波展开  

Hamiltonian Long Wave Expansions for Internal Waves Over a Periodically Varying Bottom

作　　者：周红燕[1] 朴大雄[1] 

机构地区：[1]中国海洋大学应用数学研究中心,山东青岛266071

出　　处：《应用数学和力学》2008年第6期676-686,共11页Applied Mathematics and Mechanics

摘　　要：给出了周期底部边界条件下两层密度成层流体中2-维非线性长波问题的Hamilton公式.从该公式出发,应用Hamilton摄动理论,导出了底地形短尺度变化下描述双向长波运动的有效Boussinesq方程和描述单向长波运动的近似KdV方程.结果的推导都是在多重尺度算子渐近分析理论框架下完成的.A Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom was derived. From the formulation, using the Hamiltonian perturbation theory, effective Boussinesq equations that describe the motion of bidirectional long waves and unidirectional equations that are similar to the KdV equation for the case in which the bottom possesses short length scale were obtained. The computations for these results are performed in the framework of an asymptotic analysis of multiple scale operators.

关 键 词：内波 Hamilton摄动理论 势函数 Dirichlet-Neumann算子 BOUSSINESQ方程 KDV方程 

分 类 号：O302[理学—力学]