有限深两层流体中内孤立波传播演化理论模型研究  

Investigation on propagation and evolution models for internal solitary waves in a two layer fluid system of finite depth

作　　者：盛立[1] 王怡然[2,3] 尤云祥[2,3] 张新曙[2,3] 

机构地区：[1]中国人民解放军92537部队 [2]上海交通大学海洋工程国家重点实验室 [3]高新船舶与深海开发装备协同创新中心

出　　处：《水动力学研究与进展（A辑）》2016年第6期659-672,共14页Chinese Journal of Hydrodynamics

基　　金：国家自然科学基金项目(11372184);国家重大基础研究计划(973项目;2015CB251203;2013CB036103)~~

摘　　要：该文对Choi和Camassa给出的一个内孤立波方程模型中的系数进行了修正,并给出了基于方程的内孤立波定态解表达式,将其称为内孤立波me Kd V理论解,进而采用有限体积/有限差分混合方法数值求解内孤立波的三类(Kd V、e Kd V和me Kd V型)非线性传播演化方程,分别以内孤立波的Kd V、e Kd V、MCC和me Kd V定态解作为初始输入波,研究其非线性传播演化特性,并获得其适用性条件。结果表明,三类非线性传播演化方程,只适合于相应内孤立波定态解初始波的定态传播,而对其他定态解初始波将发生波形变形、分裂等非线性现象。在此基础上,定量地给出了三类非线性传播演化方程的适用性条件,为采用何种非线性方程来研究实际海洋中内孤立波的传播演化问题提供了理论依据。The paper presents a modification for the coefficients of a unidirectional model for internal solitary waves given by Choi and Camassa, and a steady-state solution based on the modified unidirectional model is derived, which is called as the meKdV solution. A finite-difference/finite-volume method is then proposed to solve three classes of unidirectional models with KdV, eKdV and meKdV tpyes where four classes of steady-state solutions with KdV, eKdV, meKdV and MCC types for internal solitary waves are taken as initial conditions, the nonlinear propagation and evolution characteristics for such four classes of initial solitary waves under three classes of unidirectional models are considered. The applicability conditions for the three classes of unidirectional models are investigated. Results show that three classes of unidirectional models can only be applicable for steady-state propagation of the initial solitary wave with the same type, while for other initial solitary waves, nonlinear phenomena such as distortion and fission will happen during their propagations. The investigation quantitatively characterizes the applicability conditions on three classes of unidirectional models for internal solitary waves and provides an important theoretical foundation for that, what kinds of nonlinear equations can be chosen to model propagation and evolution characteristics of internal solitary waves in the ocean.

关 键 词：内孤立波 非线性模型 传播演化 数值模拟 

分 类 号：TV139.2[水利工程—水力学及河流动力学]