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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。
In this paper, the coefficients in an internal solitary wave equation model given by Choi and Camassa are modified and an equation based solution to the internal solitary wave steady state solution is given, which is called the internal solitary wave me Kd V theory solution (Kd V, e Kd V and me Kd V) nonlinear propagation evolution equations of internal solitary waves are numerically solved by the finite volume / finite difference method. The internal solitary wave Kd V, e Kd V, MCC And me Kd V as the initial input wave, the nonlinear propagation characteristics are studied and their applicability conditions are obtained. The results show that the three kinds of nonlinear propagation evolution equations are only suitable for the steady state propagation of the initial wave of the soliton in the soliton of the corresponding soliton, while the nonlinear phenomena such as the deformation and splitting of the wave on the initial wave of the other solitons will occur. On this basis, the applicability conditions of three kinds of nonlinear propagation evolution equations are given quantitatively, which provides a theoretical basis for using what nonlinear equations to study the propagation and evolution of internal solitary waves in the real ocean.