Numerical analysis of the overtaking of internal solitary waves based on potential flow theory

Abstract

In a two-layer fluid system, the multidomain boundary element method considering the free surface of the top layer and the KdV equation Fourier spectrum method are used to solve the overtaking problem of internal solitary waves (ISWs), and the waveform evolution characteristics with different initial amplitude ratios are analyzed in the two methods. In the multidomain boundary element method, the manifestation of free surface waves when ISWs catch up with each other is revealed considering the free surface effect. Results show that the overtaking of ISWs can be divided into three types according to the ratio of initial amplitude based on the possible merging of two ISWs into a quasi-solitary wave shape and the possible interaction of two ISWs. The classification criteria are consistent with classification in the overtaking of solitary waves. Many differences are observed in the amplitude variation curves obtained by the two methods, but the minimum amplitudes of the action center are both located near the boundary point of the possible interaction of the two ISWs. The evolution process of the free surface waves induced by ISWs is almost consistent with that of ISWs considering shape and time.