Abstract Head-on collision of two internal solitary waves (ISWs) in a two-layer inviscid fluid with fully nonlinear free-surface (FS) condition is investigated numerically in this paper. The collision process of and nonlinear interaction of internal solitary waves is studied based on nonlinear potential flow theory and a series of numerical simulations are conducted using a multi-domain boundary element method (MDBEM). The numerical model is validated by experiment for the simulation of ISWs propagating. The computation results show that the collision of ISWs is the asymmetric and nonlinear process in which the rundown motion causes the interface displacement penetrates the interface. The collision leaves imprints on small dispersive trailing waves which accounts for the attenuation with each departing ISW tilting slightly backward with respect to the direction of its propagation. In addition, the characteristic of collision process including run up, residence time, surface wave feature is discussed. During the collision, the wave spends more time falling than rising for all cases and the residence time is very long for waves of small amplitude, large depth ratios and density ratios. Considering the free surface of the top layer whether or not makes contributions to the run up and the residence time is larger if the top boundary is free surface.

中文翻译：

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分层流体中两个非线性内部孤立波的正面碰撞

摘要 本文数值研究了具有完全非线性自由表面（FS）条件的两层无粘性流体中两个内部孤立波（ISW）的正面碰撞。基于非线性势流理论研究了内部孤立波的碰撞过程和非线性相互作用，并采用多域边界元法(MDBEM)进行了一系列数值模拟。该数值模型通过实验验证了ISWs传播的模拟。计算结果表明，ISWs的碰撞是一个非对称的非线性过程，在这个过程中，滑移运动导致界面位移穿透界面。碰撞在小的色散拖尾波上留下印记，这说明了每个离开的 ISW 相对于其传播方向略微向后倾斜的衰减。此外，还讨论了碰撞过程的特性，包括加速、停留时间、表面波特征。在碰撞过程中，波在所有情况下下降的时间都比上升的时间长，并且对于小振幅、大深度比和密度比的波，停留时间很长。考虑顶层的自由表面是否对爬升有贡献，如果顶层边界是自由表面，停留时间更大。在所有情况下，波浪下降的时间多于上升的时间，并且对于小振幅、大深度比和密度比的波浪，停留时间非常长。考虑顶层的自由表面是否对爬升有贡献，如果顶层边界是自由表面，停留时间更大。在所有情况下，波浪下降的时间多于上升的时间，并且对于小振幅、大深度比和密度比的波浪，停留时间非常长。考虑顶层的自由表面是否对爬升有贡献，如果顶层边界是自由表面，停留时间更大。