On the oblique reflection of a solitary wave

The solitary wave is a gravity water wave that travels with permanent shape and constant phase speed. It has long characteristic wavelength in the longitudinal direction and uniform transverse cross-sections. The present study is concerned with both the surface solitary wave on a homogeneous fluid and the internal solitary wave within a rigid-lid two-layer model. When two identical solitary waves with different propagation directions interact with each other, the collision problem can be converted to an oblique reflection problem replacing the symmetric plane with a rigid slip wall. This work focuses on a specific scenario called the Mach reflection. It is a strongly nonlinear phenomenon. Based on the existing theoretical and experimental research on the surface solitary wave, study has been extended to the internal solitary wave. The analyses are mainly based on the 3D fully nonlinear simulations utilising the CFD software OpenFOAM on UCL’s supercomputers. The third-order weakly nonlinear solution of an internal solitary wave has been derived and used to initialise the flow field in corresponding simulations. The code has been verified and validated through test cases on a single solitary wave and 2D collisions. The oblique reflection of a surface solitary wave with moderate amplitude has been simulated. Large-amplitude wave induced by the Mach reflection as observed in the experiment has been analysed. Two cases for internal solitary waves have been simulated where the incident wave amplitudes are small and moderate, respectively. The KP theory is only valid for the small-amplitude case. The wave profile of the moderate-amplitude case shows some distinct features that cannot be well predicted by the existing approximate models. Analyses have also been made on the physical quantities in terms of mass, momentum and energy to understand the transverse variation of the wave field. The research benefits the understanding of rogue waves induced by long wave interaction in order to protect life and property at coastal areas and in deep sea operations