Oblique reflection of large internal solitary waves in a two-layer fluid

Abstract

The oblique reflection of an incident internal solitary wave is investigated using a fully-nonlinear and strongly-dispersive internal wave model. The 3rd order theoretical solution for an internal solitary wave in a two-layer system is used for the incident solitary wave. Two different incident wave amplitude cases are investigated, in which nine and eleven different incident angles are used for the small and large incident amplitude cases respectively. Under both amplitudes, at least for the cases investigated here, relatively smaller incident angles result in Mach reflection while relatively larger incident angles result in regular reflection. Under Mach-like reflection generation of a ‘stem’ is observed for a certain range of incident angles, in addition to the reflected wave. The stem is found to have, in a certain sense, the characteristics of an internal solitary wave, though the maximum stem wave amplitude is less than four times as large as the original incident internal solitary wave. The stem length is confirmed to increase faster for the larger incident wave amplitude. The maximum amplification factor for the small incident wave is the same as in previous studies. However, the maximum amplification factor for the large incident wave is less than that for the small wave. The results of these calculations are compared with those of the corresponding KP theory and it is found that a lower amplification factor may be a significant characteristic of internal solitary waves.