Oblique interactions of mode-1 and mode-2 internal solitary waves in the presence of variable topography

Abstract

Oblique interactions between internal solitary waves (ISWs) are frequently observed in oceanic environments. However, interactions involving different vertical modes, particularly between the most common mode-1 and mode-2 ISWs, remain poorly understood. To address this gap in knowledge, this study investigates the oblique interactions between mode-1 and mode-2 ISWs using a three-dimensional, high-resolution MITgcm ocean model. We consider three scenarios involving initial idealized V-shaped ISWs in a continuously stratified environment. The results show that interactions between two mode-1 ISWs over flat bottom topography align well with theoretical predictions. In contrast, interactions between two mode-2 ISWs demonstrate stronger attenuation due to potential instabilities arising from their complex vertical structures. When examining interactions between one mode-1 ISW and one mode-2 ISW, the differing phase speeds prevent the formation of Mach stems, resulting in non-resonant, refraction-like patterns. However, in the presence of a submarine cliff, where the phase speeds of these two modes become comparable, the interactions showed Mach stem-like features, along with energy transfer from mode-1 to mode-2 ISWs. Additionally, the presence of shoaling topography can lead to the emergence of mode-3 ISWs and polarity reversals.