Interaction of two oblique internal solitary waves in the presence of shoaling topography and rotation

Abstract

The oblique interactions between internal solitary waves frequently occur in the ocean owing to their different propagation directions after originated from more than one potential generation sites, which can further be modulated and reshaped by the varying topography and the Earth’s rotation. Here a variable-coefficient rotational Kadomtsev–Petviashvili (KP) equation is devoted to investigate the interaction of initial X-shaped waves in presence of the respective one-dimensional (1D) and two-dimensional (2D) slope-shelf topography and rotations at different latitudes. Based on the analytical solutions, the long-time results can be classified as three types depending on the initial amplitudes and oblique angles. Then, numerical results suggest that the sufficiently shallow 1D shoaling topography can render polarity change, which reshapes the waveform of oblique interactions to resemble webs composed of straight wave crest lines. If the rotation were also taken into account, then the nonlinear interactions are inhibited resulting in less waves in the eventual long-time wave packets and more junction points in the webs of waveform. More importantly, the combined effect of rotation and localized small and narrow canyons and plateaus resting on 1D shoaling topography can significantly modulate the waveforms induced by oblique interactions to make them more like rank-ordered wavetrains.