Dynamics of internal solitary waves with nonlocal coupling via a two-dimensional modified intermediate long wave model

Abstract

This study presents a novel (2+1)-dimensional modified Intermediate Long Wave (2D-mILW) model to characterize the internal solitary waves (ISWs) in finite-depth, stratified oceans. Unlike classical one-dimensional models, the proposed model incorporates nonlocal interfacial coupling with a finite-depth lower layer and weak transverse propagation, enabling the description of oblique wave fronts and two-dimensional modulations. Derived via a multi-scale perturbation expansions from the three-dimensional Euler equations, the model satisfies mass, momentum, and energy conservation laws. An approximate analytical solution is obtained, and numerical simulations confirm that the model accurately captures steady ISW propagation, with wave speeds matching theoretical predictions. This work provides a unified theoretical framework for studying two-dimensional ISWs in finite-depth stratified oceans with a flat bottom, while the extension to variable bottom topography is left for future investigation.