Oceanic internal solitary waves in three-layer fluids of great depth

This paper is mainly concerned with modeling nonlinear internal waves in the ocean of great depth. The ocean is assumed to be composed of three homogeneous fluid layers of different densities in a stable stratified configuration. Based on the Ablowitz-Fokas-Musslimani formulation for irrotational flows, strongly nonlinear and weakly nonlinear models are developed for the "shallow-shallow-deep" and "deep-shallow-deep" scenarios. Internal solitary waves are computed using numerical iteration schemes, and their global bifurcation diagrams are obtained by a numerical continuation method and compared for different models. For the "shallow-shallow-deep" case, both mode-1 and mode-2 internal solitary waves can be found, and a pulse broadening phenomenon resulting in conjugate flows is observed in the mode-2 branch. While in the "deep-shallow-deep" situation, only mode-2 solitary waves can be obtained. The existence and stability of mode-2 internal solitary waves are confirmed by solving the primitive equations based on the MITgcm model.