Large-amplitude solitary waves in two-layer density stratified water

TL;DR

This paper develops a comprehensive theory for large-amplitude solitary waves in a two-layer stratified water system, providing existence results for waves with various amplitudes and detailed wave properties.

Contribution

It introduces a global bifurcation framework for large-amplitude solitary waves in stratified water, extending beyond small-amplitude approximations and including waves near stagnation points.

Findings

Existence of a global solution curve for solitary waves in stratified water.

Construction of small-amplitude waves via center manifold reduction.

Identification of waves approaching stagnation points.

Abstract

We present a large-amplitude existence theory for two-dimensional solitary waves propagating through a two layer body of water. The domain of the fluid is bounded below by an impermeable flat ocean floor and above by a free boundary at constant pressure. For any piecewise smooth upstream density distribution and laminar background current, we construct a global curve of solutions. This curve bifurcates from the background current and, following along the curve, we find waves that are arbitrarily close to having horizontal stagnation points. The small-amplitude waves are constructed using a center manifold reduction technique. The large-amplitude theory is obtained through analytical global bifurcation together with refined qualitative properties of the waves.