Finite-amplitude wave propagation in a stratified fluid of variable depth

TL;DR

This paper models how solitary waves behave in a stratified fluid with variable depth using the variable-coefficient Korteweg-de Vries equation, revealing wave breaking points and amplitude dependencies.

Contribution

It applies the variable-coefficient Korteweg-de Vries equation to analyze interfacial wave transformation and soliton dynamics in variable-depth two-layer fluids, identifying key breaking points.

Findings

Soliton breaks at two transient points during transformation.

Soliton amplitude depends on the lower layer's thickness.

Wave behavior changes with fluid depth variations.

Abstract

Variable-coefficient Korteweg - de Vries equation is applied to describe the interfacial wave transformation in two-layer fluid of variable depth. The soliton dynamics in this fluid is studied. The solitary wave breaks in two transient points. One of them is the point when two-layer fluid transforms to the on-layer flow. The second one is the point where layer thickness are equaled. The soliton amplitude dependence on the thickness of lower layer is found.