Hyperbolic model of internal solitary waves in a three-layer stratified fluid

TL;DR

This paper introduces a new hyperbolic model for internal solitary waves in a three-layer stratified fluid, enabling efficient simulation and analysis of wave propagation and interactions in complex stratified environments.

Contribution

The paper develops a novel hyperbolic model reducing the multi-layer Green--Naghdi equations to a first-order system for better analysis and numerical simulation of internal waves.

Findings

Model accurately predicts internal solitary wave behavior.

Numerical results agree with experimental data.

Study of wave interactions reveals new insights.

Abstract

We derive a new hyperbolic model describing the propagation of internal waves in a stratified shallow water with a non-hydrostatic pressure distribution. The construction of the hyperbolic model is based on the use of additional `instantaneous' variables. This allows one to reduce the dispersive multi-layer Green--Naghdi model to a first-order system of evolution equations. The main attention is paid to the study of three-layer flows over uneven bottom in the Boussinesq approximation with the additional assumption of hydrostatic pressure in the intermediate layer. The hyperbolicity conditions of the obtained equations of three-layer flows are formulated and solutions in the class of travelling waves are studied. Based on the proposed hyperbolic and dispersive models, numerical calculations of the generation and propagation of internal solitary waves are carried out and their comparison with experimental data is given. Within the framework of the proposed three-layer hyperbolic model, a numerical study of the propagation and interaction of symmetric and non-symmetric soliton-like waves is performed.