Strongly nonlinear models for internal waves: an application for the dam-break problem

TL;DR

This paper investigates strongly nonlinear models for internal wave propagation, comparing their predictions to direct numerical simulations of the Euler system, demonstrating their accuracy and efficiency in modeling wave dynamics in stratified fluids.

Contribution

It introduces and assesses nonlinear models for internal waves, demonstrating their robustness and computational efficiency compared to full Euler simulations.

Findings

Models accurately predict near-solitary wave formation.

Models are computationally less expensive than DNS.

Good agreement with Euler system simulations.

Abstract

Strongly nonlinear models of internal wave propagation for incompressible stratified Euler fluids are investigated numerically and analytically to determine the evolution of a class of initial conditions of interest in laboratory experiments. This class of step-like initial data severely tests the robustness of the models beyond their strict long-wave asymptotic validity, and model fidelity is assessed by direct numerical simulations (DNS) of the parent Euler system. It is found that the primary dynamics of near-solitary wave formation is remarkably well predicted by the models for both wave and fluid properties, at a fraction of the computational costs of the DNS code.