Medium amplitude model for internal waves over large topography variation

TL;DR

This paper derives and analyzes a new asymptotic model for medium amplitude internal waves over highly variable topography, relaxing previous assumptions and demonstrating improved mathematical properties and applicability.

Contribution

It introduces a generalized asymptotic model that handles large topography variations and proves its well-posedness, extending prior models with less restrictive assumptions.

Findings

Model accurately describes internal waves over complex topography.

Relaxed assumptions improve model applicability.

Proved well-posedness of the new model.

Abstract

The purpose of this paper is to present the derivation and mathematical analysis of a new asymptotic model that describes the evolution of medium amplitude internal waves propagating between a flat rigid-lid and a highly variable topography. The smallness assumptions on the topographic variation parameter used in [Communications on Pure & Applied Analysis, 2015, 14 (6): 2203-2230] and in [Asymptotic Analysis, vol. 106, no. 2, pp. 61-98, 2018] are now relaxed and the results of the aforementioned papers are improved and generalized to the complex case of large topography variation. Limiting the flow to one-layer, we also emphasize our model's well-posedness in comparison to the original asymptotic model.