Medium amplitude model for internal waves over large topography variation

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 Lteif et al. (2015) [19] and in Lteif and Israwi (2018) [18] 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.