Layer-averaged Euler and Navier-Stokes equations

TL;DR

This paper introduces a novel multilayer approach to approximate incompressible hydrostatic free surface Euler and Navier-Stokes models, allowing for a fixed domain formulation and improved closure relations.

Contribution

It extends previous multilayer models by using an energy-based optimality criterion for closure, applicable to both Euler and Navier-Stokes systems with general stress tensors.

Findings

Water depth becomes a dynamical variable

Closure relations derived from energy optimality

Model successfully applied to Navier-Stokes with general stress tensor

Abstract

In this paper we propose a strategy to approximate incompressible hydrostatic free surface Euler and Navier-Stokes models. The main advantage of the proposed models is that the water depth is a dynamical variable of the system and hence the model is formulated over a fixed domain.The proposed strategy extends previous works approximating the Euler and Navier-Stokes systems using a multilayer description. Here, the needed closure relations are obtained using an energy-based optimality criterion instead of an asymptotic expansion. Moreover, the layer-averaged description is successfully applied to the Navier-Stokes system with a general form of the Cauchy stress tensor.