Derivation of stochastic models for coastal waves

TL;DR

This paper develops stochastic versions of classical coastal wave models incorporating location uncertainty, leading to modified advection and noise terms, through asymptotic expansion techniques.

Contribution

It introduces stochastic formulations of well-known coastal wave models using asymptotic expansion under location uncertainty, a novel approach in this context.

Findings

Stochastic models include modified advection terms.

Emergence of advection noise terms due to LU formalism.

Models derived for Serre-Green-Naghdi, Boussinesq, and shallow water waves.

Abstract

In this paper, we consider a stochastic nonlinear formulation of classical coastal waves models under location uncertainty (LU). In the formal setting investigated here, stochastic versions of the Serre-Green- Nagdi, Boussinesq and classical shallow water wave models are obtained through an asymptotic expansion, which is similar to the one operated in the deterministic setting. However, modified advection terms emerge, together with advection noise terms. These terms are well-known features arising from the LU formalism, based on momentum conservation principle.