Visco-potential free-surface flows and long wave modelling

TL;DR

This paper introduces a visco-potential formulation for free-surface flows, incorporating local and nonlocal dissipative effects, and analyzes their impact on wave dispersion and attenuation through theoretical and computational methods.

Contribution

It presents a novel visco-potential model with nonlocal dissipation terms for free-surface flows and analyzes their effects on wave behavior.

Findings

Nonlocal dissipative term affects wave attenuation.

Dispersion relation properties are characterized.

Spectral methods are used for numerical solutions.

Abstract

In a recent study [DutykhDias2007] we presented a novel visco-potential free surface flows formulation. The governing equations contain local and nonlocal dissipative terms. From physical point of view, local dissipation terms come from molecular viscosity but in practical computations, rather eddy viscosity should be used. On the other hand, nonlocal dissipative term represents a correction due to the presence of a bottom boundary layer. Using the standard procedure of Boussinesq equations derivation, we come to nonlocal long wave equations. In this article we analyse dispersion relation properties of proposed models. The effect of nonlocal term on solitary and linear progressive waves attenuation is investigated. Finally, we present some computations with viscous Boussinesq equations solved by a Fourier type spectral method.