Visco-potential free-surface flows and long wave modelling
arXiv:0804.1086 · doi:10.1016/j.euromechflu.2008.11.003
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.
29 pages, 13 figures. Some figures were updated. Revised version for European Journal of Mechanics B/Fluids. Other author's papers can be downloaded from http://www.lama.univ-savoie.fr/~dutykh
References in corpus (3)
Cited by in corpus (9)
- The VOLNA code for the numerical modelling of tsunami waves: generation, propagation and inundation
- On the use of finite fault solution for tsunami generation problems
- On the relevance of the dam break problem in the context of nonlinear shallow water equations
- Derivation of dissipative Boussinesq equations using the Dirichlet-to-Neumann operator approach
- Group and phase velocities in the free-surface visco-potential flow: new kind of boundary layer induced instability
- On the motion of gravity-capillary waves with odd viscosity
- Visco-potential flows in electrohydrodynamics
- Global well-posedness and decay for viscous water wave models
- Derivation of an intermediate viscous Serre-Green-Naghdi equation