Visco-potential free-surface flows and long wave modelling

In a previous study [D. Dutykh, F. Dias, Viscous potential free-surface flows in a fluid layer of finite depth, C. R. Acad. Sci. Paris, Ser. I 345 (2007) 113–118] 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 analyze 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.