Visco-potential free-surface flows and long wave modelling. (English) Zbl 1167.76323
Summary: In a previous study [D. Dutykh, F. Dias, C. R., Math., Acad. Sci. Paris 345, No. 2, 113–118 (2007; Zbl 1117.76023)] 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.
MSC:
| 76D33 | Waves for incompressible viscous fluids |
Keywords:
free-surface flows; viscous damping; long wave models; Boussinesq equations; dissipative Korteweg-de Vries equation; bottom boundary layerCitations:
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