Influence d’un coefficient de frottement dépendant de la profondeur sur la propagation des vagues sur un lit poreux

Abstract

Many maritime structures are made of submerged permeable rubble mound breakwaters. Most numerical models dealing with wave propagation on a porous bed linearize Forchheimer's equation through Lorentz's hypothesis of equivalent work. The friction coefficient f is found by iteration and always averaged on the structure volume. In this paper we write and solve the dispersion relationship for a friction coefficient that is variable on the water depth. It is shown that a constant friction coefficient is only valid for water depth hp and wavelength L with hp/L < 1/10. Above this threshold, the errors on the imaginary part of the wavenumber are not negligible and reach 20% of the peak value. Calculations with constant and depth-dependent friction coefficient produce a different decay of waveheight. Mots cles. Lit poreux, houle, relation de dispersion, bicouche, elements finis.