The damping of gravity waves in shallow water by energy dissipation in a turbulent boundary layer

The method of matched asymptotic expansions is applied to the determination of the damping of gravity waves propagating in turbulent conditions. The effect of the turbulence is introduced by a general system of coefficients of eddy viscosity, whilst the turbulence itself is supposed to be confined to boundary layers adjacent to a rigid impermeable bottom and the free surface. The lowest order damping in the system is found to be independent of surface turbulence and computations are made for a physically meaningful distribution of eddy viscosity in the lower boundary layer.