Bottom frictional effects on periodic long wave propagation

A new Boussinesq-type model describing periodic wave propagation over a constant depth has been developed for the cases where the effects of a turbulent boundary layer are significant. In this paper, the eddy viscosity model is employed in the turbulent boundary layer and is further approximated as a linear function of the distance measured from the seafloor. The boundary-layer velocities are coupled with the irrotational velocity in the core region through the boundary conditions. The leading order effects of the boundary layer on wave propagation appear in the depthintegrated continuity equation to account for the velocity deficit inside the boundary layer. The bottom stress, the boundary layer thickness and the magnitude of the turbulent eddy viscosity are part of the solutions. An iterative scheme is introduced to find them. A numerical example for the evolution of periodic waves propagating in a one-dimensional channel is discussed to illustrate the numerical procedure and the physics involved.