A terrain-following modeling of wave boundary layers

Applying the method of conformal transformation, we put forward a terrain-following modeling approach for Stokes boundary layer flows. This complements the recent new development of the exact Floquet theory of water waves, that gives a complete basis of solutions for time harmonic potential flows over an arbitrarily periodic seabed. The theory applies for any given frequency, including the resonant waves. For a non-steep seabed profile, but not necessarily small undulation height comparing with the water depth, the analytical solutions can be obtained for the boundary layer velocities, bed shear stresses and rate of viscous dissipation, explicitly showing the variations both across the boundary layer and along the bed. For a relatively steep bed profile, a remedy is proposed that allows the velocity profiles to be locally determined across the boundary layer avoiding solving the 2-D differential equation for the vorticity. The modeling methodology is presented here for a constant viscosity, including the case of constant eddy viscosity, but can be extended to the case of variable eddy viscosity to improve turbulence modeling.