A terrain-following model of wave boundary layers

Abstract

Over a variable seabed, conventional boundary layer approximations are rendered to be inadequate because of the large variations in bed elevation in the direction of wave propagation. Applying the method of conformal transformation to map the flow domain with a corrugated boundary onto a uniform strip, we put forward a terrain-following modeling approach for Stokes boundary layer flows, accompanying the recent development of the exact Floquet theory of water waves over a generally periodic seabed. For a non-steep seabed profile, but not necessarily small undulation height compared with the water depth, we solve the vorticity equation to obtain the analytical solutions for the boundary layer velocities, bed shear stress 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.