TURBULENT ROUGH BED BOUNDARY LAYERS IN THE PRESENCE OF NON-LINEAR SURFACE WAVES

Wind-generated surface waves give rise to the development of periodic unsteady boundary layers on the sea bed. Naturally-occurring waves may have highly non-linear characteristics which will affect the boundary layer through the action of the horizontal pressure gradient at the bed. The frictional characteristics of the boundary layer will, in turn, influence the subsequent evolution of a wave, causing the dissipation of wave energy and hence wave attenuation. In the present work we investigate the effect of a periodic (but non-sinusoidal) pressure gradient 'input' to the calculation of turbulent flow over a rough bed. A k-ε turbulence closure is used to obtain values for the wave friction factor, f_w and wave energy dissipation factor, f_e for different values of the relative roughness a/k_s, where a is the amplitude of fluid motion at the bed and k_s is the Nikuradse equivalent sand roughness of the bed. At given a/k_s the importance of wave non-linearity effects is examined for different values of H/d and d/L, where H is the peak-to-trough wave height, d is the water depth, and L is the wavelength. In the final part of the paper the propagation of wave power is considered in relation to the computed values of f_e.