The Vertical Structure of the Wave Bottom Boundary Layer over a Sloping Bed: Theory and Field Measurements

Abstract

Theoretical solutions for the wave bottom boundary layer (WBL) over a sloping bed are compared with field measurements in the nearshore zone. The WBL theory is constructed using both viscoelastic?diffusion and conventional eddy viscosity turbulent closure models. The velocity solutions are then matched with those of the interior flow, given by Chu and Mei potential theory for surface gravity waves over a sloping bottom. The field measurements were obtained with a coherent Doppler profiler over a 2° bed slope. Results are presented for both flat and rippled bed conditions, the latter being characterized by low steepness, linear transition ripples. Close to the bed, the observed velocity profiles change rapidly in amplitude and phase relative to potential flow theory, indicating the presence of a wave boundary layer with a thickness of 3?6 cm. The observed velocity and shear stress profiles are in good agreement with the theory. The sloping bottom has significant effects on the vertical velocity, but not on the horizontal velocity and shear stress. Bottom roughness and friction velocity are estimated from optimizing the model?data comparisons. The friction velocities and wave friction factors are found to be consistent with values obtained from the momentum integral method and from the nearbed turbulence intensity, and with Tolman's semiempirical formulation.