Boundary layer dynamics and bottom friction in combined wave–current flows over large roughness elements

Abstract

In the coastal ocean, interactions of waves and currents with large roughness elements, similar in size to wave orbital excursions, generate drag and dissipate energy. These boundary layer dynamics differ significantly from well-studied small-scale roughness. To address this problem, we derived spatially and phase-averaged momentum equations for combined wave–current flows over rough bottoms, including the canopy layer containing obstacles. These equations were decomposed into steady and oscillatory parts to investigate the effects of waves on currents, and currents on waves. We applied this framework to analyse large-eddy simulations of combined oscillatory and steady flows over hemisphere arrays (diameter $D$ ), in which current ( $U_c$ ), wave velocity ( $U_w$ ) and period ( $T$ ) were varied. In the steady momentum budget, waves increase drag on the current, and this is balanced by the total stress at the canopy top. Dispersive stresses from oscillatory flow around obstacles are increasingly important as $U_w/U_c$ increases. In the oscillatory momentum budget, acceleration in the canopy is balanced by pressure gradient, added-mass and form drag forces; stress gradients are small compared to other terms. Form drag is increasingly important as the Keulegan–Carpenter number $KC=U_wT/D$ and $U_c/U_w$ increase. Decomposing the drag term illustrates that a quadratic relationship predicts the observed dependences of steady and oscillatory drag on $U_c/U_w$ and $KC$ . For large roughness elements, bottom friction is well represented by a friction factor ( $f_w$ ) defined using combined wave and current velocities in the canopy layer, which is proportional to drag coefficient and frontal area per unit plan area, and increases with $KC$ and $U_c/U_w$ .