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

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