Interaction of Waves with Idealized High-Relief Bottom Roughness

Abstract

Considerable uncertainty exists about how to represent wave bottom friction in coastal systems like reefs where orbital excursions are similar to roughness element size. Here, interactions between waves and large bottom roughness were investigated using Large Eddy Simulations of oscillatory flow over infinite hemisphere arrays. Wave amplitude, period, and hemisphere spacing were varied to investigate the dependence of kinematics and dynamics on dimensionless parameters. The net effect of topography on the oscillatory flow was assessed using a spatially and phase-averaged Navier-Stokes framework. Dynamics depended strongly on Keulegan-Carpenter number (KC), the ratio of wave orbital excursion to roughness element size. For 1 < KC < 10, flow separation was weak, form drag was small, stress gradients were negligible, and the main effect of topography on the flow was the inertial force associated with acceleration around roughness elements. For 10 < KC < 20, strong flow separation occurred, and both drag and inertial forces were important. Phase-dependent dispersive stresses were the main mechanism for vertical momentum transfer between the canopy layer and the overlying water column. Friction factors based on the drag force increased with KC for 1 < KC < 20, different from previously proposed empirical curves, but approached these curves for high KC. Friction factors based on the total force decreased with increasing KC and were consistent with previously proposed curves. These results highlight the importance of distinguishing the total force on the bottom, the drag force that removes energy from the flow, and the shear stress above the canopy layer, which were very different for the parameter range in this study.