Dynamics of wave setup across a steeply-sloping reef with large bottom roughness

High-resolution observations from a wave flume were used to investigate the dynamics of wave setup over a steeply-sloping fringing reef profile with the effect of bottom roughness modeled using roughness elements scaled to mimic a coral reef. Results with roughness were compared with smooth bottom runs across sixteen offshore wave and still water level conditions. The time-averaged and depth-integrated force balance was evaluated from observations collected at seventeen locations across the flume, which was found to consist of cross-shore pressure and radiation stress gradients whose sum was balanced by mean quadratic bottom stresses. We found that when radiation stress gradients were calculated from observations of the radiation stress derived from linear wave theory, both wave setdown and setup were under predicted for the majority of wave and water level conditions tested. Inaccuracies in the predicted setdown and setup were improved by including a wave roller model, which provides a correction to the kinetic energy predicted by linear wave theory for breaking waves and produces a spatial delay in the wave forcing that was consistent with the observations. The introduction of roughness had two primary effects. First, the amount of wave energy dissipated during wave breaking was reduced due to frictional wave dissipation that occurred on the reef slope offshore of the breakpoint. Second, offshore directed mean bottom stresses were generated by the interaction of the combined wave-current velocity field with the roughness elements. These two mechanisms acted counter to one another. As a result, setup on the reef flat was comparable (7% mean difference) between corresponding rough and smooth runs. These findings are used to assess prior results from numerical modelling studies of reefs, and also to discuss the broader implications for how steep slopes and large roughness influences setup dynamics for general nearshore systems.