Effects of wave rollers and bottom stress on wave setup

Abstract

Setup, the increase in the mean water level associated with breaking waves, observed between the shoreline and about 6-m water depth on an ocean beach is predicted well by a model that includes the effects of wave rollers and the bottom stress owing to the mean flow. Over the 90-day observational period, the measured and modeled setup are correlated (squared correlation above 0.59), and agree within about 30%. Although rollers may affect setup significantly on beaches with large amplitude (several meters high) sandbars and may be important in predicting the details of the cross-shore profile of setup, for the data discussed here, rollers have only a small effect on the amount of setup. Conversely, bottom stress (calculated using eddy viscosity and undertow formulations based on the surface dissipation, and assuming that the eddy viscosity is uniform throughout the water column) significantly affects setup predictions. Neglecting bottom stress results in underprediction of the observed setup in all water depths, with maximum underprediction near the shoreline where the observed setup is largest.