Effects of wave rollers and bottom stress on wave setup

Author Posting. © American Geophysical Union, 2007. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 112 (2007): C02003, doi:10.1029/2006JC003549.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.Funding was provided by the Office of Naval Research, the National Science Foundation, and the Army Research Office

Wave setup over a Pacific Island fringing reef

International audienceMeasurements obtained across a shore-attached, fringing reef on the southeast coast of the island of Guam are examined to determine the relationship between incident waves and wave-driven setup during storm and nonstorm conditions. Wave setup on the reef flat correlates well (r > 0.95) and scales near the shore as approximately 35% of the incident root mean square wave height in 8 m water depth. Waves generated by tropical storm Man-Yi result in a 1.3 m setup during the peak of the storm. Predictions based on traditional setup theory (steady state, inviscid cross-shore momentum and depth-limited wave breaking) and an idealized model of localized wave breaking at the fore reef are in agreement with the observations. The reef flat setup is used to estimate a similarity parameter at breaking that is in agreement with observations from a steeply sloping sandy beach. A weak (∼10%) increase in setup is observed across the reef flat during wave events. The inclusion of bottom stress in the cross-shore momentum balance may account for a portion of this signal, but this assessment is inconclusive as the reef flat currents in some cases are in the wrong direction to account for the increase. An independent check of fringing reef setup dynamics is carried out for measurements at the neighboring island of Saipan with good agreement