Effects of wave rollers and bottom stress on wave setup

Abstract

[1] 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 setups 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.

Integrated modeling framework to quantify the coastal protection services supplied by vegetation

“…The energy of the roller E r is modeled following Reniers and Battjes [1997] and Apotsos et al [2007].…”

Hydrodynamic and morphodynamic responses to surfzone seafloor perturbations

“…Assuming that the cross-shore pressure gradient and wave breaking accelerations are the dominant terms [Longuet-Higgins and Stewart, 1964;Lentz and Raubenheimer, 1999;Raubenheimer et al, 2001], and that the wave height is depth-limited at breaking , = (ℎ + ), the sea-level profile ( ) is given by [Bowen et al, 1968] These relationships assume that is small compared with the total water depth, and that bottom stress and wave rollers do not have a first-order impact on the sea-level profile [Apotsos et al, 2007], and ignore setdown of the water level during wave shoaling and the effects of wave refraction and wave-current interaction. The wave angle is approximated as constant and equal to the wave angle at breaking .…”

Modeling waves, currents and sandbars on natural beaches: The effect of surface rollers

“…This formulation proved to simulate accurate rms wave height when compared against field data at USA beaches (Lippmann et al, 1996;Apotsos et al, 2007). We assume that B =1, so that the entire front of the wave is conceived to be covered with foam, consistent with the derivation of the roller equations (Lippmann et al, 1996).…”

“…Many studies have performed a calibration of wave transformation models. Usually a single parameter is adjusted, the saturation ratio of rms wave height over water depth, γ b , which is considered to be a free model parameter (Lippmann et al, 1996;Apotsos et al, 2007). In order to model longshore current profiles accurately, especially on beaches comprising shore-parallel bars, the inclusion of the surface rollers as well as the forcing by wind and tidal waves was proved to be essential (Reniers et al, 1997;Feddersen et al, 1998;Ruessink et al, 2001).…”