A Model-Derived Empirical Formulation for Wave Run-Up on Naturally Sloping Beaches

A new set of empirical formulations has been derived to predict wave run-up at naturally sloping sandy beaches. They are obtained by fitting the results of hundreds of XBeach-NH+ model simulations. The simulations are carried out over a wide range of offshore wave conditions (wave heights ranging from 1 to 12 m and periods from 6 to 16 s), and surf zone (Dean parameters aD ranging from 0.05 to 0.30) and beach geometries (slopes ranging from 1:100 to 1:5). The empirical formulations provide estimates of wave set-up, incident and infragravity wave run-up, and total run-up R2%. Reduction coefficients are included to account for the effects of incident wave angle and directional spreading. The formulations have been validated against the Stockdon dataset and show better skill at predicting R2% run-up than the widely used Stockdon relationships. Unlike most existing run-up predictors, the relations presented here include the effect of the surf zone slope, which is shown to be an important parameter for predicting wave run-up. Additionally, this study shows a clear relationship between infragravity run-up and beach slope, unlike most existing predictors.

Hydrodynamic Modeling of a Reef-Fringed Pocket Beach Using a Phase-Resolved Non-Hydrostatic Model

The non-hydrostatic wave-flow model SWASH was used to investigate the hydrodynamic processes at a reef fringed pocket beach in southwestern Australia (Gnarabup Beach). Gnarabup Beach is a ~1.5 km long beach with highly variable bathymetry that is bounded by rocky headlands. The site is also exposed to large waves from the Southern Ocean. The model performance was evaluated using observations collected during a field program measuring waves, currents and water levels between June and July 2017. Modeled sea-swell wave heights (periods 5–25 s), infragravity wave heights (periods 25–600 s), and wave-induced setup exhibited moderate to good agreement with the observations throughout the model domain. The mean currents, which were highly-spatially variable across the study site, were less accurately predicted at most sites. Model agreement with the observations tended to be the worst in the areas with the most uncertain bathymetry (i.e., areas where high resolution survey data was not available). The nearshore sea-swell wave heights, infragravity wave heights and setup were strongly modulated by the offshore waves. The headlands and offshore reefs also had a strong impact on the hydrodynamics within the lagoon (bordered by the reefs) by dissipating much of the offshore sea-swell wave energy and modifying the pattern of the nearshore flows (magnitude and direction). Wave breaking on the reef platforms drove strong onshore directed mean currents over the reefs, resulting in off-shore flow through channels between the reefs and headlands where water exchanges from the lagoon to ocean. Our results demonstrate that the SWASH model is able to produce realistic predictions of the hydrodynamic processes within bathymetrically-complex nearshore systems.