A modeling investigation of the breaking wave roller with application to cross‐shore currents

A mathematical model is developed for the creation and evolution of the aerated region, or “roller,” that appears as a wave breaks and passes through the surf zone. The model, which calculates the roller's cross-sectional area, is based on a short-wave averaged energy balance. The vertically integrated energy flux is split between the turbulent motion in the roller and the underlying organized wave motion, and the dissipation of energy is assumed to take place in the shear layer that exists at the interface between the two flow regimes. Calibration of the roller model is done by numerically solving equations for the cross-shore balances of mass and momentum, with roller contributions included, and then optimizing predictions of depth-averaged cross-shore currents. The laboratory data of Hansen and Svendsen [1984] for setup and cross-shore currents, driven by regular waves breaking on a planar beach, are used to set the roller model's fitting coefficient. The model is then validated utilizing five additional laboratory data sets found in the literature. Results indicate that employing stream function theory in calculating integral properties for the organized wave motion (wave celerity, and mass, momentum, and energy fluxes) significantly improves agreement as compared to results generated using linear wave theory. Using the roller model and stream function theory, root-mean-square error for the mean current is typically 19%. The bed stress is found to play a negligible role in the cross-shore mean momentum balance, relative to the radiation stress, setup, roller momentum flux, and convective acceleration of the current.

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