Scaling Breaking Wave Vorticity Generation in the Surfzone

Abstract Spatially variable wave breaking generates vorticity in the surfzone, leading to transient rip currents (TRCs), driving exchange between the surfzone and inner shelf. However, breaking wave vorticity forcing is poorly understood, including its dependence on wave dissipation, directional spread, and beach slope. Using 72 Boussinesq model simulations on a planar beach, we examine the alongshore, cross-shore, and time-lagged covariance of the vorticity forcing. The covariance is decomposed into separable functions, whose form and associated four dimensional parameters (forcing standard deviation , peak alongshore wavenumber , propagation speed , and decorrelation time scale ) are derived from the simulations. The alongshore wavenumber spectrum can be represented by a Weibull distribution. In a crest-following reference frame, the time-lagged covariance decays exponentially. The cross-crest lagged covariance changes sign as seen in example vorticity forcing. The parameters and are nondimensionlized by water depth, beach slope, and wave dissipation. The resulting nondimensional parameters scale well and increase with breakpoint wave directional spread σ θb up to 13.5°. The propagation speed is scaled by . Breakpoint significant wave height and gravity nondimensionalize and the nondimensional depend upon the normalized vorticity forcing magnitude . With a focus upon covariance, we lose phase information on the alongshore wave crest coherence. The simulations are limited in parameter space. We present a pathway for parameterizing vorticity forcing. As wave-averaged (WA) models do not include vorticity forcing, a parameterization could enable the WA model study of interacting TRC and inner-shelf processes over large regions. Significance Statement Rip currents are crucial for cross-shore exchange of larvae, pathogens, and sediment, thus playing a key role in human and ecosystem health. Breaking wave generates vorticity in the surfzone, leading to transient rip currents (TRCs). However, the breaking wave vorticity forcing is poorly understood and is often not represented in models that span the surfzone and inner shelf. The purpose of this study is to better understand breaking wave vorticity forcing. Our finding suggests that the forcing statistics can be predicted using beach slope, wave dissipation, and other bulk wave properties. The study points to a pathway toward a parameterization of breaking wave vorticity forcing that could enable the model study of interacting TRC and inner-shelf processes over large regions.