Scaling Breaking-Wave Vorticity Generation in the Surfzone

Spatially variable wave breaking generates vorticity in the surfzone, leading to transient rip currents (TRC), 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- 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 non-dimensional 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 non-dimensional depends upon the normalized vorticity forcing magnitude / . With 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 WA model study of interacting TRC and inner shelf processes over large regions.