Wave forced vorticity and dissipation scaling on a rip channeled beach

Rip-currents, commonly observed on natural beaches, are vorticity induced and part of large scale near-shore circulations. The questions arise: how do bathymetric gradients magnitudes relate to rip velocities? how does rip current vorticity scale with wave characteristics and dissipation? What is the dynamics of the large scale 2D vorticity? To address these questions, we utilize a Non Linear Shallow Water model with a shock-capturing scheme. It is validated with preexisting experiments of wave induced rip-currents on uneven bathymetries generated by irregular waves. To do so the enstrophy (spatially averaged square of the vorticity) is shown to be a relevant metric to calibrate the bottom friction coefficient of the model. The numerical study based on a large number of simulations with monochromatic wave forcing shows that the more non-uniform the bathymetry is, the stronger the gradients in wave dissipation are and the stronger the enstrophy is. The rip current velocity is shown to linearly increase with the square root of the local enstrophy. The wave-averaged shallow water vorticity equation terms are evaluated. It is suggested that large scale 2D vorticity dynamics mainly result from an equilibrium between vorticity production, vorticity advection by the circulation and dissipation by bottom friction.