Parameterizing the Surfzone Cross-shore Diffusivity

Two-dimensional horizontal surfzone eddies are responsible for surfzone diffusion and contribute to the cross-shore exchange between the surfzone and inner shelf. Similar to other turbulent diffusivities, the surfzone horizontal eddy diffusivity depends on Lagrangian properties of the flow such that K = u² T_L where u² is the turbulent velocity variance and T_L is the Lagrangian decorrelation time. Recent work has determined how the surfzone rotational velocity variance u² depends on properties of the incident wave field, however, what determines the surfzone Lagrangian time-scale T_L is not completely understood. Two possibilities are explored: 1) the classic frozen field turbulent scaling in which T_L is proportional to the time to traverse an eddy, hence T_L approx L_E/u where L_E is the eddy length-scale; 2) T_L is proportional to the time to traverse the surfzone, hence T_L approx L_S/u where L_S is the surfzone width. Either case results in a classic mixing length parameterization so that K approx ul, where l is either the eddy size L_E or the surfzone width L_S. These two parameterizations are investigated using Eulerian and Lagrangian statistics of surfzone eddies calculated from simulations (with the model funwaveC) of alongshore homogeneous waves, currents, and bathymetry. Simulations are performed for various incident significant wave heights, incident wave directional spreads, and beach slopes. From this suite of simulations, the dependence of the surfzone cross-shore diffusivity on eddy velocities u, eddy lengths L_E, and surfzone widths L_S, is determined. Surfzone retention rates are also calculated and implications for the exchange of material between the surfzone and inner shelf are discussed.