Relating Surfzone Eddy Scales to the Eddy Diffusivity Using a Wave-resolving Model

Abstract:

Two-dimensional horizontal surfzone eddies are responsible for surfzone diffusion. However, how the eddy diffusivity is related to Eulerian properties of the turbulence is not understood. Eulerian and Lagrangian statistics of surfzone eddies are calculated using wave-resolving simulations (with the model funwaveC) of observed SandyDuck conditions. For strong alongshore currents, the model has been validated by comparing modeled and observed Eulerian frequency-wavenumber spectra [Feddersen, 2013]. Here, the model is further validated by comparing observed and modeled characteristic turbulent length and time scales. These Eulerian time T_E and length L_E scales are found from the moments of the frequency-wavenumber spectra and time-space lagged correlation functions. Lagrangian time T_L and length scales L_L are also calculated from statistics of virtual drifters advected by the modeled velocity fields. As the turbulent diffusivity K depends on these Lagrangian statistics, K = u² T_L where u² is the turbulent velocity variance, surfzone eddy diffusivities are also calculated. The cross-shore dependence of both Lagrangian and Eulerian statistics (e.g. T_L, L_L, T_E, L_E) are determined and the validity of homogeneous surfzone diffusion is addressed. The relationship between surfzone Lagrangian and Eulerian statistics is also explored and the feasibility of parameterizing surfzone diffusion from incident wave conditions is discussed.