A Lagrangian stochastic model of surf zone drifter dispersion

Abstract

Drifter‐derived cross‐shore and alongshore surf zone diffusivities were previously estimated on an alongshore uniform beach over 1000 s for five Huntington Beach, California, 2006 (HB06) experiment release days. The cross‐shore diffusivity Kx had a nonmonotonic time dependence, potentially due to the shoreline or to weaker diffusivity seaward of the surf zone. The alongshore diffusivities Ky were qualitatively consistent with shear dispersion but differed from the classic Taylor laminar theory. Here, modeled and analytic diffusivities for the five release days are derived from a Lagrangian stochastic model (LSM) that uses the drifter‐derived bulk (cross‐shore averaged) velocity variance and cross‐shore‐dependent mean alongshore current. The LSM modeled and analytic cross‐shore diffusivities are nonmonotonic due to the shoreline and strongly suggest that the observed cross‐shore diffusivity is shoreline affected. The LSM typically reproduce well the observed Kx with Lagrangian time scale between 75 and 200 s, consistent with surf zone eddy time scales. HB06 drifter trajectories were too short to observe the analytic long‐time Kx limit, and weaker diffusivity seaward of the surf zone may be important at longer times (>1000 s). On all release days, the LSM model and analytic alongshore diffusivity reproduce well the observed Ky with alongshore Lagrangian time scales between 95 and 155 s. The isolated shear‐induced diffusivity is very well represented by an analytic theory which incorporates a nonzero Lagrangian time scale. Many of the stochastic model parameters can be specified a priori with reasonable assumptions to predict surf zone dispersion of an initial value problem pollution spill.