Lagrangian Drifter Dispersion in the Surf Zone: Directionally Spread, Normally Incident Waves

Abstract

Lagrangian drifter statistics in a surf zone wave and circulation model are examined and compared to single- and two-particle dispersion statistics observed on an alongshore uniform natural beach with small, normally incident, directionally spread waves. Drifter trajectories are modeled with a time-dependent Boussinesq wave model that resolves individual waves and parameterizes wave breaking. The model reproduces the cross-shore variation in wave statistics observed at three cross-shore locations. In addition, observed and modeled Eulerian binned (means and standard deviations) drifter velocities agree. Modeled surf zone Lagrangian statistics are similar to those observed. The single-particle (absolute) dispersion statistics are well predicted, including nondimensionalized displacement probability density functions (PDFs) and the growth of displacement variance with time. The modeled relative dispersion and scale-dependent diffusivity is consistent with the observed and indicates the presence of a 2D turbulent flow field. The model dispersion is due to the rotational components of the modeled velocity field, indicating the importance of vorticity in driving surf zone dispersion. Modeled irrotational velocities have little dispersive capacity. Surf zone vorticity is generated by finite crest-length wave breaking that results, on the alongshore uniform bathymetry, from a directionally spread wave field. The generated vorticity then cascades to other length scales as in 2D turbulence. Increasing the wave directional spread results in increased surf zone vorticity variability and surf zone dispersion. Eulerian and Lagrangian analysis of the flow indicate that the surf zone is 2D turbulent-like with an enstrophy cascade for length scales between approximately 5 and 10 m and an inverse-energy cascade for scales of 20 to 100 m. The vorticity injection length scale (the transition between enstrophy and inverse-energy cascade) is a function of the wave directional spread.