Breaking wave induced cross-shore tracer dispersion in the surf zone: Model results and scalings

The dispersion of surf zone tracers including pollutants and bacteria is determined many processes acting over a range of timescales and space scales. Breaking waves ( bores) are clearly important to cross-shore tracer dispersion in the surf zone, but little known about the dispersal effects of bores. Here, a simple model for bore induced cross-shore dispersion are developed based upon the diffusion equation with an eddy diffusivity that propagates with the bores. Depth-uniform tracer and bore-induced along with alongshore uniformity are assumed. The bores are assumed well and the dispersion results are for a self-similar ( constant wave height to water depth surf zone. Four nondimensional parameters are identified and solution space is explored. The tracer center of mass is approximately constant, and tracer width grows the square root of time. Tracer distribution becomes initially skewed after the passage of the first bore but becomes symmetric after multiple bores have passed. The nondimensional tracer patch growth and dilution rates depend strongly upon the nondimensional phase speed and wave period. The simple model results are with the a Boussinesq wave model where the breaking-wave eddy viscosity is used for the bore eddy diffusivity. The scaling of the dimensional parameters regarding the eddy diffusivity and the ranges of the nondimensional parameters are examined. Covariation of the nondimensional phase speed and wave period suggest that nondimensional tracer dispersion is largely cross-shore independent.