Breaking wave induced cross-shore tracer dispersion in the surfzone: Model results and scaling

Understanding the dispersion of surfzone tracers is important for predicting the the evolution of pollutants or bacteria in the nearshore. Many processes act over a range of time- and space scales to disperse surfzone tracer. The role of breaking waves (bores) in cross-shore tracer dispersion is unique to the surfzone, however little is known about the dispersal-effect of bores. Here, a series of simple models for bore induced cross-shore dispersion are developed based upon the heat equation with an eddy diffusivity that propagates with the bores. The model assumes alongshore uniformity. The dimensional parameters and four non-dimensional parameters for the problem are identified and solution space is explored. Generally solutions have a near-constant cross-shore position for the tracer center of mass. The tracer width grows with the square-root of time, and the tracer distribution is initially skewed after the passage of the first bore, but becomes symmetric with the passage of multiple bores. The non-dimensional phase speed and wave period are the most important parameters in governing the tracer patch growth rate and dilution. The simple model results are confirmed by studying tracer dispersion in 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 bore eddy-diffusivity and the ranges of the non-dimensional parameters are examined. The covariation of the non-dimensional phase speed and wave period suggest that nondimensional tracer dispersion is largely self similar.