Particle Tracking Simulation of Pollutant Discharges

A two-dimensional particle tracking simulation of pollutant discharges in a vertically well-mixed tidal current is performed for an idealized straight coast with parametrically defined parallel bathymetry and realistic spatially and temporally varying longshore velocity and diffusivity fields. Two methods of random-walk simulation in varying diffusivity media are compared: one where the random walk is performed in a transformed (spatially) uniform diffusivity space and the other where the random walk takes place in the untransformed space. For the special case of a steady coastal current—and subject to a suitable choice of a random-number generator, time step, and particle flux—the stochastic solutions in either case are found to be in reasonable agreement with the analytic solution of a previous researcher. Further simulations of steady and of “optimal” discharges in tidal flows with and without a mean longshore current are presented. The major conclusion is that in the absence of shorelines, discharging optimally—in the sense of maintaining a constant global maximum concentration in the presence of a varying current—allows a much greater mass of pollutant to be discharged over the tidal cycle. However, in the presence of shorelines discharging optimally leads to much higher shoreline concentrations and thus has little effect in reducing global maximum concentrations. This suggests that there is little advantage to be gained by varying the discharge in such cases.