Simple estimate of entrainment rate of pollutants from a coastal discharge into the surf zone.

Microbial pollutants from coastal discharges can increase illness risks for swimmers and cause beach advisories. There is presently no predictive model for estimating the entrainment of pollution from coastal discharges into the surf zone. We present a novel, quantitative framework for estimating surf zone entrainment of pollution at a wave-dominant open beach. Using physical arguments, we identify a dimensionless parameter equal to the quotient of the surf zone width l(sz) and the cross-flow length scale of the discharge la = M(j) (1/2)/U(sz), where M(j) is the discharge's momentum flux and U(sz) is a representative alongshore velocity in the surf zone. We conducted numerical modeling of a nonbuoyant discharge at an alongshore uniform beach with constant slope using a wave-resolving hydrodynamic model. Using results from 144 numerical experiments we develop an empirical relationship between the surf zone entrainment rate α and l(sz)/(la). The empirical relationship can reasonably explain seven measurements of surf zone entrainment at three diverse coastal discharges. This predictive relationship can be a useful tool in coastal water quality management and can be used to develop predictive beach water quality models.