Model for Estimating Tidal Flushing of Small Embayments

A model is developed for tidal flushing of a small, well‐mixed embayment, based on the classic tidal prism flushing formation. Both a flushing expression and a steady‐state concentration expression for a nonconservative tracer are derived. The return flow factor is identified as an important, but previously poorly constrained, input to the flushing model. A model for estimating the return flow factor is derived considering the fate of the plume of effluent water, which exits the embayment mouth on ebb tide, mixes with coastal waters, and partially returns to the embayment on flood tide. The predicted return flow factor depends primarily on the relative phases and speeds of the embayment channel currents and coastal currents and on the amount of mixing that occurs outside the embayment. The return flow factor model is solved for a range of representative cases, and the results are plotted for reference. The complete flushing model is compared to the results of a dye study performed in a marina basin in Indian River Bay, Del., with favorable results.