A Simplified Model for Predicting the Pollution Exchange Coefficient of Small Tidal Embayments

In recent years there has been a significant increase in the development and application of ever more sophisticated multi-dimensional models for solving the hydrodynamic and constituent transport equations which govern the flushing of pollution. However, advanced numerical modelling techniques can sometimes be augmented by alternative mathematical approaches which use simplified analytical solutions to predict the dispersion of contaminants. In the present article, a novel analytical tidal prism model is described for predicting the pollution flushing characteristics of small tidal embayments. The model relates the water quality response of the basin to the external forcing effects of the tide, the initial pollutant loading and the freshwater inflow rate. In general, the pollution flushing not only depends upon the geometry of the embayment and the tidal range but also on the proportion of effluent water which leaves the basin on an ebb tide, mixes with the surrounding coastal water and returns on subsequent flood tides. This effect has been taken into account in the mathematical model by the inclusion of a ‘pollution-return’ parameter. The analytical approach offers a viable and computationally inexpensive alternative to conventional multi-dimensional pollutant transport simulations and, more importantly, provides an increased understanding of the flushing characteristics of semi-enclosed tidal basins. The efficiency of the tidal flushing can be expressed in terms of the pollution exchange coefficient which measures the proportion of water exchanged with the sea each tidal cycle. To demonstrate the accuracy of the proposed mathematical formulation, analytical water quality predictions are compared against experimental pollution data from a 1:400 scale laboratory model of a generic square harbour. The results demonstrate that the analytical approach provides a simple and robust method of determining the water quality response of well-mixed tidal embayments.