New analytical equation for dispersion in estuaries with a distinct ebb-flood channel system

Tidal pumping caused by residual horizontal circulation is an important but ill-understood mechanism producing longitudinal salt dispersion in well-mixed estuaries. There are two types of residual circulation that cause tidal pumping: (1) interaction of the tidal flow with a pronounced flood-ebb channel system; and (2) interaction of the tidal flow with an irregular bathymetry. Residual ebb-flood channel circulation is an important large-scale mixing mechanism for salinity intrusion, as shown in the Western Scheldt in the Netherlands, which is a well-mixed estuary with a distinct ebb-flood channel system. This paper provides a new simplified conceptual model and a new analytical equation for this type of mixing. Firstly, using a fully three-dimensional hydrodynamic model as a ‘‘virtual laboratory’’ and employing a decomposition method, the characteristics of the residual ebb-flood channel circulation in the Western Scheldt are analysed. Secondly, a conceptual model and an analytical equation determining the dispersion coefficient are developed, which take into account relevant parameters for tidal pumping, such as the tidal pumping efficiency, the tidal excursion and the length of the branches. Subsequently, the newly developed equation is compared to the results of the ‘‘virtual laboratory’’. The comparison confirms an agreement between the newly developed equation and the ‘‘virtual laboratory’’ in determining the residual transport and the tidal pumping dispersion coefficient. Finally, the equation is applied to observations in the Western Scheldt. The application yields good results in determining the longitudinal dispersion compared to dispersion values obtained from the salt budget.