Lagrangian Solution of St. Venant's Equations for Alluvial Estuary

An analytical solution of St. Venant's equations for tidal flow in alluvial estuaries is presented using a Lagrangian approach. The solution is not fully exact; it is obtained on the basis of an assumed combination of harmonics for the velocity of the moving water particle. In addition, the alluvial estuary is assumed to have an exponentially varying cross section. The assumptions made, however, are few compared to the assumptions needed for earlier analytical solutions. Moreover, they do not impose serious restrictions on application to real estuaries. The accuracy obtained with the analytical method is quite acceptable compared to results obtained with a numerical model which does not require an assumed combination of harmonics. The advantage of an analytical method over a numerical method is that the former method provides insight into the phenomena involved in tidal hydraulics. In addition, the Lagrangian approach enhances understanding, as it forces one to follow the movement of an individual water particle in the vertical, horizontal, and lateral sense.