Propagation of tides in the Mandovi and Zuari estuaries

The Mandovi and the Zuari are two shallow estuaries that are located in Goa and join the Arabian Sea. The main channel of each is about 50 km long, ha s its cross-sectional area decreasing rapidly-in the upstream direction, an d receives large amounts of riverine freshwater during the southwest Monsoo n and little during the rest of the year. Tides in the:channels exhibit the following characteristics: (a) The speed of propagation is about 6.5 m s(- 1); (b) tidal amplitude remains unchanged over a distance of about 40 km fr om the mouth; (c) mean water level near the head increases with increase in runoff; (d) tidal amplitude decays rapidly over approximate to 10 km near the head, the decay is more rapid during periods of higher runoff. A nonlinear numerical model based on the equations for conservation of mome ntum and mass reproduces all the observed features. The model fields show t hat momentum balance in the channels is primarily between pressure gradient and friction. Assuming such a balance, we formulate a linear analytic mode l for tidal propagation in a channel whose cross-sectional area decreases e xponentially with distance from the mouth and has influx of riverine freshw ater at its head. The model solution mimics the observed features (a)-(c) c ited above but not (d). Our conjecture is that the quadratic friction term in the momentum balance and the nonlinear term in the continuity equation a re essential to simulate the decay of tidal amplitude at the upstream end.