Propagation of tides in the Mandovi and Zuari estuaries

Abstract

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, has its cross-sectional area decreasing rapidly in the upstream direction, and receives large amounts of riverine freshwater during the southwest Monsoon 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 from the mouth; (c) mean water level near the head increases with increase in runoff; (d) tidal amplitude decays rapidly over ≈ 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 momentum and mass reproduces all the observed features. The model fields show that momentum balance in the channels is primarily between pressure gradient and friction. Assuming such a balance, we formulate a linear analytic model for tidal propagation in a channel whose cross-sectional area decreases exponentially with distance from the mouth and has influx of riverine freshwater at its head. The model solution mimics the observed features (a)-(c) cited above but not (d). Our conjecture is that the quadratic friction term in the momentum balance and the nonlinear term in the continuity equation are essential to simulate the decay of tidal amplitude at the upstream end.