3D Analytic Model for Testing Numerical Tidal Models

A 3D analytic solution is presented for tides in channels with arbitrary lateral depth variation. The solution is valid for narrow channels in which the lateral variation of the amplitude of tidal elevation is small. The error introduced by the solution is on the order of a few percent in a tidal channel of a few kilometers in width. The solution allows an arbitrary lateral depth variation and thus provides a wide choice of depth functions, especially those with large bottom slopes. The largest amplitude of the along-estuary velocity appears on the surface in the deepest water. The depth-averaged velocity is the largest in the deepest water. The time of flood (ebb) in deep water lags that in shallow water. The time of flood (ebb) on the surface lags that at the bottom. Since this solution is simple and allows arbitrary lateral depth variations, it can be used to demonstrate the first-order tidal flow in narrow tidal channels of variable depth, and to test high-resolution numerical models with large depth gradients.