3D analytic model for testing numerical tidal models

A 3D analytic solution is presented for tides in channels with arbitrary la teral depth variation. The solution is valid for narrow channels in which t he lateral variation of the amplitude of tidal elevation is small. The erro r introduced by the solution is on the order of a few percent in a tidal ch annel of a few kilometers in width. The solution allows an arbitrary latera l depth variation and thus provides a wide choice of depth functions, espec ially those with large bottom slopes. The largest amplitude of the along-es tuary velocity appears on the surface in the deepest water. The depth-avera ged velocity is the largest in the deepest water. The time of flood (ebb) i n deep water lags that in shallow water. The time of flood (ebb) on the sur face lags that at the bottom. Since this solution is simple and allows arbi trary lateral depth variations, it can be used to demonstrate the first-ord er tidal flow in narrow tidal channels of variable depth, and to test high- resolution numerical models with large depth gradients.