An algorithm is described for the computation of the three-dimensional velocity fields due to tides and storm surges. The surface elevation and depth-averaged velocity components are first computed from the shallow-water equations. These equations are then used as part of the input to the second part of the algorithm, in which the velocity profiles are computed from the momentum equations. The nonlinear terms in the momentum equations and both the advective terms and the bottom friction terms in the shallow-water equations are fully included. The shallow-water equations are solved by a finite difference scheme that achieves third-order local truncation errors in all the dominant terms and that permits correct parallel flow on coastal boundaries of any orientation. Two alternative algorithms are discussed for computation of the velocity profiles, one based on finite elements in the vertical coordinate direction, the other based on a generalized Crank-Nicolson scheme. The complete algorithm has been tested on several model problems and has been found to be accurate and fast.
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Lardner et al. (1990) studied this question.
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