A finite element model for tidal and residual circulation

Harmonic decomposition is applied to the shallow water equations, thereby creating a system of equations for the amplitude of the various tidal constituents and for the residual motions. The resulting equations are elliptic in nature, are well posed and in practice are shown to be numerically well-behaved. There are a number of strategies for choosing elements: the two extremes are to use a few high-order elements with continous derivatives, or to use a large number of simpler linear elements. In this paper simple linear elements are used and prove effective.