FORMULATION OF A VARIABLE-FUNCTION 3-DIMENSIONAL MODEL, WITH APPLICATIONS TO THE M(2) AND M(4) TIDE ON THE NORTH-WEST EUROPEAN CONTINENTAL-SHELF

The major steps in the mathematical formulation of a three-dimensional (3D) tidal model using a variable modal approach to represent current profiles in the vertical are presented in the initial section of this paper. Using this method the number of functions through the vertical can be increased locally where enhanced resolution is required, while ensuring mass and momentum conservation, and reducing computational t ime using a time-splitting technique. Calculations of the M(2) and M(4 ) tidal elevations and currents on the North-West European Continental Shelf are performed, initially with bed stress determined from the de pth mean current, a hybrid 2D-3D model, the advantages of which are di scussed in the paper, and subsequently computing the bed stress from t he bottom current (a full 3D model). Computations are made using a ran ge of viscosity formulations and bed-friction coefficients. A rigorous comparison of computed currents against the harmonic analysis of obse rvations from 278 measured time-series is performed in order to determ ine the accuracy of the computed currents, which were found to agree t o within +/- 5 cm s(-1) with observations at over 200 locations. Copyr ight (C) 1996 Elsevier Science Ltd.