A Three-Dimensional Model of the Northwest European Continental Shelf, with Application to the M₄Tide

The solution of the fully nonlinear three-dimensional hydrodynamic equations in polar coordinates, for tides, is developed using a finite-difference grid in the horizontal and the Galerkin method in the vertical. Using this method a three-dimensional model of the northwest European continental shelf is used to investigate the spatial distribution of the M4 tidal elevations and currants over the shelf. Computed M4 currents are compared with observations and found to he in good agreement in the Celtic Sea, although there are significant errors in the North Sea. The reasons for these discrepancies and the spatial and depth variations in the M4 currants are discussed in detail.