A three‐dimensional model of diurnal and semidiurnal tides on the European shelf

Abstract

A three‐dimensional hydrodynamic model of the continental shelf is used to examine the sensitivity of computed diurnal (K1 and O1) and semidiurnal (M2, S2, and N2) tidal elevations and currents to changes in eddy viscosity profile, friction coefficient, and water depth. The influence of the tide‐generating potential is also considered. The model uses a standard finite difference grid in the horizontal, with a functional approach in the vertical, thereby giving a continuous tidal current profile from sea surface to seabed. The magnitude of the vertical eddy viscosity depends upon the flow field. Comparisons are made between model‐computed profiles and harmonic analyses of 278 current time series, at a range of locations in varying water depths, with particular emphasis on locations where there are current measurements at a number of points in the vertical. A detailed examination of these comparisons shows that frictional effects in the near‐bed region are particularly important in determining near‐bed shear and that an accurate specification of water depth is critical for tidal current magnitude. The spatial distribution of computed current ellipses shows that the semidiurnal currents are strongest in shallow water, with the diurnal currents exhibiting an intensification in the shelf edge region. The inclusion of the equilibrium tide is particularly important for the correct determination of the magnitude of the K1 tidal current as well as K1 elevations in the North Sea. The detailed comparisons show that the magnitude of the tidal currents is correctly determined to within ±5 cm s−1 at 220 locations, with the model accurately (to within ±2 cm s−1) reproducing the vertical variation (the most sensitive test of a three‐dimensional model) of the tidal current at most locations.