A three dimensional model of the M 2, S 2, N 2, K 1, and O 1 tides in the Faeroe-Shetland Channel

Abstract

The spatial distributions of the M 2, S 2, N 2, K 1, and O 1 tidal elevations and currents in the Faeroe-Shetland and northern North Sea region are examined using two different modelling approaches in the vertical. In the first, tidal current profiles are computed using a functional expansion (a spectral approach) with vertical eddy viscosity related to the flow field. This method yields a continuous current profile from sea surface to sea bed. In the second, a sigma coordinate finite difference grid is used in the vertical, and eddy viscosity is computed from a one- or two-equation turbulence energy model. This region is chosen for a comparison of the modelling methods, because it covers a range of water depths and tidal velocities. Also the diurnal tides are enhanced in the shelf edge region by a shelf wave resonance and a significant observational data base is available for model validation. Calculations, using the spectral model with an eddy viscosity depending upon water depth and current magnitude, show that the tidal elevations and currents can be accurately reproduced, although with a bias to under-predict M 2 tidal elevations and over-predict currents. In the case of the other constituents, there was no significant bias in the S 2 elevations, although for N 2, O 1, and K 1 these were over-predicted. For currents the model had a bias to over-predict their amplitude for all constituents except N 2. The parameterisation of viscosity in terms of current and water depth is consistent with that found in the turbulence energy models, which are not significantly more accurate than the simpler spectral viscosity model, and exhibit a similar bias in the solution. No appreciable difference in accuracy was found between the one- and two-equation turbulence models. The only significant difference between these models was in the magnitude of the very near bed (of order 1 m layer) turbulence energy intensity. This suggests that to differentiate between the accuracy of these models, accurate turbulence measurements are required close to the sea bed.