A detailed comparison of a range of three-dimensional models of the M-2 tide in the Faeroe-Shetland Channel and northern North Sea

A three-dimensional hydrodynamic model of the Faeroe-Shetland Channel and n orthern North Sea is used to investigate the spatial variability of M-2 tid al elevations and currents in the region. This area is chosen because it co vers a range of water depths. Also, there is a significant database of tida l elevations (namely 41 gauges) and current meters (namely 89 observations) with which comparisons can be made. With the exception of a couple of meas urements made at the shelf edge, which may be influenced by the internal ti de, namely a 180 degrees phase shift across the thermocline due to a first mode internal tide, the observations correspond to those of a barotropic ti de. Two different approaches are used to represent the profile of tidal cur rents in the vertical. In the first a spectral/functional method is used, w hile in the second a finite difference grid is applied. A range of paramete rizations of vertical eddy viscosity (suitable for deep water regions) are used, from ones in which viscosity is related to the flow field and water d epth, to the flow field only, with a final calculation involving a Prandtl mixing length formulation. Calculations with the flow and depth dependent v iscosity model show that in deep water, this parameterization leads to an a rtificially high viscosity and hence to a boundary layer thickness that is too large. Both the Prandtl mixing length model and the one in which viscos ity is related to only the flow field give low viscosity in deep water, wit h tidal current profiles showing a high sheared bottom boundary layer with little shear above this. In shallow water comparable viscosity values and c urrent profiles are computed with all the various parameterizations of eddy viscosity. On average the mean error in tidal elevation amplitude was 3.6 cm, with a p hase error of -8 deg, although there was a bias to underpredict tidal eleva tions. For tidal currents in general there was a slight bias to overpredict currents, with the magnitude of the semimajor axis being reproduced on ave rage with an rms error of 2.3 cm s(-1). A calculation in which the open bou ndary input was adjusted to give a mean elevation amplitude error of zero, with a phase error of -1.9 degreesE, and no significant bias in the elevati ons, did however show a bias to underpredict tidal currents, with an rms er ror of 3.6 cm s(-1) in the semimajor axis. Model calculations showed that the most sensitive test of the model's accur acy was a detailed comparison of tidal current profiles, in the near-bed re gion. Also the accuracy of computed tidal currents in deep water was determ ined more by the uncertainty in the boundary forcing to the model than the exact form of the eddy viscosity parameterization.