A three-dimensional model of diurnal and semidiurnal tides and tidal mixing in the North Channel of the Irish Sea

The spatial variability of the M-2, S-2, N-1, K-1 and O-1 tides are examine d using a high-resolution model of the North Channel of the Irish Sea. The sensitivity of computed currents and elevations to two formulations of the vertical eddy viscosity, one involving a turbulence energy submodel, and an other in which it is computed from the flow field, are examined. Tidal elev ation amplitudes and phases are compared at 20 gauges and shown to be in go od agreement with observations. Root mean square (rms) errors of 7.85 cm, 3 2 degrees (turbulence energy model) and 7.93 cm, 41 degrees(flow dependent viscosity model) were found for the M-2 tide. Comparable errors were found for the other semidiurnal tides. Differences in the amplitude errors betwee n the two models are below the uncertainty associated with open boundary fo rcing and measurement errors and are therefore not statistically significan t. Computed cotidal charts showed good agreement with published cotidal cha rts derived from observations. Comparison with observed M-2 tidal current p rofiles suggests that at some locations a more accurate profile is determin ed with the turbulence model, while at others the flow-dependent solution i s more accurate. A comparison of M-2 tidal current shear in the vertical sh owed that the turbulence energy model had a slight bias to underestimate th is shear. This bias was not found in the flow-dependent viscosity model. Fo r the other tidal constituents the uncertainty in the accuracy of the curre nts prevented such a comparison. Also, it is not possible to decide with an y confidence which closure method is more accurate, due to possible errors in the data and the small number of locations where significant shear is fo und in the vertical. The spatial variability of tidal elevations and curren ts shows an amphidromic point for the semidiurnal tides but none for the di urnal tides, in the northern part of the North Channel. Significant differe nces in tidal current are found between the North Channel and the Clyde Sea , where tidal currents are strong and weak, respectively, This difference i s related to the tidal energy flux in the region which is confined to the N orth Channel. The spring-neap temporal and spatial variability of tidal tur bulence shows a close correlation with tidal current magnitude and water de pth. This in part explains why the simple flow-related viscosity model give s comparable results to those from the turbulence model.