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

Abstract

The spatial variability of the M2, S2, N2, K1 and O1 tides are examined 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 another in which it is computed from the flow field, are examined. Tidal elevation amplitudes and phases are compared at 20 gauges and shown to be in good agreement with observations. Root mean square (rms) errors of 7.85 cm, 32° (turbulence energy model) and 7.93 cm, 41° (flow dependent viscosity model) were found for the M2 tide. Comparable errors were found for the other semidiurnal tides. Differences in the amplitude errors between the two models are below the uncertainty associated with open boundary forcing and measurement errors and are therefore not statistically significant. Computed cotidal charts showed good agreement with published cotidal charts derived from observations. Comparison with observed M2 tidal current profiles suggests that at some locations a more accurate profile is determined with the turbulence model, while at others the flow‐dependent solution is more accurate. A comparison of M2 tidal current shear in the vertical showed that the turbulence energy model had a slight bias to underestimate this shear. This bias was not found in the flow‐dependent viscosity model. For the other tidal constituents the uncertainty in the accuracy of the currents prevented such a comparison. Also, it is not possible to decide with any confidence which closure method is more accurate, due to possible errors in the data and the small number of locations where significant shear is found in the vertical. The spatial variability of tidal elevations and currents shows an amphidromic point for the semidiurnal tides but none for the diurnal tides, in the northern part of the North Channel. Significant differences in tidal current are found between the North Channel and the Clyde Sea, where tidal currents are strong and weak, respectively. This difference is related to the tidal energy flux in the region which is confined to the North Channel. The spring‐neap temporal and spatial variability of tidal turbulence shows a close correlation with tidal current magnitude and water depth. This in part explains why the simple flow‐related viscosity model gives comparable results to those from the turbulence model.