The influence of eddy viscosity parameterization and turbulence energy closure scheme upon the coupling in tidal and wind induced currents

A three-dimensional model of the Irish Sea, and the shelf and shelf-edge re gion off the west coast of Scotland is used to examine the interaction of w ind induced surface currents and M-2 tidal currents which can lead to an in creased near surface M-4 tidal current in the region. Calculations are perf ormed using uniform southerly and westerly wind stresses, with vertical edd y viscosity computed using either a simple flow dependent form of viscosity , or one related to the flow and surface wind stress or derived using a two -equation turbulence model. Resulting M-4 tidal distributions computed with the various viscosity formulations are compared with each other. The spati al distribution the M-4 tidal current in the case of the flow dependent vis cosity, shows a significant enhancement of the surface M-4 tide due to non- linear coupling between the surface shear and the tidally dependent viscosi ty. In deep water this is the dominant mechanism giving rise to an enhancem ent in near surface M-4 current. In shallow water, however, where other non -linear processes are important in generating the M-4 tide, namely changes in water depth and friction, these are significant as well as the non-linea r surface shear effect, in changing the M-4 tidal distribution. However, wh en an eddy viscosity formulation depending upon flow and surface wind stres s is used, the non-linear coupling mechanism producing an enhanced M-4 tida l surface current is reduced, and no increase in M-4 surface current occurs . Calculations with the two equation turbulence model, do not produce an incr ease in the near surface M-4 tide, as the near surface viscosity in this mo del is determined principally by the wind stress rather than the tidal curr ent. Some conclusions concerned with developing a simple eddy viscosity mod el having similar characteristics to the turbulence energy model, and exper imental data sets for validation are considered at the end of the paper. (C ) 2001 Academic Press.