Review of Recent Developments in Tidal Hydrodynamic Modeling. II: Turbulence Energy Models

Abstract

The second part of this review deals with three-dimensional tidal models for homogeneous and stratified sea regions in which the vertical eddy viscosity and diffusivity are computed from turbulence energy submodels. The formulation of a range of turbulence energy models is presented, and the solution of the three-dimensional equations using finite difference methods in the vertical on a number of transformed grid (log, log-linear) is described. The application of turbulence energy models is illustrated using results from a three-dimensional model of tides in the Irish Sea. A comparison of computed tidal current profiles determined using a two-equation turbulence closure model with those derived using a simple flow-dependent eddy viscosity model, and with observations, did not reveal any significant differences between the models. Recent work on the effect of stable stratification on turbulence energy and tidal currents is also considered, as this is the more critical test of the accuracy of turbulence energy models. Processes influencing the internal tide generation in regions of steep topography are also examined using the three-dimensional turbulence energy model with a prognostic density field. The role of the nonlinear terms in the generation of short internal waves at the top of the shelf break, and intense surface and bed mixing in this region is examined together with the effects of an upwelling and downwelling favorable wind.