The Influence of Mixing Length Formulation and Stratification upon Tidal Currents in Shallow Seas

The mathematical formulation of a three-dimensional shallow sea hydro-dynamic model using a slip condition at the sea-bed with sigma coordinates in the vertical and a range of turbulence energy closure schemes is briefly presented in this paper. The equations are solved using finite difference methods in both the horizontal and the vertical, and a time splitting approach is used to reduce the computational time. The influence of changes in bed friction coefficient, and formulation of the turbulence energy scheme, upon tidal elevations, currents and mixing intensities in a homogeneous sea is examined in detail. Comparisons are made with observations and with previous published current profiles in the Irish Sea using models of identical resolution and similar closure schemes but a no-slip condition at the sea-bed. Also comparisons are made with models using simple closure schemes in terms of a flow-dependent eddy viscosity, and a spectral approach in the vertical. The influence of an imposed and maintained idealized vertical stratification upon tidal elevations, current profiles, turbulence profiles and mixing lengths is also considered. The resulting changes in vertical structure of tidal current profiles both in terms of amplitude and phase are explained using previously published results from an idealized point model.