Application of three dimensional turbulence energy models to the determination of tidal mixing and currents in a shallow sea

Abstract

A three dimensional hydrodynamic model, using a sigma coordinate grid in the vertical, with subgrid scale diffusion represented using a range of turbulence energy closure schemes, is used to examine M 2 tidal elevations and currents in the Irish Sea. Changes in turbulence energy intensity in particular surface turbulence with variations in mixing length formulation is also considered. A no-slip condition is applied at the sea bed and the sensitivity of tidal elevations and particular tidal currents to changes in bottom roughness length and formulation of mixing length are examined; also detailed comparisons are made with measurements. From these comparisons it is evident that the bed roughness has a major influence upon tidal elevations, and current profiles in the near bed region. Near bed currents are also influenced by the form of the mixing length close to the sea bed, although its value in the upper part of the water column is of less importance. However, the vertical variation of turbulent energy, in particular its surface value, is very sensitive to the mixing length. Elevations computed with the three dimensional model with various closure assumptions are compared with those from a 2D-vertically integrated hydrodynamic model. In general the two dimensional model appears to reproduce elevations slightly more accurately than the three dimensional model. A ‘hybrid’ three dimensional model using an identical bed stress formulation to that in a two dimensional model is used as a means to compute currents and turbulence energy intensities while maintaining the same elevation distribution as that computed with a two dimensional model.