A Bottom Boundary Layer-resolving Three-Dimensional Tidal Model: A Sensitivity Study of Eddy Viscosity Formulation

Abstract

A three-dimensional hydrodynamic model of the Irish Sea that resolves the bottom boundary layer, including the logarithmic layer, is developed. A finite-difference grid is employed in the horizontal, with the current profile through the vertical being determined from an expansion of functions satisfying a no-slip bottom boundary condition. By this means a continuous current profile in the vertical, resolving the bottom boundary layer, is determined. The sensitivity of computed tidal current profiles and tidal elevations to a range of eddy viscosity parameterizations and profiles is examined, with a view to determining appropriate formulations to use in three-dimensional hydrodynamic models with no-slip bottom boundary conditions. The importance of near-bed eddy viscosity in determining the dissipation of tidal energy (in a model with a no-slip condition) and hence tidal elevations, is considered together with its influence upon current profiles. Computed and observed tidal elevations and currents are compared at a number of locations over the Irish Sea and, in general, good agreement is obtained with the observations. The thickness of the turbulent bottom boundary layer is computed with the model. Comparison of the location of observed tidal fronts, with positions where this layer intersects the sea surface shows that regions of tidally well-mixed water correspond to areas where the computed turbulent boundary layer reaches the sea surface.