The influence of bottom and internal friction upon tidal currents: Taylor's problem in three dimensions

Abstract

Idealised calculations using a three-dimensional model of the North Sea, represented by a flat bottom rectangular basin, open at its northern end, are used to examine the influence of bottom topography, internal friction (parameterised using an eddy viscosity formulation) and bottom friction upon the position of M 2 tidal amphidromes and tidal current distributions over the North Sea. Calculations show that the bottom slope of the North Sea, from deep in the north to shallow in the south, together with the coefficient of bottom friction, influence the position of the tidal amphidromes. In a three-dimensional model, it is not just bottom friction which influences the position of tidal amphidromes, but also the magnitude of eddy viscosity. In the case of a no-slip condition applied at the sea bed, the magnitude of near-bed viscosity has a major influence upon the position of tidal amphidromes, and tidal current profiles. In a non-linear model in which bed stress and eddy viscosity magnitude depend upon the total tidal current, calculations show that enhanced levels of turbulence due to the M 2 tide have a significant influence upon other tidal constituents (e.g. the S 2 tide). By using a combination of a single point model in the vertical, based upon a rotary decomposition of the tide, and the full three-dimensional model of the basin, significant insight into the parameters (e.g. water depth, bottom friction, internal friction and tidal frequency) influencing the spatial distribution of tidal ellipses, and the profile of tidal currents is obtained.