On the importance of time varying eddy viscosity in generating higher tidal harmonics

Abstract

By using a spectral/modal expansion in the vertical, a method is developed for determining tidal current profiles subject to either a slip or no‐slip bottom boundary condition. An arbitrary vertical profile of eddy viscosity can be used in the calculation, the magnitude of which can be related to the flow field. The nature of the modal solution is such that the high shear bottom boundary layer can be accurately resolved using a few modes (of order five), compared with the order of 45 grid boxes on a logarithmic transformation which would be required in a finite difference approach. Calculations show the importance of a time‐varying eddy viscosity in generating higher harmonics when a no‐slip condition is applied at the seabed. By relating the current one meter above the bed to the bed stress, a value of friction coefficient C100 in reasonable agreement with observations was obtained from these no slip calculations. However the value of friction coefficient was strongly dependent upon the height above the bed, at which the current was calculated, with friction coefficient increasing rapidly in the near‐bed region. Current profiles on the continental shelf determined using the modal method developed in the paper were in good agreement with observations, with computed profiles in the Celtic Sea giving the observed midwater maximum.