Tidally Forced Internal Wave Mixing in ak–ε Model Framework Applied to Fjord Basins

A simple method for including tidally forced internal wave mixing in a two-equation turbulence closure framework, the k–ε model, is presented. The purpose is to model the vertical mixing in the basin waters of stagnant sill fjords. An internal wave energy (IWE) term of the form aN, where N is the buoyancy frequency and a is a weighted average of the locally available IWE, is added to the equation for the turbulent kinetic energy (TKE). The total available IWE, F, is given by the energy flux from the barotropic tide to baroclinic internal waves, and a is determined assuming that all the available IWE is transferred to TKE, namely F = ∫ aN dV, where the integral is taken over the entire volume of the fjord. Comparisons with observations from two Scandinavian fjords show that the model successfully describes the vertical mixing in the basin water. Further, the buoyancy term in the equation for dissipation of TKE, ε, is found to be irrelevant during stable stratification; that is, the empirical parameter c3 in the ε equation should be zero under such conditions.