Abstract. A new two-equation, closure-like turbulence model for stably stratified flows is introduced which uses the turbulent kinetic energy (K) and the turbulent enstrophy (Ω) as primary variables. It accounts for mean shear – and internal wave-driven mixing in the two limits of mean shear and no waves and waves but no mean shear, respectively. The traditional TKE balance is augmented by an explicit energy transfer from internal waves to turbulence. A modification of the Ω-equation accounts for the effect of the waves on the turbulence time and space scales. The latter is based on the assumption of a non-zero constant flux Richardson number in the limit of vanishing mean-flow shear when turbulence is produced exclusively by internal waves. The new model reproduces the wave-turbulence transition analyzed by D'Asaro and Lien (2000). At small energy density E of the internal wave field, the turbulent dissipation rate (ε) scales like ε~E2. This is what is observed in the deep sea. With increasing E, after the wave-turbulence transition has been passed, the scaling changes to ε~E1. This is observed, for example, in the swift tidal flow near a sill in Knight Inlet. The new model further exhibits a turbulent length scale proportional to the Ozmidov scale, as observed in the ocean, and predicts the ratio between the turbulent Thorpe and Ozmidov length scales well within the range observed in the ocean.
Preliminary simulations of internal waves and mixing generated by finite amplitude tidal flow over isolated topography
