Modelling the effects of horizontal and vertical shear in stratified turbulent flows

Direct numerical simulations (DNS) and model results from a number of one-point turbulence models are compared for homogeneous, stably stratified flows. Because of their wide spread use in numerical ocean modelling, only explicit algebraic second-moment models are investigated. Considered are two types of shear flows with either purely vertical or purely horizontal shear. The dissipation rate is evaluated from the observation that the shear-number becomes independent of stratification for low to moderate Richardson numbers as soon as the flow approaches self-similarity. For the cases with vertical shear, it is found that all statistical models essentially reproduced the DNS results, though with different accuracy. In contrast, only the most recent model was able to predict the salient features of horizontally sheared flows, i.e. a steady-state Richardson number that is about an order of magnitude larger and a vertical mixing efficiency that is about twice as large compared to the case with vertical shear. This model also reproduced other key parameters like the turbulent Froude number and the turbulent Prandtl number with good accuracy, but it failed to predict quantitatively the reduction of the shear anisotropy with increasing stratification. For strong stratification, none of the models was able to describe the rapid decrease of the mixing efficiency associated with the collapse and fossilisation of turbulence.