On gradient transport turbulence models for stably stratified shear flow

The gradient transport model for stably stratified horizontal shear flow in which eddy diffusivity and viscosity are assumed to depend on the gradient Richardson number, Ri, is augmented with terms representing a finite adjustment time of the exchange coefficients. Barenblatt et al. (J, Fluid Mech., 253: 341-358, 1993) showed that using such a model, initial value problems for the formation of a stepwise structure of the buoyancy distribution are well posed. The model proposed is analysed taking into account the interaction between buoyancy and velocity fields. A condition for the formation of steps is derived from a linear stability analysis. Numerical computations show that a realistic stepwise finestructure develops, provided linear instability is allowed on a finite interval of Ri only.