Two phenomenological constants explain similarity laws in stably stratified turbulence

In stably stratified turbulent flows, the mixing efficiency associated with eddy diffusivity for heat, or equivalently the turbulent Prandtl number (Prt), is fraught with complex dynamics originating from the scalewise interplay between shear generation of turbulence and its dissipation by density gradients. A large corpus of data and numerical simulations agree on a near-universal relation between Prt and the Richardson number (Ri), which encodes the relative importance of buoyancy dissipation to mechanical production of turbulent kinetic energy. The Prt-Ri relation is shown to be derivable solely from the cospectral budgets for momentum and heat fluxes if a Rotta-like return to isotropy closure for the pressure-strain effects and Kolmogorov's theory for turbulent cascade are invoked. The ratio of the Kolmogorov to the Kolmogorov-Obukhov-Corrsin phenomenological constants, and a constant associated with isotropization of the production whose value (=3/5) has been predicted from Rapid Distortion Theory, explain all the macroscopic nonlinearities.