The parametrization of small-scale turbulent fluctuations in convective systems and in the presence of strong stratification is a key issue for many applied problems in oceanography, atmospheric science, and planetology. In the presence of stratification, one needs to cope with bulk turbulent fluctuations and with inversion regions, where temperature, density, or both develop highly nonlinear mean profiles due to the interactions between the turbulent boundary layer and the unmixed—stable—flow above or below it. We present a second-order closure able to cope simultaneously with both bulk and boundary layer regions, and we test it against high-resolution state-of-the-art two-dimensional numerical simulations in a convective and stratified belt for values of the Rayleigh number up to $\mathrm{Ra}\sim {10}^{10}$. Data are taken from a Rayleigh-Taylor system confined by the existence of an adiabatic gradient.

• Received 7 January 2011

DOI:https://doi.org/10.1103/PhysRevE.84.016305