Second order closure for stratified convection: bulk region and overshooting

The parameterization of small-scale turbulent fluctuations in convective systems and in the presence of strong stratification is important for many applied problems in oceanography, atmospheric science and planetology. In the presence of stratification, both bulk turbulent fluctuations and inversion regions, where temperature, density -or both-develop highly nonlinear mean profiles, are crucial. We present a second order closure able to reproduce simultaneously both bulk and boundary layer regions. We test it using high-resolution state-of-the- art 2D numerical simulations in a Rayleigh-Taylor convective and stratified belt for values of the Rayleigh number, up to Ra similar to 10(9). The system is confined by the existence of an adiabatic gradient. Our numerical simulations are performed using a thermal Lattice Boltzmann Method (Sbragaglia et al, 2009) able to reproduce the Navier-Stokes equations for momentum, density and internal energy (see also (Biferale et al, 2011b) for an extension to a case with forcing on internal energy). Validation of the method can be found in (Biferale et al, 2010; Scagliarini et al, 2010). Here we present numerical simulations up to 4096 x 10000 grid points obtained on the QPACE supercomputer (Goldrian et al, 2008).