Convective mesoscale turbulence at very low Prandtl numbers

Horizontally extended turbulent convection, termed mesoscale convection in natural systems, remains a challenge to investigate in both experiments and simulations. This is particularly so for very low molecular Prandtl numbers, such as occur in stellar convection and in the Earth's outer core. The present study reports three-dimensional direct numerical simulations of turbulent Rayleigh-Bdnard convection in square boxes of side length L and height H with the aspect ratio Gamma = L/H of 25, for Prandtl numbers that span almost 4 orders of magnitude, 10(-3) <= Pr <= 7, and Rayleigh numbers 10(5) <= Ra <= 10(7) , obtained by massively parallel computations on grids of up to 5.36 x 10(11) points. The low end of this Pr-range cannot be accessed in controlled laboratory measurements. We report the essential properties of the flow and their trends with the Rayleigh and Prandtl numbers, in particular, the global transport of momentum and heat - the latter decomposed into convective and diffusive contributions - across the convection layer, mean vertical profiles of the temperature and temperature fluctuations and the kinetic energy and thermal dissipation rates. We also explore the degree to which the turbulence in the bulk of the convection layer resembles classical homogeneous and isotropic turbulence in terms of spectra, increment moments and dissipative anomaly, and find close similarities. Finally, we show that a characteristic scale of the order of the mesoscale seems to saturate to a wavelength of lambda greater than or similar to 3H for Pr less than or similar to 0.005. We briefly discuss possible implications of these results for the development of subgrid-scale parameterization of turbulent convection.