Convective mesoscale turbulence at very low Prandtl numbers

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