Convective mesoscale turbulence at very low Prandtl numbers

TL;DR

This study uses large-scale simulations to explore turbulent convection at very low Prandtl numbers, revealing flow properties, heat transport mechanisms, and turbulence characteristics relevant to stellar and planetary contexts.

Contribution

It provides the first comprehensive numerical analysis of mesoscale turbulence at extremely low Prandtl numbers, covering a wide parameter range and connecting flow features to classical turbulence.

Findings

Flow and heat transport properties vary with Rayleigh and Prandtl numbers.

Turbulence in the bulk resembles classical homogeneous and isotropic turbulence.

A mesoscale wavelength saturates at about 3 times the layer height for very low Prandtl numbers.

Abstract

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 as in stellar convection and in Earth's outer core. The present study reports three-dimensional direct numerical simulations of turbulent Rayleigh-B\'{e}nard 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, $10^{-3}\le Pr \le 7$, and Rayleigh numbers $10^5 \le Ra \le 10^7$, obtained by massively parallel computations on grids of up to $5.36\times 10^{11}$ 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 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 on the order of the mesoscale seems to saturate to a wavelength of $\lambda\gtrsim 3H$ for $Pr\lesssim 0.005$. We briefly discuss possible implications of these results for the development of subgrid scale parameterization of turbulent convection.