Convective mesoscale turbulence at 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-Bénard 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.

27 pages, 14 figures, 4 tables

References in corpus (14)

• Comparison between two and three dimensional Rayleigh-Bénard convection
• Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection
• Scaling of large-scale quantities in Rayleigh-Bénard convection
• Global and local statistics in turbulent convection at low Prandtl numbers
• Local boundary layer scales in turbulent Rayleigh-Benard convection
• Transitional boundary layers in low-Prandtl-number convection
• Thermal boundary layer structure in low-Prandtl-number turbulent convection
• Mesoscale flows in large aspect ratio simulations of turbulent compressible convection
• Collapse of Coherent Large Scale Flow in Strongly Turbulent Liquid Metal Convection
• Combined particle image velocimetry and thermometry of turbulent superstructures in thermal convection
• Non-Boussinesq low-Prandtl number convection with a temperature-dependent thermal diffusivity
• Lagrangian heat transport in turbulent three-dimensional convection
• Convective heat transport in slender cells is close to that in wider cells at high Rayleigh and Prandtl numbers
• Proof of the zeroth law of turbulence in one-dimensional compressible magnetohydrodynamics and shock heating