TY - JOUR
T1 - Convective mesoscale turbulence at very low Prandtl numbers
AU - Pandey, Ambrish
AU - Krasnov, Dmitry
AU - Sreenivasan, Katepalli R.
AU - Schumacher, Jörg
N1 - Funding Information:
A.P. acknowledges support from the Deutsche Forschungsgemeinschaft (DFG) within the Priority Programme ‘Turbulent Superstructures’ under Grant No. DFG-SPP 1881. This work was also supported by Grant No. SCHU 1410/30-1 of DFG and NYUAD Institute Grant G1502 ‘NYUAD Center for Space Science.’ D.K. is partly supported by Grant No. KR 4445/2-1 of DFG.
Funding Information:
The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. ( https://www.gauss-centre.eu ) for funding this project by providing computing time on the GCS Supercomputer SuperMUC-NG at Leibniz Supercomputing Centre ( https://www.lrz.de ).
Publisher Copyright:
© 2022 The Author(s). Published by Cambridge University Press.
PY - 2022/10/10
Y1 - 2022/10/10
N2 - 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-Bénard convection in square boxes of side length and height with the aspect ratio of 25, for Prandtl numbers that span almost 4 orders of magnitude, and Rayleigh numbers, obtained by massively parallel computations on grids of up to points. The low end of this -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 for. We briefly discuss possible implications of these results for the development of subgrid-scale parameterization of turbulent convection.
AB - 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-Bénard convection in square boxes of side length and height with the aspect ratio of 25, for Prandtl numbers that span almost 4 orders of magnitude, and Rayleigh numbers, obtained by massively parallel computations on grids of up to points. The low end of this -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 for. We briefly discuss possible implications of these results for the development of subgrid-scale parameterization of turbulent convection.
KW - Bénard convection
KW - homogeneous turbulence
KW - turbulent convection
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U2 - 10.1017/jfm.2022.694
DO - 10.1017/jfm.2022.694
M3 - Article
AN - SCOPUS:85136519808
SN - 0022-1120
VL - 948
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
M1 - A23
ER -