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Asymptotic ultimate regime of homogeneous Rayleigh–Bénard convection on logarithmic lattices

Published online by Cambridge University Press:  26 April 2023

Amaury Barral Open the ORCID record for Amaury Barral [Opens in a new window]  and
Berengere Dubrulle Open the ORCID record for Berengere Dubrulle [Opens in a new window]
Amaury Barral
Affiliation:
Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette, France
Berengere Dubrulle*
Affiliation:
Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette, France
*
†Email address for correspondence: berengere.dubrulle@cea.fr
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Abstract

We investigate how the heat flux $Nu$ scales with the imposed temperature gradient $Ra$ in homogeneous Rayleigh–Bénard convection using one-, two- and three-dimensional simulations on logarithmic lattices. Logarithmic lattices are a new spectral decimation framework which enables us to span an unprecedented range of parameters ($Ra$, $Re$, $\Pr$) and test existing theories using little computational power. We first show that known diverging solutions can be suppressed with a large-scale friction. In the turbulent regime, for $\Pr \approx 1$, the heat flux becomes independent of viscous processes (‘asymptotic ultimate regime’, $Nu\sim Ra ^{1/2}$ with no logarithmic correction). We recover scalings coherent with the theory developed by Grossmann and Lohse, for all situations where the large-scale frictions keep a constant magnitude with respect to viscous and diffusive dissipation. We also identify another turbulent friction-dominated regime at $\Pr \ll 1$, where deviations from the Grossmann and Lohse prediction are observed. These two friction-dominated regimes may be relevant in some geophysical or astrophysical situations, where large-scale friction arises due to rotation, stratification or magnetic field.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 962 , 10 May 2023 , A2
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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