Asymptotic ultimate regime of homogeneous Rayleigh–Bénard convection on logarithmic lattices. (10th May 2023)

• Record Type: Journal Article
• Authors: Barral, Amaury; Dubrulle, Berengere
• Is Part Of: Journal of fluid mechanics. Volume 962(2023)
• Publication Date: 2023-05-10
• Subjects: Bénard convection -- low-dimensional models -- turbulence simulation; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2023.204
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: 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.