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

We investigate how the heat flux $Nu$ scales with 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 ( , $Re$ $\Pr$ ) test existing theories little computational power. first show that known diverging solutions can be suppressed large-scale friction. In turbulent regime, for $\Pr \approx 1$ becomes independent viscous processes (‘asymptotic ultimate regime’, $Nu\sim Ra ^{1/2}$ no correction). recover scalings coherent theory developed by Grossmann Lohse, all situations where frictions keep constant magnitude respect diffusive dissipation. also identify another friction-dominated regime at \ll deviations from Lohse prediction observed. These two regimes may relevant some geophysical or astrophysical situations, friction arises due rotation, stratification magnetic field.