The ultimate state of thermal convection in Rayleigh–Taylor turbulence

This paper discusses the so-called ultimate state of thermal convection, first proposed by Kraichnan almost 50 years ago and recently observed in numerical simulations of turbulent convection in the absence of boundaries. We focus on numerical simulations of turbulence generated by the Rayleigh–Taylor instability in a wide range of Rayleigh and Prandtl numbers. Our results point out to the conclusion that RT turbulence provides a natural realization of the ultimate state of thermal convection thus highlighting the relationship between the absence of boundaries and the emergence of the ultimate state scaling for global statistical quantities.

► We simulate 2D and 3D Rayleigh–Taylor turbulence at various Prandtl numbers.
► The ultimate state of thermal convection is observed at late times.
► The dependence of NuNu and ReRe on RaRa and PrPr is measured.
► The expected behavior at very high Prandtl number is discussed.