Direct numerical simulations towards ultimate turbulence

Both in experiments and simulations of Rayleigh-Bénard (RB) convection it is a major challenge to reach the ultimate regime in which the boundary layers transition from laminar to turbulent. In the ultimate regime the scaling exponent γ in the relation Nu∼Ra^γ, where Nusselt Nu is the dimensionless heat transport and Rayleigh Ra is the dimensionless temperature difference between the plates, increases. The critical Rayleigh number (Ra*) for the transition to the ultimate regime has been observed in the Göttingen experiments around Ra*≈2x10¹³. So far, the highest Ra obtained in direct numerical simulations (DNS) is Ra=2x10¹² for aspect ratio Γ=0.5 (Stevens, Lohse, Verzicco, JFM 688, 31 (2011)). Here we present a comparison between the Göttingen experiments and DNS up to Ra=10¹³. We find perfect agreement between experiments and simulations, both for the heat transfer and for the mean and temperature variance profiles close to the sidewall. We will also provide flow visualizations and analysis, and results from resolution checks up to Ra=10¹³. In addition, we discuss simulations for Γ=0.23 up to Ra=10¹⁴, which are performed on grids with almost 100x10⁹ nodes. These results agree well with measurements by Roche et al., NJP 12, 085014 (2010).