Transition to the ultimate regime in two-dimensional Rayleigh-B\'enard convection

TL;DR

This study uses two-dimensional simulations to identify the transition to the ultimate turbulent regime in Rayleigh-Bénard convection at high Rayleigh numbers, revealing enhanced heat transport and turbulent boundary layers.

Contribution

First numerical demonstration of the transition to the ultimate regime in 2D Rayleigh-Bénard convection at Ra=10^{13}, showing detailed flow and boundary layer characteristics.

Findings

Transition to ultimate regime at Ra* = 10^{13}

Enhanced heat transport with Nu scaling as Ra^{0.38}

Turbulent boundary layers with logarithmic velocity profiles

Abstract

The possible transition to the so-called ultimate regime, wherein both the bulk and the boundary layers are turbulent, has been an outstanding issue in thermal convection, since the seminal work by Kraichnan [Phys. Fluids 5, 1374 (1962)]. Yet, when this transition takes place and how the local flow induces it is not fully understood. Here, by performing two-dimensional simulations of Rayleigh-B\'enard turbulence covering six decades in Rayleigh number Ra up to $10^{14}$ for Prandtl number Pr $=1$, for the first time in numerical simulations we find the transition to the ultimate regime, namely at $\textrm{Ra}^*=10^{13}$. We reveal how the emission of thermal plumes enhances the global heat transport, leading to a steeper increase of the Nusselt number than the classical Malkus scaling $\textrm{Nu} \sim \textrm{Ra}^{1/3}$ [Proc. R. Soc. London A 225, 196 (1954)]. Beyond the transition, the mean velocity profiles are logarithmic throughout, indicating turbulent boundary layers. In contrast, the temperature profiles are only locally logarithmic, namely within the regions where plumes are emitted, and where the local Nusselt number has an effective scaling $\textrm{Nu} \sim \textrm{Ra}^{0.38}$, corresponding to the effective scaling in the ultimate regime.