On the Absence of the Ultimate Regime in Turbulent Thermal Convection

Quantifying heat transport in turbulent convection remains a challenge. The two competing models of heat transport predict the nondimensional heat flux (Nusselt number, Nu) to be proportional to Ra^{⅓} (classical scaling) and to Ra^{½} (ultimate-regime scaling), where Ra is the Rayleigh number.   Our synergetic and comparative study of heat fluxes in Rayleigh-

Benard, compressible, and periodic convection indicate a likely absence of the ultimate regime in turbulent thermal convection. We show that up to Ra = 10^{16} in two dimensions and up to

Ra = 10^{13} in three dimensions, the positive and negative energy fluxes in Rayleigh-Benard and compressible convection are nearly equal. However, the positive flux has a longer tail in the distribution function. This flux difference scales as Ra^{-0.20}, which leads to Nu ~ Ra^{0.30}. The above robust and universal properties, even in the presence of a logarithmic layer in compressible convection, are attributed to the confining thermal plates. These heat flux features differ significantly from those of periodic convection, which is often related to the ultimate regime.

Reference: H. Tiwari, L. Sharma, and M. K. Verma, On the Absence of the Ultimate Regime in Turbulent Thermal Convection, to appear in PNAS (2025)