We report on the theory of logarithmic temperature profiles in very strongly developed thermal convection in the geometry of a Rayleigh-Bénard cell with aspect ratio (defined by cell width divided by cell height) Γ = 1, and discuss the degree of agreement with the recently measured profiles in the ultimate state of very large Rayleigh number flow. The parameters of the log-profile are calculated and compared with the measured ones. Their physical interpretation as well as their dependence on the radial position are discussed.
Grossmann, S., & Lohse, D. (2012). Logarithmic temperature profiles in the ultimate regime of thermal convection. Physics of fluids, 24(12), 125103-1-125103-8. . https://doi.org/10.1063/1.4767540