Logarithmic temperature profiles in the ultimate regime of thermal   convection
  We report on the theory of logarithmic temperature profiles in very strongly developed thermal convection in the geometry of a Rayleigh-Benard cell with aspect ratio one 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 measure ones. Their physical interpretation as well as their dependence on the radial position are discussed. 
Siegfried Grossmann and Detlef Lohse
physics.flu-dyn nlin.CD