Structure of thermal boundary layers in turbulent Rayleigh-Benard convection

We report high-resolution local-temperature measurements in the upper boundary layer of turbulent Rayleigh-Benard (RB) convection with variable Rayleigh number Ra and aspect ratio Gamma. The primary purpose of the work is to create a comprehensive data set of temperature profiles against which various phenomenological theories and numerical simulations can be tested. We performed two series of measurements for air (Pr = 0.7) in a cylindrical container, which cover a range from Ra approximate to 10(9) to Ra approximate to 10(12) and from Gamma approximate to 1 to Gamma approximate to 10. In the first series Gamma was varied while the temperature difference was kept constant, whereas in the second series the aspect ratio was set to its lowest possible value, Gamma = 1.13, and Ra was varied by changing the temperature difference. We present the profiles of the mean temperature, root-mean-square (r.m.s.) temperature fluctuation, skewness and kurtosis as functions of the vertical distance z from the cooling plate. Outside the (very short) linear part of the thermal boundary layer the non-dimensional mean temperature Theta is found to scale as Theta(z)similar to z(alpha), the exponent alpha approximate to 0.5 depending only weakly on Ra and Gamma. This result supports neither Prandtl's one-third law nor a logarithmic scaling law for the mean temperature. The r.m.s. temperature fluctuation or is found to decay with increasing distance from the cooling plate according to sigma(z)similar to z(beta), where the value of beta is in the range -0.30 > beta > -0.42 and depends on both Ra and Gamma. Priestley's beta = -1/3 law is consistent with this finding but cannot explain the variation in the scaling exponent. In addition to profiles we also present and discuss boundary-layer thicknesses, Nusselt numbers and their scaling with Ra and Gamma.