Structure of thermal boundary layers in turbulent Rayleigh–Bénard convection

Abstract

We report high-resolution local-temperature measurements in the upper boundary layer of turbulent Rayleigh–Bénard (RB) convection with variable Rayleigh number Ra and aspect ratio Γ. 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 ≈10 9 to Ra ≈10 12 and from Γ≈1 to Γ≈10. In the first series Γ was varied while the temperature difference was kept constant, whereas in the second series the aspect ratio was set to its lowest possible value, Γ=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 Θ is found to scale as Θ( z )∼ z α , the exponent α≈0.5 depending only weakly on Ra and Γ. This result supports neither Prandtl's one-third law nor a logarithmic scaling law for the mean temperature. The r.m.s. temperature fluctuation σ is found to decay with increasing distance from the cooling plate according to σ( z )∼ z β, where the value of β is in the range -0.30>β>-0.42 and depends on both Ra and Γ. Priestley's β=−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 Γ.