Temperature gradients, and search for non-Boussinesq effects, in the interior of turbulent Rayleigh-Bénard convection

Department of Physics and iQCD, University of California - Santa Barbara, CA 93106, USA

Received: 6 July 2007
Accepted: 3 August 2007

Abstract

We report temperature measurements for a cylindrical sample of turbulent Rayleigh-Bénard convection (RBC) at points in the interior, well away from the thermal boundary layers near the top and bottom of the sample. The aspect ratio was equal to 1.00 and the Prandtl number was equal to 4.4 or 5.5. The data are in the range 510⁷ < R < 10¹⁰, where R is the Rayleigh number. Measurements of the temperatures T(r, z, θ) at the side wall (r = L/2) at eight equally spaced azimuthal positions and on three horizontal planes located at vertical positions z = -L/4, 0, L/4 (the sample height and diameter are equal to L and is located at half height) are reported. An analysis of the harmonic contents of T(L/2, 0, θ) did not reveal any symmetry-breaking deviations from the Oberbeck-Boussinesq approximation even under conditions where the azimuthal average of the center temperature T_w(z) = T(L/2, z, θ) at differed appreciably from the mean temperature T_m = (T_t + T_b)/2 (T_t and T_b are the top and bottom temperatures, respectively). The azimuthal average of the vertical temperature variation (/4)-T_w(L/4)] /(T_b-T_t) at the side wall, presumably dominated by plume activity, was found to be destabilizing and quite large, ranging from about 0.2 at R = 510⁷ to about 0.06 at R = 10¹⁰. We also report data for the temperature T₀(z) along the center line () at z = -L/4, 0, L/4. In contrast to T_w(z), T₀(z) revealed a small stabilizing gradient (-L/4)-T₀(L/4)] /(T_b-T_t) that depended only weakly on R and was about equal to -0.007 for σ = 4.4 and -0.013 for σ = 5.5.