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

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 σ was equal to 4.4 or 5.5. The data are in the range 5 × 10 7 < R <10 10 , 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 θ 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 z =0 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)⟩ θ at z =0 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 2 T w (− L /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 =5 × 10 7 to about 0.06 at R =10 10 . We also report data for the temperature T 0 ( z ) along the center line ( r =0) at z =− L /4, 0, L /4. In contrast to T w ( z ), T 0 ( z ) revealed a small stabilizing gradient 2 T 0 (− L /4)− T 0 ( 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.