We present measurements of the orientation theta0(t) of the large-scale circulation (LSC) of turbulent Rayleigh-Bénard convection in cylindrical cells of aspect ratio 1. Theta0(t) undergoes irregular reorientations. It contains reorientation events by rotation through angles delta theta with a monotonically decreasing probability distribution p(delta theta), and by cessations (where the LSC stops temporarily) with a uniform p(delta theta). Reorientations have Poissonian statistics in time. The amplitude of the LSC and the magnitude of the azimuthal rotation rate have a negative correlation.

We present high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for cylindrical samples of water (Prandtl number σ = 4.38) with diameters D = 49.7, 24.8, and 9.2 cm, all with aspect ratio Γ ≡ D/L ≃ 1 (L is the sample height). In addition, we present data for D = 49.7 and Γ = 1.5, 2, 3, and 6. For each sample the data cover a range of a little over a decade of R. For Γ ≃ 1 they jointly span the range 10Where needed, the data were corrected for the influence of the finite conductivity of the top and bottom plates and of the side walls on the heat transport in the fluid to obtain estimates of N ∞ for plates with infinite conductivity and sidewalls of zero conductivity. For Γ ≃ 1 the effective exponent γ ef f of N ∞ = N 0 R γ ef f ranges from 0.28 near R = 10 8 to 0.333 near R ≃ 7 × 10 10 . For R < ∼ 10 10 the results are consistent with the Grossmann-Lohse model. For larger R, where the data indicate that N ∞ (R) ∼ R 1/3 , the theory has a smaller γ ef f than 1/3 and falls below the data. The data for Γ > 1 are only a few percent smaller than the Γ = 1 results.

We describe three apparatus, known as the large, medium, and small apparatus, used for highprecision measurements of the Nusselt number N as a function of the Rayleigh number R for cylindrical samples of fluid and present results illustrating the influence of the finite conductivity of the top and bottom plates on the heat transport in the fluid. We used water samples at a mean temperature of 40 • C (Prandtl number σ = 4.4). The samples in the large apparatus had a diameter D of 49.69 cm and heights L ≃ 116.33, 74.42, 50.61, and 16.52 cm. For the medium apparatus we had D = 24.81 cm, and L = 90.20 and 24.76 cm. The small apparatus contained a sample with D = 9.21 cm, and L = 9.52 cm. For each aspect ratio Γ ≡ D/L the data covered a range of a little over a decade of R. The maximum R ≃ 1 × 10 12 with Nusselt numbers N ≃ 600 was reached for Γ = 0.43. Measurements were made with both Aluminum (conductivity λ p = 161 W/m K) and Copper (λ p = 391 W/m K) top and bottom plates of nominally identical size and shape. For the large and medium apparatus the results with Aluminum plates fall below those obtained with Copper plates, thus confirming qualitatively the prediction by Verzicco that plates of finite conductivity diminish the heat transport in the fluid. The Nusselt number N ∞ for plates with infinite conductivity was estimated by fitting simultaneously Aluminum-and Copper-plate data sets to an effective powerlaw for N ∞ multiplied by a correction factor f (X) = 1−exp[−(aX) b ]that depends on the ratio X of the thermal resistance of the fluid to that of the plates as suggested by Verzicco. Within their uncertainties the parameters a and b were independent of Γ for the large apparatus and showed a small Γ-dependence for the medium apparatus. The correction was larger for the large, smaller for the medium, and negligible for the small apparatus.

We report experimental results for the influence of a tilt angle β relative to gravity on These results are consistent with measurements of the amplitude δ of the azimuthal sidewall temperature-variation at the mid-plane that gave δ(β) = δ(0)×[1+(1.84±0.45)|β|− (3.1 ± 3.9)β 2 ] for the same R. An important conclusion is that the increase of the speed (i.e. of R e ) with β of the LSC does not significantly influence the heat transport. Thus the heat transport must be determined primarily by the instability mechanism operative in the boundary layers, rather than by the rate at which "plumes" are carried away by the LSC. This mechanism apparently is independent of β.Over the range 10 9 < ∼ R < ∼ 10 11 the enhancement of R cc e at constant β due to the tilt could be described by a power law of R with an exponent of −1/6, consistent with a simple model that balances the additional buoyancy due to the tilt angle by the shear stress across the boundary layers.Even a small tilt angle dramatically suppressed the azimuthal meandering and the sudden reorientations characteristic of the LSC in a sample with β = 0.For large R the azimuthal mean of the temperature at the horizontal mid-plane differed significantly form the average of the top-and bottom-plate temperatures due to nonBoussinesq effects, but within our resolution was independent of β.

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