The search for slow transients, and the effect of imperfect vertical alignment, in turbulent Rayleigh-Benard convection

We report experimental results for the influence of a tilt angle beta relative to gravity on turbulent Rayleigh-Benard convection of cylindrical samples. The measurements were made at Rayleigh numbers R up to 10(11) with two samples of height L equal to the diameter D (aspect ratio Gamma = D/L similar or equal to 1), one with L similar or equal to 0.5 m (the 'large' sample) and the other with L similar or equal to 0.25m (the 'medium' sample). The fluid was water with a Prandtl number sigma = 4.38. In contrast to the experiences reported by Chilla et al. (Eur. Phys. J. B, vol. 40, 2004, p. 223) for a similar sample but with Gamma similar or equal to 0.5 (D = 0.5 and L = 1.0 m), we found no long relaxation times. For R = 9.4 x 10(10) we measured the Nusselt number N as a function of beta and obtained a small beta dependence given by N(beta) = N-0[1-(3.1 +/- 0.1) x 10(-2) vertical bar beta vertical bar] when P is in radians. This reduction of N is about a factor of 50 smaller than the result found by Chilla et al. (2004) for their Gamma similar or equal to 0.5 sample. We measured sidewall temperatures at eight equally spaced azimuthal locations on the horizontal mid-plane of the sample and used them to obtain cross-correlation functions between opposite azimuthal locations. The correlation functions had Gaussian peaks centred about t(1)(cc) > 0 that corresponded to half a turnover time of the large-scale circulation (LSC) and yielded Reynolds numbers Re-cc of the LSC. For the large sample and R = 9.4 x 10(10) we found Re-cc(P) = Re-cc(0) x [1 + (1.85 +/- 0.21)vertical bar beta vertical bar - (5.9 +/- 1.7)beta(2). Similar results were obtained from the auto-correlation functions of individual thermometers. These results are consistent with measurements of the amplitude 8 of the azimuthal sidewall temperature variation at the mid-plane that gave delta(beta) =delta(0) x [1 + (1.84 +/- 0.45)vertical bar beta vertical bar - (3.1 +/- 3.9)beta(2)] for the same R. An important conclusion is that the increase of the speed (i.e. of Re) of the LSC with 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 is apparently independent of beta. Over the range 10(9) less than or similar to R less than or similar to 10(11) the enhancement of Re-cc at constant beta 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 beta = 0. For large R the azimuthal mean of the temperature at the horizontal mid-plane differed significantly from the average of the top- and bottom-plate temperatures due to non-Boussinesq effects, but within our resolution was independent of beta.