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

Abstract

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 = 1). The fluid was water with a Prandtl number sigma = 4.38. In contrast to the experiences reported by Chilla et. al. (2004) for a similar sample but with Gamma = 0.5 (D = 0.5 and L = 1.0 m), we found no long relaxation times. For R = 9.4 times 10^10 we measured the Nusselt number N as a function of tilt angle beta and obtained a small beta dependence about a factor of 50 smaller than the result found by Chilla et. al. (2004) for their Gamma = 0.5 sample. We measured side-wall temperatures at eight equally spaced azimuthal locations on the horizontal mid-plane of the sample and used their cross-correlation functions to find the turn-over time of the large-scale circulation (LSC). The resulting Reynolds numbers R_e^cc were found to increase with beta. An important conclusion is that the increase of R_e^cc with beta of the LSC does not significantly influence the heat transport. Over the range 10^9 < R < 10^11 the enhancement of R_e^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. The azimuthal mean of the temperature at the horizontal mid-plane within our resolution was independent of beta.