A model of diffusion in a potential well for the dynamics of the large-scale circulation in turbulent Rayleigh-Benard convection

Abstract

Experimental measurements of properties of the large-scale circulation (LSC) in turbulent convection of a fluid heated from below in a cylindrical container of aspect ratio one are presented and used to test a model of diffusion in a potential well for the LSC. The model consists of a pair of stochastic ordinary differential equations motivated by the Navier-Stokes equations. The two coupled equations are for the azimuthal orientation theta_0, and for the azimuthal temperature amplitude delta at the horizontal midplane. The dynamics is due to the driving by Gaussian distributed white noise that is introduced to represent the action of the small-scale turbulent fluctuations on the large-scale flow. Measurements of the diffusivities that determine the noise intensities are reported. Two time scales predicted by the model are found to be within a factor of two or so of corresponding experimental measurements. A scaling relationship predicted by the model between delta and the Reynolds number is confirmed by measurements over a large experimental parameter range. The Gaussian peaks of probability distributions p(delta) and p(\dotθ_0) are accurately described by the model; however the non-Gaussian tails of p(delta) are not. The frequency, angular change, and amplitude bahavior during cessations are accurately described by the model when the tails of the probability distribution of $\delta$ are used as experimental input.

arXiv comment17 pages, 17 figures

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• Effects of tilt on the orientation dynamics of the large-scale circulation in turbulent Rayleigh-B{é}nard convection
• Effect of weak rotation on large-scale circulation cessations in turbulent convection
• Chaos from turbulence: stochastic-chaotic equilibrium in turbulent convection at high Rayleigh numbers
• Taylor rolls on tour: Slow drift of turbulent large-scale structures in flows with continuous symmetries