A model of diffusion in a potential well for the dynamics of the large-scale circulation in turbulent Rayleigh–Bénard 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 1 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 θ0 and for the azimuthal temperature amplitude δ 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 2 or so of corresponding experimental measurements. A scaling relationship predicted by the model between δ and the Reynolds number is confirmed by measurements over a large experimental parameter range. The Gaussian peaks of probability distributions p(δ) and p(θ̇0) are accurately described by the model; however, the non-Gaussian tails of p(δ) are not. The frequency, angular change, and amplitude behavior during cessations are accurately described by the model when the tails of the probability distribution of δ are used as experimental input.