 
Summary: A model of diffusion in a potential well for the dynamics of the largescale
circulation in turbulent RayleighBénard convection
Eric Browna
and Guenter Ahlers
Department of Physics and iQCD, University of California, Santa Barbara, California 93106, USA
Received 1 December 2007; accepted 1 April 2008; published online 1 July 2008
Experimental measurements of properties of the largescale 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 NavierStokes equations. The two
coupled equations are for the azimuthal orientation 0 and for the azimuthal temperature amplitude
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 smallscale turbulent fluctuations on the largescale
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 and the
Reynolds number is confirmed by measurements over a large experimental parameter range. The
Gaussian peaks of probability distributions p and p
0 are accurately described by the model;
however, the nonGaussian tails of p are not. The frequency, angular change, and amplitude
