 
Summary: LargeScale Circulation Model for Turbulent RayleighBeŽnard Convection
Eric Brown and Guenter Ahlers
Department of Physics and iQCD, University of California, Santa Barbara, California 93106, USA
(Received 8 December 2006; published 26 March 2007)
A model for the largescalecirculation (LSC) of turbulent RayleighBeŽnard convection in cylindrical
samples is presented. It consists of two physically motivated stochastic ordinary differential equations,
one each for the strength and the azimuthal orientation of the LSC. Stochastic forces represent
phenomenologically the influence of turbulent fluctuations. Consistent with measurements, the model
yields an azimuthally meandering LSC with occasional rotations, and with more rare cessations. As in
experiment, cessations have a uniform distribution of LSC orientation changes.
DOI: 10.1103/PhysRevLett.98.134501 PACS numbers: 47.27.te, 05.65.+b, 47.27.eb
RayleighBeŽnard convection (RBC) consists of a fluid
filled container heated from below [1]. Cylindrical contain
ers with aspect ratio ÿ D=L (D is the sample diameter
and L the height) and 0:5 & ÿ & 3 have a largescale
circulation (LSC) [29] that consists of warm upflowing
and cool downflowing fluid on opposite sides of the
sample. Its nearvertical circulation plane has an orienta
tion 0 that undergoes azimuthal diffusion [1012]. An
interesting aspect is that 0, in addition to its diffusive
