2008/07/01 by Eric Brown, Guenter Ahlers · 63 citations
Engineering · Physics and Astronomy · #Aerodynamics and Acoustics in Jet Flows #Amplitude #Circulation (fluid dynamics) #Convection #Diffusion #Fluid Dynamics and Turbulent Flows #Gaussian #Particle Dynamics in Fluid Flows #Reynolds number #Scaling #Turbulence #Turbulent diffusion #White noise #physics.flu-dyn
paper · pdf · doi:10.1063/1.2919806
published in Physics of Fluids 20(7) (American Institute of Physics) · 17 pages, 17 figures
openalex publication_date 2008/07/01 · arxiv created 2008/07/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.