Wind reversals in turbulent Rayleigh-Bénard convection.
The phenomenon of irregular cessation and subsequent reversal of the large-scale circulation in turbulent Rayleigh-Bénard convection is theoretically analyzed. The force and thermal balance on a single plume detached from the thermal boundary layer yields a set of coupled nonlinear equations, whose dynamics is related to the Lorenz equations. For Prandtl and Rayleigh numbers in the range 10(-2) < or = Pr < or = 10(3) and 10(7) < or = Ra < or = 10(12), the model has the following features: (i) chaotic reversals may be exhibited at Ra > or = 10(7); (ii) the Reynolds number based on the root mean square velocity scales as Re(rms) approximately Ra([0.41...0.47]) (depending on Pr), and as Re(rms) approximately Pr(-[0.66...0.76]) (depending on Ra); and (iii) the mean reversal frequency follows an effective scaling law omega/(nu L(-2)) approximately Pr(-(0.64 +/- 0.01))Ra(0.44 +/- 0.01). The phase diagram of the model is sketched, and the observed transitions are discussed.
Araujo
Francisco Fontenele
FF
Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, University of Twente, 7500 AE Enschede, The Netherlands.
Grossmann
Siegfried
S
Lohse
Detlef
D