The phenomenon of irregular cessation and subsequent reversal of the large-scale circulation in turbulent Rayleigh-Be´nard 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 102 Pr 103 and 107 Ra 1012, the model has the following features: (i) chaotic reversals may be exhibited at Ra 107; (ii) the Reynolds number based on the root mean square velocity scales as Rerms Ra0:410:47 (depending on Pr), and as Rerms Pr0:660:76 (depending on Ra); and (iii) the mean reversal frequency follows an effective scaling law !=L2 Pr0:64 0:01 Ra0:44 0:01. The phase diagram of the model is sketched, and the observed transitions are discussed.
Fontenele Araujo Junior, F., Grossmann, S., & Lohse, D. (2005). Wind reversals in turbulent Rayleigh-Bénard convection. Physical review letters, 94(8), 084502-1-084502-4. https://doi.org/10.1103/PhysRevLett.95.084502