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≤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 Re_rms∼Ra^{[0.41⋯0.47]} (depending on Pr), and as Re_rms∼Pr^{-[0.66⋯0.76]} (depending on Ra); and (iii) the mean reversal frequency follows an effective scaling law ω/(νL^-2)∼Pr^{-(0.64±0.01)}Ra^0.44±0.01. The phase diagram of the model is sketched, and the observed transitions are discussed.