Wind reversals in turbulent Rayleigh-Benard convection

The phenomenon of irregular cessation and subsequent reversal of the large-scale circulation in turbulent Rayleigh-B'enard convection is theoretically analysed. 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 ${10}^{-2}\le \mathrm{Pr}\le {10}^3$ and $10^{7} \leq \Ra \leq 10^{12}$, the model has the following features: (i) chaotic reversals may be exhibited at Ra $\ge {10}^7$; (ii) the Reynolds number based on the root mean square velocity scales as $\Re_{rms} \sim \Ra^{[0.41 … 0.47]}$(dependingonPr),andas$\Re_{rms} \sim \Pr^{-[0.66 … 0.76]}$ (depending on Ra); and (iii) the mean reversal frequency follows an effective scaling law $\omega / (\nu L^{-2}) \sim \Pr^{-(0.64 \pm 0.01)} \Ra^{0.44 \pm 0.01}$. The phase diagram of the model is sketched, and the observed transitions are discussed.