  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 $10^{-2} \leq \Pr \leq 10^{3}$ and $10^{7} \leq
\Ra \leq 10^{12}$, the model has the following features: (i) chaotic reversals
may be exhibited at Ra $\geq 10^{7}$; (ii) the Reynolds number based on the
root mean square velocity scales as $\Re_{rms} \sim \Ra^{[0.41 ...
  0.47]}$ (depending on Pr), and as $\Re_{rms} \sim \Pr^{-[0.66 ... 0.76]}$
(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.
