We investigate large-scale circulation reversals in a two-dimensional Rayleigh-Bénard cell using a proper orthogonal decomposition (POD)-based, five-mode model. The Rayleigh number considered is $\text{Ra}=5\times {10}^7$ and the Prandtl number is $\text{Pr}=4.3$. A precursor event, corresponding to the action of a mode $L_{*}$ which disconnects the core region from the boundary layers before the onset of the reversal, is identified in the simulation. The five-mode model predicts correctly the behavior of the POD modes observed in the simulation, and in particular that of mode $L_{*}$. The presence of mode $L_{*}$, which was not included in an earlier, lower-dimensional version of the model [Podvin and Sergent, J. Fluid Mech. 766, 172 (2015)], is found to be instrumental for the reversal dynamics of the model, which suggests that it may also be important for those of the simulation. Reversals can therefore be characterized by three time scales: the transition duration, the interreversal time, and the precursor duration, which separates the precursor event from the onset of the reversal. The distribution of the time scales is found to agree well with the simulation when small-scale intermittency is taken into account through the introduction of noise in the model coefficients.

• Received 8 April 2016

DOI:https://doi.org/10.1103/PhysRevE.95.013112