Large-Scale Circulation Reversals in a 2D Rayleigh-Bénard cell

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We consider the numerical simulation of a two-dimensional Rayleigh-B\'enard cell in the turbulent regime $Ra=5$ $10^{7}$ and $Pr=4.3$. The flow is dominated by a large-scale inclined roll, the orientation of which switches intermittently in time. We use Proper Orthogonal Decomposition to identify the most energetic modes. We find that the first two modes respectively correspond to an antisymmetric and a symmetric mode. The next most energetic mode breaks the symmetry of the flow. During reversals, sharp variations in the temporal amplitudes of the modes are observed. We derive a low-dimensional model based on the first three most energetic modes which is able to reproduce the large-scale circulation reversals, in quantitative agreement with the simulation.