Cessation and reversals of large-scale structures in square Rayleigh–Bénard cells

Abstract

We consider direct numerical simulations of turbulent Rayleigh–Bénard convection inside two-dimensional square cells. For Rayleigh numbers $Ra=10^{6}$ to $Ra=5\times 10^{8}$ and Prandtl numbers $Pr=3$ and $Pr=4.3$, two types of flow regimes are observed intermittently: consecutive flow reversals (CR), and extended cessations (EC). For each regime, we combine proper orthogonal decomposition (POD) and statistical tools on long-term data to characterise the dynamics of large-scale structures. For the CR regime, centrosymmetric modes are dominant and display a coherent dynamics, while non-centrosymmetric modes fluctuate randomly. For the EC regime, all POD modes follow Poissonian statistics and a non-centrosymmetric mode is dominant. To explore further the differences between the CR and EC regimes, an analysis based on a cluster partition of the POD phase space is proposed. This data-driven approach confirms the successive mechanisms of the generic reversal cycle in CR as proposed in Castillo-Castellanos et al. (J. Fluid Mech., vol. 808, 2016, pp. 614–640). However, these mechanisms may take one of multiple paths in the POD phase space. Inside the EC regime, this approach reveals the presence of two types of coherent time sequences (weak reversals and actual cessations) and more rarely intense plume crossings. Finally, we analyse within a range of Rayleigh numbers up to turbulent flow, the relation between dynamical regimes and the POD energetic contents as well as the residence time in each cluster.