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

Andrés Castillo-Castellanos (1, 2, 3) , Anne Sergent (2, 3) , Bérengère Podvin (2) , Maurice Rossi (1)

1 DALEMBERT - Institut Jean Le Rond d'Alembert
2 LIMSI - Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur
3 SU - Sorbonne Université

We consider direct numerical simulations of turbulent Rayleigh-Bénard convection inside two-dimensional square cells. For Rayleigh numbers Ra = 10^6 to Ra = 5 · 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 regime CR, centrosymmetric modes are dominant and display a well-defined dynamics, while the less energetic non-centrosymmetric modes (here, two double roll modes) fluctuate randomly. For the regime EC, a non-centrosymmetric mode is dominant and the overall dynamics display a stochastic behaviour. Furthermore, an additional simplification of the dynamics is proposed based on a K-means clustering of the POD phase-space. It reduces the problem to a network dynamics of finite number of clusters. This simplified analysis captures the main features of the CR and EC dynamics. 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.

Mots clés: Bénard convection; Convection in cavities; Turbulent convection

Domaines: Thermique [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Andrés Castillo-Castellanos, Anne Sergent, Bérengère Podvin, Maurice Rossi. Cessation and reversals of large-scale structures in square Rayleigh-Bénard cells. Journal of Fluid Mechanics, 2019, 877, pp.922-954. ⟨hal-01921361v1⟩