POD investigation of Rayleigh-Bénard convection in a rectangular cavity
Résumé
We consider the large-eddy simulation of turbulent Rayleigh-B Ìenard convection for air in a parallepipedic cavity of ratio (1:5:1) over the range Ra = 6 108 up to Ra = 1010 previously studied in Sergent and Le Qu Ìer Ìe (Proceedings ETC 2011). Using POD analysis, we confirm the existence of a large-scale circulation (LSC) consisting of quasi-stationary cross-stream rolls (y-rolls) which are aligned with the small direc- tion of the box. Strong changes in the LSC are observed to take place over a few hundred convective time units, defined as κ/(L2xRa1/2), where κ is the fluid diffusiv- ity, Lx is the height of the box and Ra is the Rayleigh number. We also show the existence of a secondary flow, which consists of horizontal rolls (z-rolls) surrounding the core of the cavity and orthogonal to the cross-stream rolls. The amplitude of these longitudinal rolls oscillates on a time scale of 50 convective units. The longitu- dinal rolls are associated with strong variations in the vertical momentum transfer, while cross-stream rolls are primarily responsible for more than half of the convec- tive heat transfer and make little contribution to the convective momentum transfer. Integration of a simplified dynamical model with stationary y-rolls leads to an os- cillation in the z-rolls with a characteristic period of 70 units, which supports the idea that the oscillation of the secondary rolls is determined by the primary flow structure. Using 2-D linear stability analysis based on the contributions from POD modes, we show that the presence of longitudinal shear leads to the stabilization of the high wavenumber range, and we predict a roll size which is reasonably close to that observed in the LES. We conjecture that changes in the large-scale circulation of the flow are related to the fluctuating shear created by the secondary rolls and higher-order modes outside the boundary layer.