Dynamics of large-scale circulation and energy transfer mechanism in turbulent Rayleigh–Bénard convection in a cubic cell

Abstract

We present the characteristics and dynamics of large-scale circulation (LSC) in turbulent Rayleigh–Bénard convection (RBC) inside a cubic cell. The simulations are carried out for a Rayleigh number range of 2 × 106 ≤ Ra ≤ 109 and using air (at Prandtl number Pr = 0.7) as the working fluid. Using the Fourier mode analysis, the strength, orientation, and associated dynamics of LSC are characterized. Following previous two-dimensional studies in RBC, we propose a mechanism of flow reversals based on the dynamics of corner vortices, which is less attempted in three-dimensional counterparts. We observe that the plane containing LSC is generally aligned along one of the diagonals of the box accompanied by a four-roll structure in the other. In addition to the primary roll, two secondary corner-roll structures are also observed in the LSC plane, which grow in size and destabilize the LSC, resulting in partial (ΔΦ1 ≈ π/2) and complete (ΔΦ1 ≈ π) reversals. In addition to previously reported rotation-led reorientations, we also observe cessation events that are rare in cubic cells. We observe that as the Rayleigh number is increased from Ra = 2 × 106 to 107, the number of reorientations reduces by one third. With an increase in Ra, the strength of LSC (SLSC) increases and the corner rolls reduce in size, which leads to the reduction in the occurrence of reorientations. At higher Rayleigh numbers (Ra > 108), the strength saturates around SLSC ≈ 0.75. To connect the dynamics between different coherent structures, we evaluate the turbulent kinetic energy (TKE) budget. Notably, our novel approach to study the variation of TKE along the azimuthal direction helps in identifying the dynamical coupling between the LSC and non-LSC planes. The analysis suggests that TKE is generally produced in localized regions in both the planes, while its dissipation mainly happens in the vicinity of the plane that contains LSC. The transport mechanism redistributes the energy between these planes and thus sustains the LSC and other coherent structures.