The influence of aspect ratio on flow states in the buoyancy-driven turbulence with free slip boundaries

Abstract

Buoyancy driven turbulence with free-slip top and bottom plates in a confined box is studied via direct numerical simulations (DNS). The Rayleigh number is fixed to Ra=108 and the Prandtl number is Pr=10. The length/height aspect ratio Γy is fixed to 2, while the depth/height aspect ratio Γx varies from 0.125 to 0.3. With the variation of Γx, the hysteresis-like behavior of the heat and momentum transfer is found due to the emergence of two stable states of flow organization. For small Γx, the sheared flow occurs with disordered plumes occupying the entire bulk region, while it is replaced by convection rolls with increasing Γx. The striking feature is that the heat and momentum transport is greatly suppressed in the shear flow (SF) state, compared with that in the convection roll (CR) state. The turbulent kinetic energy budget is performed to delineate the relative contributions of physical processes that govern energy transport. It is found that the kinetic energy in the SF state is mainly produced by the buoyancy force, while it is dominated by the shear production near the plates in the CR state. During energy transport, it seems that the buoyancy force plays a more important role in the SF state than in the CR state, particularly in the bulk. Furthermore, through the analysis of dynamic mode decomposition of temperature fields, we illustrate that the flow in the SF state is dominated by the cloud-like spatially coherent structures with low frequencies, while the low-frequency roll structures play a leading role in the CR state. The flow state transition from SF to CR corresponds to the process that the cloud-like coherent structures form roll structures.