Tristable flow states and reversal of the large-scale circulation in two-dimensional circular convection cells

We present a numerical study of the flow states and reversals of the large-scale circulation (LSC) in a two-dimensional circular Rayleigh-Benard cell. Long-time direct numerical simulations are carried out in the Rayleigh number (Ra) range 10(7) <= Ra <= 10(8) and Prandtl number (Pr) range 2.0 <= Pr <= 20.0. We found that a new, long-lived, chaotic flow state exists, in addition to the commonly observed circulation states (the LSC in the clockwise and counterclockwise directions). The circulation states consist of one primary roll in the middle and two secondary rolls near the top and bottom circular walls. The primary roll becomes stronger and larger, while the two secondary rolls diminish, with increasing Ra. Our results suggest that the reversal of the LSC is accompanied by the secondary rolls growing, breaking the primary roll and then connecting to form a new primary roll with reversed direction. We mapped out the phase diagram of the existence of the LSC and the reversal in the Ra-Pr space, which reveals that the flow is in the circulation states when Ra is large and Pr is small. The reversal of the LSC can only occur in a limited Pr range. The phase diagram can be understood in terms of competition between the thermal and viscous diffusions. We also found that the internal flow states manifested themselves into global properties such as Nusselt and Reynolds numbers.

Automated summary

A numerical study on flow states and reversals in a two-dimensional circular Rayleigh-Benard cell revealed a new chaotic flow state, with the primary roll becoming stronger as Ra increases, while LSC reversals are accompanied by growth in secondary rolls. The phase diagram in Ra-Pr space shows that circulation states occur at large Ra and small Pr, and LSC reversals are limited to a specific range of Pr. Competition between thermal and viscous diffusions explains the phase diagram. Global properties such as Nusselt and Reynolds numbers are affected by internal flow states.