Prandtl number dependence of flow topology in quasi-two-dimensional turbulent Rayleigh–Bénard convection

To date, a comprehensive understanding of the influence of the Prandtl number ( $Pr$ ) on flow topology in turbulent Rayleigh–Bénard convection (RBC) remains elusive. In this study, we present an experimental investigation into the evolution of flow topology in quasi-two-dimensional turbulent RBC with 7.0 ≤ Pr ≤ 244.2 and 2.03× 10⁸ ≤ Ra ≤ 2.81× 10⁹ . Particle image velocimetry (PIV) measurements reveal the flow transitions from multiple-roll state to single-roll state with increasing $Ra$ , and the transition is hindered with increasing $Pr$ , i.e. the transitional Rayleigh number Raₜ increases with $Pr$ . We mapped out a phase diagram on the flow topology change on $Ra$ and $Pr$ , and identified the scaling of Raₜ on $Pr$ : Raₜ ~ Pr0.93 in the low $Pr$ range, and Raₜ ~ Pr3.3 in the high $Pr$ range. The scaling in the low $Pr$ range is consistent with the model of balance of energy dissipation time and plume travel time that we proposed in our previous study, while the scaling in the high $Pr$ range implies a new governing mechanism. For the first time, the scaling of $Re$ on $Ra$ and $Pr$ is acquired through full-field PIV velocity measurement, Re ~ Ra0.63\,Pr-0.87 . We also propose that increasing horizontal velocity promotes the formation of the large-scale circulation (LSC), especially for the high $Pr$ case. Our proposal was verified by achieving LSC through introducing horizontal driving force RaH by tilting the convection cell with a small angle.