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

Abstract

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 $7.0 \leq Pr \leq 244.2$ and $2.03\times 10^{8} \leq Ra \leq 2.81\times 10^{9}$ . 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 $Ra_t$ increases with $Pr$ . We mapped out a phase diagram on the flow topology change on $Ra$ and $Pr$ , and identified the scaling of $Ra_t$ on $Pr$ : $Ra_t \sim Pr^{0.93}$ in the low $Pr$ range, and $Ra_t \sim Pr^{3.3}$ 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, $Re \sim Ra^{0.63}\,Pr^{-0.87}$ . 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 $Ra_H$ by tilting the convection cell with a small angle.