Measured multiple flow states in turbulent thermal convection with aspect ratio 10

Abstract

We report an experimental investigation of turbulent Rayleigh-Benard convection in a rectangular cell of large aspect ratio ($\Gamma = 10$) over the Rayleigh number range $5.4\times10^7 \le Ra \le 7.2\times10^9$ and Prandtl number range $4.3 \le Pr \le 67.3$. Planar particle image velocimetry measurements show that the flow self organises into several horizontally stacked convection rolls, and repeated experiments under identical parameters (both $Ra$ and $Pr$) reveal that the number of rolls varies within the range of 3 to 7 with 6 being the most probable, which demonstrates the presence of multiple flow states. When $Pr$ is increased to 67.3, the number of roll like structures increases significantly, indicating a structural transition from a roll dominated to a plume dominated flow. This transition is reflected in the global momentum transport, for $Pr \leq 18.3$ the Reynolds number scales as $Re \sim Ra^{0.58}Pr^{-0.97}$, whereas the scaling is changed to $Re \sim Ra^{0.72}$ when $Pr$ reaches 67.3. Within individual rolls, we further examine the Reynolds numbers based on horizontal and vertical velocity components, $Re_{u,\text{roll}}$ and $Re_{w,\text{roll}}$, and find that the former increases while the latter decreases with roll size (quantified as the aspect ratio of the roll $\Gamma_\text{roll}$) due to continuity constraints, with their ratio following $Re_{w,\text{roll}}/Re_{u,\text{roll}} \sim \Gamma_\text{roll}^{-0.61}$. We impose different initial flow conditions (roll structures) with controlled perturbations, and demonstrate that the initial condition can influence the final turbulent state. We show that the number of horizontally stacked rolls regulates the global transport, larger number of rolls induces greater vertical momentum and heat transfer.