Flow Reversals in Thermally Driven Turbulence

We analyze the reversals of the large-scale flow in Rayleigh-Bénard convection both through particle image velocimetry flow visualization and direct numerical simulations of the underlying Boussinesq equations in a (quasi-) two-dimensional, rectangular geometry of aspect ratio 1. For medium Prandtl number there is a diagonal large-scale convection roll and two smaller secondary rolls in the two remaining corners diagonally opposing each other. These corner-flow rolls play a crucial role for the large-scale wind reversal: They grow in kinetic energy and thus also in size thanks to plume detachments from the boundary layers up to the time that they take over the main, large-scale diagonal flow, thus leading to reversal. The Rayleigh vs Prandtl number space is mapped out. The occurrence of reversals sensitively depends on these parameters.

Figure 1

Top panel: Snapshots of the temperature (color) and velocity (arrows) field and time trace of angular momentum from numerical simulations ($\mathrm{Ra}={10}^8$ and $\mathrm{Pr}=4.3$). Bottom panel: Snapshots of the velocity field and time trace of angular momentum from experiment ($\mathrm{Ra}=3.8\times {10}^8$ and $\mathrm{Pr}=5.7$). (a), (b), and (c) show the instantaneous dimensionless temperature $(T-T_t)/\Delta$ distribution. (d) shows the temporal change of the dimensionless angular momentum $L(t)/L_0$, where $L_0$ is the maximum of the absolute value of $L$. The positive and negative signs indicate the anticlockwise and clockwise circulations, respectively. (e), (f), and (g) show the PIV-measured instantaneous velocity field and (h) the normalized instantaneous angular momentum $L(t)/L_0$. The color bar indicates the magnitude of the velocity (in unit of cm/sec). The snapshots in (a), (b), and (c) give numerical, and those in (e), (f), and (g) give experimental examples of the large-scale circulation before, during, and after a reversal process, as indicated in (d) and (h), respectively. Note that (b) and (f) show clearly the key role played by the growth of the corner rolls in the reversal process. Corresponding movies are offered in the supplementary material [18].

Figure 2

Time series of the center vorticity ${\omega }_c(t)$ (rescaled by its maximum) (lower panel) and the heights $h(t)$ of the lower left [blue (above positive ${\omega }_c$)] and right [red (above negative ${\omega }_c$)] corner flows, revealing their approximate linear growth. Not all growth processes need to lead to an immediate successful reversal, as seen for $t/t_E\approx 1300$. $\mathrm{Ra}={10}^8$, $\mathrm{Pr}=4.3$.

Figure 3

Log-log plot of the Ra dependence of the mean time intervals $⟨\tau ⟩$ between successive reversals, normalized in terms of the large eddy turnover time $t_E$. Filled symbols are from experiment and open symbols from simulation. The error bar originates from the statistics of the reversals; for the numerical case it is smaller than the symbol size.

Figure 4

Phase diagrams in the Ra-Pr plane. Red symbols (which are the symbols with $5<\mathrm{Pr}<6$) are from experiment and the black ones from DNS. Circles correspond to detected reversals [23], crosses to no detected reversals, in spite of excessive simulation (or observation) time. The straight lines are guides to the eye; they have (from left to right) slopes 0.25 and 1.00.