Higher-order flow modes in turbulent Rayleigh–Bénard convection

Abstract

We present experimental studies of higher-order modes of the flow in turbulent thermal convection in cells of aspect ratio ($\unicode[STIX]{x1D6E4}$) 1 and 0.5. The working fluid is water with the Prandtl number ($Pr$) kept at around 5.0. The Rayleigh number ($Ra$) ranges from $9\times 10^{8}$ to $6\times 10^{9}$ for $\unicode[STIX]{x1D6E4}=1$ and from $1.6\times 10^{10}$ to $7.2\times 10^{10}$ for $\unicode[STIX]{x1D6E4}=0.5$. We found that in $\unicode[STIX]{x1D6E4}=1$ cells, the first mode, which corresponds to the large-scale circulation (LSC), dominates the flow. The second mode (quadrupole mode), the third mode (sextupole mode) and the fourth mode (octupole mode) are very weak, on average these higher-order modes each contains less than 4 % of the total flow energy. In $\unicode[STIX]{x1D6E4}=0.5$ cells, the first mode is still the strongest but less dominant, the second mode becomes stronger which contains 13.7 % of the total flow energy and the third and the fourth modes are also stronger (containing 6.5 % and 1.1 % of the total flow energy respectively). It is found that during a reversal/cessation, the amplitude of the second mode and the remaining modes experiences a rapid increase followed by a decrease, which is opposite to the behaviour of the amplitude of the first mode – it decreases to almost zero then rebounds. In addition, it is found that during the cessation (reversal) of the LSC, the second mode dominates, containing 51.3 % (50.1 %) of the total flow energy, which reveals that the commonly called cessation event is not the cessation of the entire flow but only the cessation of the first mode (LSC). The experiment reveals that the second mode and the remaining higher-order modes play important roles in the dynamical process of the reversal/cessation of the LSC. We also show direct evidence that the first mode is more efficient for heat transfer. Furthermore, our study reveals that, during the cessation/reversal of the LSC, $Nu$ drops to its local minimum and the minimum of $Nu$ is ahead of the minimum of the amplitude of the LSC; and reversals can be distinguished from cessations in terms of global heat transport. A direct velocity measurement reveals the flow structure of the first- and higher-order modes.