Oscillations of the large-scale circulation in turbulent Rayleigh-Bénard convection: The sloshing mode and its relationship with the torsional mode

We report an experimental study of the large-scale circulation (LSC) in a turbulent Rayleigh-Bénard convection cell with aspect ratio unity. The temperature-extrema-extraction (TEE) method for obtaining the dynamic information of the LSC is presented. With this method, the azimuthal angular positions of the hot ascending and cold descending flows along the sidewall are identified from the measured instantaneous azimuthal temperature profile. The motion of the LSC is then decomposed into two different modes based on these two angles: the azimuthal mode and the translational or sloshing mode that is perpendicular to the vertical circulation plane of the LSC. Comparing to the previous sinusoidal-fitting (SF) method, it is found that both the TEE and the SF methods give the same information about the azimuthal motion of the LSC, but the TEE method in addition can provide information about the sloshing motion of the LSC. The sloshing motion is found to oscillate time-periodically around the cell's central vertical axis with an amplitude being nearly independent of the turbulent intensity and to have a π/2 phase difference with the torsional mode. It is further found that the azimuthal angular positions of the hot ascending and cold descending flows oscillate out of phase with each other by π, which leads to the observations of the torsional mode when these two flows are near the top and the bottom plates, respectively, and of the sloshing mode when they are both near the mid-height plane. A direct velocity measurement further confirms the existence of the bulk sloshing mode of the flow field.