Torsional oscillation of the large-scale circulation in turbulent Rayleigh-B\'enard convection at large Rayleigh numbers*

We present temperature measurements in turbulent Rayleigh--B\'enard convection (RBC) over the Rayleigh number range $3.0\times10^{13} \le Ra \le 1.3\times10^{14}$ and at constant Prandtl number $\Pr \approx 0.8$. The RBC sample, known as the High-Pressure Convection Facility (HPCF) of G\"ottingen [1], is an upright cylinder of aspect ratio $\Gamma = 1.00$. Using three horizontal rows of thermistors at different heights in the sample, we determined the orientation angle of the large-scale circulation (LSC) plane, similar to [2]. Results identify a well established single-roll LSC with a periodic ``torsional'' mode with a frequency $f_C$. The values of $f_C$ are consistent with the frequencies $f_L$ obtained from power spectra $P(f)$ of temperature time series taken at mid-height of the sample. The non-dimensionalized frequencies $\tilde{f}_C$ are well described by a power law: $\tilde{f}_C \propto Ra ^{\zeta_f}$ with ${\zeta_f} = 0.427 \pm0.001$.\\[4pt] [1] He, Funfschilling, Bodenschatz and Ahlers, New J.\ Phys.\ {\bf 14}, 063030 (2012).\\[0pt] [2] Weiss and Ahlers, J.\ Fluid Mech.\ {\bf 688}, 461 (2011).