# Regensburg 2013 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 29: Focus Session: Rayleigh Benard System and Convective Turbulence

### DY 29.3: Hauptvortrag

### Donnerstag, 14. März 2013, 16:00–16:30, H44

**Temperature statistics near the ultimate state of turbulent Rayleigh-Bénard convection **^{*} — •Xiaozhou He^{1}, Dennis van Gils^{1}, Eberhard Bodenschatz^{1}, and Guenter Ahlers^{1,2} — ^{1}MPI-DS, Goettingen, Germany — ^{2}UCSB, USA

We report on the study of temperature statistics in turbulent Rayleigh-Bénard convection (RBC) for Ra up to 10^{15} and for Pr ≃ 0.8. The experiment had been conducted in a pressure vessel known as the “Uboot" of Göttingen with compressed sulfur hexafluoride (SF_{6}) at a pressure up to 19 bars. We used two upright cylindrical RBC samples with the same diameter *D*=112 cm but different heights *L*=112 and 224 cm, corresponding to aspect-ratios Γ ≡ *D*/*L*=1.00 and 0.50 respectively.

Using the elliptical approximation, we derived local velocities from temperature space-time cross-correlation functions *C*_{T}(*r*,τ) and found a Gaussian distribution for velocity fluctuations. We also determined an effective Reynolds number in both samples and observed a transition from the classical state to the ultimate state of turbulent RBC^{1} near Ra ≃ 10^{14}, which agrees with the prediction by GL ^{2}. Finally, we observed the Kolmogorov −5/3 scaling in temperature energy spectra *E*(*k*), *E*(*k*) ∼ *k*^{−5/3}, above Ra ≃ 10^{14} in both samples.

^{1} X. He, D. Funfschilling, H. Nobach, E. Bodenschatz and G. Ahlers, Phys. Rev. Lett. **108**, 024502 (2012)

^{2} S. Grossmann and D. Lohse, Phys. Rev. E **66**, 016305 (2002)

^{*} Supported by the Max Planck Society, the Volkswagen Stiftung, the DFG SFB963, and NSF grant DMR11-58514.