Local temperature fluctuations in turbulent Rayleigh-B{\'e}nard convection with wide-ranging aspect ratios

We report measurements of the local temperature fluctuations in 1-meter diameter cylindrical convection cells with aspect ratio $\Gamma$ ranging from 0.67 to 20 and the Rayleigh number Ra varying from 10$^7$ to 4$\times$10$^{12}$, at the Prandtl number Pr $\approx$ 4.3. Measurements are made at both cell center and the sidewall positions. The results show that the normalized temperature rms has a power-law dependence on Ra for all positions and aspect ratios, i.e. $\sigma/\Delta T\sim$ Ra$^{\alpha}$, where $\Delta T$ is the temperature difference across the convection cell. It is found that for sidewall positions $\alpha$ is approximately the same for most values of $\Gamma$, while it generally increases with $\Gamma$ for the center positions. We also found that the magnitude of the normalized temperature rms at both the center and sidewall is approximately the same for large $\Gamma$ ($\agt$ 10), while for small values of $\Gamma$ the sidewall fluctuations are roughly a factor of 2 larger than the center ones.