Measured temperature fluctuations and Reynolds number in turbulent Rayleigh-B\'enard convection with varying roughness size*

We present measurements of the temperature fluctuations $\sigma_T$ and of the Reynolds number Re in turbulent Rayleigh-B\'enard convection in cylindrical cell with pyramid-shaped rough top and bottom plates. To study the effects of roughness size, we varied a roughness parameter $\lambda$, defined as a single roughness height h (kept at a constant of 8 mm) over its base width d, from 0.5 to 4.0. Fluorinert Liquid FC-770 was used as the working fluid with the Rayleigh number Ra varying from $4.49 \times 10^{9}$ to $9.94 \times 10^{10}$ and Prandtl number Pr kept at 23.34. It is found that $\sigma_T$ in both cell center and sidewall increases dramatically with $\lambda$. The scaling exponent of the normalized $\sigma_T$ with respect to $Ra$ increases from $-0.16$ to $-0.09$ at cell center and $-0.23$ to $-0.08$ near sidewall when $\lambda$ is increased from $0.5$ to $4.0$. The Reynolds number $Re$ based on the circulation time of the large-scale circulation (LSC) also increases with $\lambda$, suggesting a faster LSC. The scaling exponent of $Re$ with respect to $Ra$ increases from 0.47 to 0.55 with $\lambda$ increased from $0.5$ to $4.0$. The study reveals that the flow and temperature fluctuations are very sensitive to the perturbation induced by rough plate with vary $\lambda$.