Time and Length Scales in Rotating Rayleigh-Bénard Convection

We report experimental results for Rayleigh-Bénard convection of a fluid $\left({\mathrm{CO}}_2\right)$ in a cylindrical cell with radius-to-height ratio 40 and rotated about a vertical axis. Near the critical rotation frequency for the Küppers-Lortz instability and for small $\epsilon \equiv \Delta T/\Delta T_c-1\mathrm{}$, we measured the frequency ${\omega }_a$ and the correlation length $\xi$ of the pattern dynamics. They could be fit by power laws in $\epsilon$ only when exponent values much smaller than those predicted from amplitude equations were used. Alternately, the predicted exponents could be retained if the threshold were shifted to negative values of $\epsilon$, thus yielding finite ${\omega }_a$ and $\xi$ at onset.