f(α) curves: Experimental results

We study the transition to chaos at the golden and silver means for forced Rayleigh-B\'enard (RB) convection in mercury. We present f({α}) curves below, at, and above the transition, and provide comparisons to the curves calculated for the one-dimensional circle map. We find good agreement at both the golden and silver means. This confirms our earlier observation that for low amplitude forcing, forced RB convection is well described by the one-dimensional circle map and indicates that the f({α}) curve is a good measure of the approach to criticality. For selected subcritical experimental data sets we calculate the degree of subcriticality. We also present both experimental and calculated results for f({α}) in the presence of a third frequency. Again we obtain agreement: The presence of random noise or a third frequency narrows the right-hand (negative q) side of the f({α}) curve. Subcriticality results in symmetrically narrowed curves. We can also distinguish these cases by examining the power spectra and Poincar\'e sections of the time series.