Thermal convection under external modulation of the driving force. II. Experiments

Experimental data are presented on the temperature response of a Rayleigh-B\'enard system to sinusoidal modulation of the heat current supplied to the lower plate near the onset of convection. Quantitative results are obtained for the average convective current as a function of the average Rayleigh number and of the amplitude and frequency of the modulation. Results are also presented on the temporal behavior of the response, above the convective threshold. The data are interpreted in terms of a previously proposed model which is a generalization of the Lorenz equations to periodic external driving. An important effect included in the model is the dynamic thermal mismatch between the sidewalls and the fluid which leads to an imperfect bifurcation between the conductive and convective states. As a result, the upward shift of the convective threshold caused by modulation in the ideal system is masked by the presence of sidewalls. In our model, this effect is controlled by a single adjustable parameter which turns out to agree in order of magnitude with previous experimental and theoretical estimates pertaining to a lower frequency range. The detailed comparison between experiment and theory shows good qualitative agreement, and some quantitative discrepancies in the parameter range explored. Suggestions are made for additional experiments to test a larger parameter range and in particular to minimize the sidewall effect in order to approximate the ideal threshold behavior more closely.