Single-mode Faraday waves in small cylinders

Experiments on single-mode Faraday waves in small rectangular and circular cylinders in which both capillary and viscous effects were significant are reported. Measurements of threshold forcing (for neutral stability) and steady-state wave amplitudes are compared with theoretical predictions. Theoretical predictions of the resonant frequency of a single mode and of the threshold amplitude for its excitation on the hypothesis of linear boundary-layer damping agree well with the measured data. (The theory must use the measured damping rate to predict these quantities for waves in the rectangular cylinder.) Theoretical predictions of wave amplitudes are in reasonable agreement with those observed in the circular cylinder however, the theory provides only qualitative predictions of amplitudes for waves in the rectangular cylinder. In experiments in which two modes are theoretically admissible, the one with the smaller damping rate is observed however, a single-mode calculation proves inadequate for the prediction of the stability boundary.