Faraday Waves

Faraday waves, the waves that are subharmonically excited by vertical oscillations of a container of fluid, were examined experimentally; some measurements are compared to previous theoretical predictions. The containers used were circular and rectangular glass cylinders in which both viscosity and surface tension are significant. Single-mode Faraday waves are examined in Chapter II. Measurements of natural frequencies and threshold forcing amplitudes for neutral stability are well-predicted when the theory includes viscous damping. (The theory must use the measured decay rate 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. Faraday waves in a circular cylinder that are internally resonant with either the subharmonic (with frequency 1/4 that of the forcing) or superharmonic (with frequency equal to that of the forcing) mode are examined in Chapter III. For subharmonic resonance both modes achieved comparable amplitudes that were steady, or were modulated with one or two periods, or exhibited quasi-periodic or chaotic motions. A stability map of these responses is presented. Theoretical predictions of linear stability and growth rates are tested. Measurements of steady amplitudes, limit-cycle frequencies and wave slopes at breaking are presented. Some of the measured phase-plane trajectories are shown to have theoretical counterparts. For superharmonic resonance the amplitude of the superharmonic was never comparable with that of the Faraday wave. For low modes an energy exchange occurred during the initial period of growth, and a precession instability sometimes developed. For high modes for which both frequencies and wavenumbers are in a 2:1 ratio, superharmonic resonance occurred irreproducibly; it appeared to be overwhelmed by 1:1 interactions among possible Faraday-wave modes. Superharmonic resonance among high modes in a rectangular cylinder are examined in an appendix; resonance was not observed for this configuration.