MODERATE AND STEEP FARADAY WAVES - INSTABILITIES, MODULATION AND TEMPORAL ASYMMETRIES

Mild to steep standing waves of the fundamental mode are generated in a narrow rectangular cylinder undergoing vertical oscillation with for cing frequencies of 3.15 Hz to 3.34 Hz. A precise, non-intrusive optic al wave profile measurement system is used along with a wave probe to accurately quantify the spatial and temporal surface elevations. These standing waves are also simulated by a two-dimensional spectral Cauch y integral code. Experiments show that contact-line effects increase t he viscous natural frequency and alter the neutral stability curves. H ence, as expected, the addition of the wetting agent Photo Flo signifi cantly changes the stability curve and the hysteresis in the response diagram. Experimentally, we find strong modulations in the wave amplit ude for some forcing frequencies higher than 3.30 Hz. Reducing contact -line effects by Photo-Flo addition suppresses these modulations. Pert urbation analysis predicts that some of this modulation is caused by n oise in the forcing signal through 'sideband resonance', i.e. the intr oduction of small sideband forcing can generate large modulations of t he Faraday waves. The analysis is verified by our numerical simulation s and physical experiments. Finally, we observe experimentally a new f orm of steep standing wave with a large symmetric double-peaked crest, while simulation of the same forcing condition results in a sharper c rest than seen previously. Both standing wave forms appear at a finite wave steepness far smaller than the maximum steepness for the classic al standing wave and a surface tension far smaller than that for a Wil ton ripple. In both physical and numerical experiments, a stronger sec ond harmonic (in time) and temporal asymmetry in the wave forms sugges t a 1:2 resonance due to a non-conventional quartet interaction. Incre asing wave steepness leads to a new form of breaking standing waves in physical experiments.