PERIOD TRIPLING AND ENERGY-DISSIPATION OF BREAKING STANDING WAVES

We examine the dynamics of two-dimensional steep and breaking standing waves generated by Faraday-wave resonance. Jiang et al. (1996) found a steep wave with a double-peaked crest in experiments and a sharp-cre sted steep wave in computations. Both waveforms are strongly asymmetri c in time and feature large superharmonics. We show experimentally tha t increasing the forcing amplitude further leads to breaking waves in three recurrent modes (period tripling): sharp crest with breaking, di mpled or flat crest with breaking, and round crest without breaking. I nteresting steep waveforms and period-tripled breaking are related dir ectly to the nonlinear interaction between the fundamental mode and th e second temporal harmonic. Unfortunately, these higher-amplitude phen omena cannot be numerically modelled since the computations fail for b reaking or nearly breaking waves. Based on the periodicity of Faraday waves, we directly estimate the dissipation due to wave breaking by in tegrating the support force as a function of the container displacemen t. We find that the breaking events (spray, air entrainment, and plung ing) approximately double the wave dissipation.