Breaking waves: Bifurcations leading to a singular wave state

Abstract

We examine free surface wave singularities that show a violent focusing of energy. Periodic, modulated, and frequency locked wave states lead to a state with fluid spikes. When the excitation of free surface waves exceeds a well defined threshold, the waves break leading to a low-dimensional aperiodic state with spikes, droplet ejection, and air entrainment. Return maps formed from wave height measurements lead to a low-dimensional model of the dynamics. Surprisingly, only a slight increase in power dissipation is observed past the transition to ejecting waves.