Threshold Dynamics of Singular Gravity-Capillary Waves

Abstract

Surface wave experiments confirm predictions of a threshold amplitude for droplet ejection. Droplet ejection and spray originate from highly focused surface singularities in the simplest states. The threshold is found to be dependent on forcing frequency and surface tension in accordance with a simple scaling theory presented here. Linear stability analysis indicates that the dynamics of the ejections at low frequency are low dimensional. Observations confirm this, and show periodic ejections as the simplest observed state. Ejecting states at higher frequency appear turbulent in nature.