Microscopic Rogue Waves in Strongly Nonlinear Capillary Wave Turbulence

When an otherwise quiescent minuscule (O(≤10−6)μl) basin of water is driven by ultrasonic vibrations at high frequencies (O(≥106)Hz) and with nanoscale (O(≤10−9)m) amplitudes, turbulent capillary waves that are visible by eye (O(10−2)m amplitudes and O(10−1)s periods) form at the air-water interface. Classical mechanisms typically attributed to such instabilities—such as Faraday wave theory—are absent. Contemporary wave turbulence studies have been mainly limited to weakly nonlinear regimes. In this talk, we present detailed measurements of strongly nonlinear, microscopic capillary wave turbulence. We show that this regime is reliably statistically characterized as an alpha-stable Lévy flight with a varying tail parameter. Our results demonstrate that as input power is increased, the heaviness of distribution tails also increases so that rogue events play an increasingly prevalent role in the overall wave system. Implications for future study and potential applications within the area of controlled atomization are discussed.