Strong microscopic capillary wave turbulence: Lévy flights and rogue waves

Tiny (O(10^-6)μL) pools of water excited by very high frequency (O(10⁶)Hz) ultrasonic vibrations at nanoscale (O(10^-9)m) amplitudes exhibit visible turbulent capillary waves (O(10^-2)m amplitudes and O(10^-1)s periods) at the free interface. In these systems, there is a complete absence of any classically predicted instability mechanisms such as Faraday wave theory. Modern studies of these systems utilize modeling approaches confined by the weakly nonlinear constraint (\ie, weak wave turbulence). We present recently acquired measurements of microscopic capillary wave turbulence occurring at high levels of nonlinearity. In this regime, we show that the wave processes may be described as an alpha-stable process with varying distribution tails. The results demonstrate that increasing input power causes a commensurate increase in tail heaviness and leads to greater commonality of rogue events. Discussion of implications and future research directions is contextualized by the problem of controlled atomization.