Observation and identification of weak to strong turbulence in capillary waves in a micro-scale system

We explore wave turbulence (WT) in capillary waves that appear in a 40 microliter sessile droplet while being oscillated by 7 MHz ultrasound using a new technique, ultra-high-speed digital holographic microscopy. The method enables capture of the wave dynamics to 10 microsecond, 1 micrometer lateral, and 10 nm vertical resolutions across the entire 1 square millimeter field of view. We observed four types of wave turbulence: (i) discrete wave turbulence (DWT), primarily influenced by the limitations of the domain; (ii) kinetic wave turbulence (KWT), generally corresponding with the principles of weak wave turbulence (WWT) theory; (iii) intermediate wave turbulence with characteristics of both DWT and KWT; and strong wave turbulence that substantially departs from WWT with a constant spectral slope shallower than WWT predictions. We find the form of WT is reliant on the input power and wavenumber, and provide WWT-derived nondimensional parameters to categorize the observed regimes of WT, including a bicoherence-based metric for overall nonlinearity that closely corresponds with our experimental results.