Data driven investigation of turbulent capillary waves*

We study a millimeter scale liquid meniscus subjected to ~7 MHz ultrasound. It is well understood that similar systems at lower frequencies generate droplets via a Faraday wave mechanism, but there is considerable debate about the atomization mechanisms at higher frequencies. Progress has been limited by the extremely small, and multi-scale, space and time scales involved relative to available experimental and numerical techniques. We present data captured at 10 us and 10 nm resolution using high speed digital holographic microscopy (DHM) and subject that data to principle component analysis (PCA) and Koopman based methods. More typical time series frequency analysis (e.g. FFT) shows that our system exhibits wave turbulence, which is well known to exchange energy between scales. We are also able to show, using spatial data of the entire surface (not single point), that energy is transfering towards smaller wavelengths as the input power to the system increases. Furthermore we identify multiple power thresholds at which turbulent wave behavior suddenly change, which are difficult to identify using frequency analysis.