Identification of weakly to strongly-turbulent three-wave processes in a micro-scale system

We find capillary wave turbulence (WT) spanning multiple dynamical regimes and geometries, all within a 40μL volume microfluidic system. This study is made viable with recent advances in ultra-high-speed digital holographic microscopy, providing 10μs time and 10nm spatial resolutions for images across the entire field at speeds sufficient to capture the salient wave phenomena. The observed WT types are: (i) discrete wave turbulence (DWT) dominated by finite domain effects, (ii) kinetic wave turbulence (KWT) that approximately satisfies weak wave turbulence (WWT) theory, and (iii) intermediate wave turbulence (IWT) that exhibits features from both DWT and KWT. We show that WT regime depends on input power and wavenumber, and we provide simple nondimensional parameters – derived from WWT theory – for intra-spectrum regime classification. Using the nondimensional parameters, a bulk nonlinearity metric is defined that employs bicoherence-based weighting. Analysis of experimental results reveals a correspondence between the theoretical regime classifiers and the observed phenomena. At sufficiently high input powers, the phenomena substantially depart from the WWT theory and reveal a regime of strongly nonlinear wave turbulence (SWT) defined by shallower spectral slopes that achieve a constant slope value over a range of input powers. This may suggest a corresponding power-law solution to the governing equations. This work augments current understanding of WT regimes and behaviors, and directly applies to many fields beyond fluid mechanics. For example, SWT appears upon the fluid interface at powers less than required for atomization, indicating that further study of SWT is needed to properly understand ultrasound-driven fuel spray atomization and drug and agricultural nebulization.