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

Abstract

We study capillary wave turbulence (WT) inherently spanning multiple dynamical regimes and geometries-from weakly to strongly nonlinear WT (SWT) and from shallow to deep domains-all within a 40 µL volume. These conditions violate idealizations used in modern WT theories. This study is now viable with recent advances in ultra-high-speed digital holographic microscopy, providing 10-µs time and 10-nm spatial resolutions for images across the entire field of view, encompassing a complete wave system. We derive tractable parameters permitting direct identification of four fundamental WT regimes, all present in this system. A proposed nonlinearity measure permits comparative analysis over varied inputs. Results indicate SWT precedes ultrasonic atomization. Our findings promote further SWT study toward improving associated applications. This work augments current understanding of WT regimes and behaviors, and directly applies to many fields beyond fluid mechanics. Curated data (300 GB) are freely provided for download [1].

Onset of Visible Capillary Waves from High-Frequency Acoustic Excitation

“…The narrow resonance peaks observed in the stable capillary wave oscillations in Figure c are broadened to essentially eliminate the peaks in Figure b, due to the nonresonant interaction between capillary waves of different frequencies that give rise to new capillary waves. These interactions generate waves with wavelengths λ and frequencies f , obeying a more generalized dispersion law than those derived from linear theory, such as ω 2 = ( 2 π f ) 2 = 4 π 2 γ ρ λ 3 from Lamb and Caflisch . The distinct change in the frequency response is the principal means to distinguish steady-state vibrations from nonlinear oscillations in this system.…”