Direct observation of small scale capillary wave turbulence using high speed digital holographic microscopy

Introduction It is now known that capillary waves driven upon a fluid interface by high frequency ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> MHz) ultrasound exhibit capillary wave turbulence: the appearance of waves with phase and wavelength far removed from the excitation signal that drives them. These waves are responsible in significant part for atomization, a useful application for ultrasound, though the physics responsible for their appearance is poorly understood. Methods We use high-speed digital holographic microscopy to observe these capillary waves, an important step towards understanding their generation and atomization phenomena. Results We observe Zakharov-Kolmogorov weak wave turbulence for a limited range of input power, and find broader turbulence phenomena outside this range. We see discrete thresholds as the input power is increased, where higher and higher frequency responses are driven in the capillary waves with sudden onset between regimes. Discussion We employed spatial analysis to find extensions of the capillary wave response to higher frequencies, suggesting there is additional information in the spatial distribution of the capillary wave that is rarely if ever measured. We verified via frequency modulation that nonlinear resonance broadening is present, which undermines the use of Faraday wave or parametric wave theories to characterize these waves, important in the context of atomization which is now, definitively, not a Faraday wave process.