Space-Time Resolved Capillary Wave Turbulence

TL;DR

This paper presents comprehensive experimental analysis of capillary wave turbulence, capturing full space-time statistics, revealing power-law spectra consistent with theory, and observing stochastic energy transfer bursts at the air-water interface.

Contribution

The study provides the first full space-time resolved measurements of capillary wave turbulence, validating theoretical predictions and uncovering dynamic energy transfer mechanisms.

Findings

Power-law spectra in frequency and wave number match theoretical predictions.

Observation of stochastic bursts in energy transfer across scales.

Full spatio-temporal characterization of capillary wave turbulence.

Abstract

We report experiments on the full space and time resolved statistics of capillary wave turbulence at the air-water interface. The three-dimensional shape of the free interface is measured as a function of time by using the optical method of Diffusing Light Photography associated with a fast camera. Linear and nonlinear dispersion relations are extracted from the spatio-temporal power spectrum of wave amplitude. When wave turbulence regime is reached, we observe power-law spectra both in frequency and in wave number, whose exponents are found in agreement with the predictions of capillary wave turbulence theory. Finally, the temporal dynamics of the spatial energy spectrum highlight the occurrence of stochastic bursts transferring wave energy through the spatial scales.