# Phase randomization of three-wave interactions in capillary waves

## TL;DR

This paper investigates how increasing parametric excitation in capillary waves causes a transition from coherent to random three-wave interactions, linked to modulation instability and wave breaking.

## Contribution

It provides new experimental insights into the phase randomization process of three-wave interactions in capillary waves under parametric excitation.

## Key findings

- Spectral broadening of wave harmonics above threshold
- Decrease in phase coupling with increased pumping amplitude
- Evidence of modulation instability causing wave breaking

## Abstract

We present new experimental results on the transition from the coherent-phase to the random-phase three-wave interactions in capillary waves under parametric excitation. Above the excitation threshold, coherent wave harmonics spectrally broaden. An increase in the pumping amplitude increases spectral widths of wave harmonics and eventually causes a strong decrease in the degree of the three-wave phase coupling. The results point to the modulation instability of capillary waves, which leads to breaking of continuous waves into ensembles of short-lived wavelets or envelope solitons, as the reason for the phase randomization of three-wave interactions.