Modulation instability and capillary wave turbulence

TL;DR

This study investigates how modulation instability causes the transition from discrete to broadband spectra in capillary wave turbulence, confirming weak turbulence theory predictions through laboratory experiments.

Contribution

It demonstrates experimentally that modulation instability drives spectral broadening and the transition to wave turbulence consistent with weak turbulence theory.

Findings

Spectral continuum scales as f^{-2.8} in agreement with WTT.

Modulation instability causes phase randomization and spectral broadening.

Transition from 4- to 3-wave interactions facilitates turbulence development.

Abstract

Formation of turbulence of capillary waves is studied in laboratory experiments. The spectra show multiple exponentially decreasing harmonics of the parametrically excited wave which nonlinearly broaden with the increase in forcing. Spectral broadening leads to the development of the spectral continuum which scales as $\propto f^{-2.8}$, in agreement with the weak turbulence theory (WTT) prediction. Modulation instability of capillary waves is shown to be responsible for the transition from discrete to broadband spectrum. The instability leads to spectral broadening of the harmonics, randomization of their phases, it isolates the wave field from the wall, eventually allows the transition from 4- to 3-wave interactions as the dominant nonlinear process, thus creating the prerequisites assumed in WTT.