Modulation instability and capillary wave turbulence

Details Modulation instability and capillary wave turbulence Modulation instability and capillary wave turbulence

2010-06-24

arxiv.org/abs/1006.4672v1

EPL 91 (2010) 14002

Physics

Fluid Dynamics

6 pages, 5 figures

Scientific paper

10.1209/0295-5075/91/14002

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.

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