Modulation instability and capillary wave turbulence

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.

6 pages, 5 figures

References in corpus (5)

• Capillary rogue waves
• Observation of gravity-capillary wave turbulence
• Observation of wave turbulence in vibrating plates
• Are there waves in elastic wave turbulence ?
• Phase randomization of three-wave interactions in capillary waves

Cited by in corpus (21)

• Experiments in Surface Gravity-Capillary Wave Turbulence
• Inverse energy cascade and emergence of large coherent vortices in turbulence driven by Faraday waves
• Direct numerical simulations of capillary wave turbulence
• Parametrically excited water surface ripples as ensembles of oscillons
• Decay of capillary wave turbulence
• Energy flux measurement from the dissipated energy in capillary wave turbulence
• Space-Time Resolved Capillary Wave Turbulence
• Frequency dispersion of small-amplitude capillary waves in viscous fluids
• Numerical simulation of surface waves instability on a discrete grid
• Nonlinear waves on the surface of a fluid covered by an elastic sheet
• Experimental study of three-wave interactions among capillary-gravity surface waves
• Experimental study of the inverse cascade in gravity wave turbulence
• Turbulence of capillary waves forced by steep gravity waves
• Energy transport in weakly nonlinear wave systems with narrow frequency band excitation
• Gravity wave turbulence revealed by horizontal vibrations of the container
• Observation of depth-induced properties in wave turbulence on the surface of a fluid
• Energy spectra of \textbf{2D} gravity and capillary waves with narrow frequency band excitation
• Direct dynamical energy cascade in the modified KdV equation
• Statistics of rogue waves in isotropic wave fields
• Identification of weakly- to strongly-turbulent three-wave processes in a micro-scale system
• Phase and amplitude evolution in the network of triadic interactions of the Hasegawa-Wakatani system