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An Isaac Newton Institute Workshop

Pattern Formation in Fluid Mechanics

Surface waves: from pattern formation to wave turbulence

15th December 2005

Author: Fauve, S (ENS - LPS)

Abstract

Parametric amplification of surface waves has been observed by Faraday in 1831. It still provides the most flexible example of pattern forming instability because of dispersive properties of surface waves. Tuning the excitation frequency selects wave number, changes dissipation and thus the coherence length of the pattern and makes the bifurcation subcritical or supercritical depending on the sign of the detuning from resonance. Two-frequency forcing can generate quasi-periodic patterns or localized structures ("oscillons"). After recalling these well-known features and discussing an analogy with patterns in vibrated granular layers of solid particles, we will consider more turbulent regimes obtained with multiplicative or additive forcing. We will present experimental results on statistical properties of wave turbulence: Kolmogorov type spectra and probability density functions of wave amplitude. Finally, we will discuss some results about the fluctuations of the energy flux in these dissipative systems.