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Effect of Phase Noise on Parametric Instabilities F. Petrelis, S. Aumai^tre, and S. Fauve

Summary: Effect of Phase Noise on Parametric Instabilities
F. Pe´tre´lis, S. Aumai^tre, and S. Fauve
Laboratoire de Physique Statistique, Ecole Normale Supe´rieure, UMR 8550, 24, rue Lhomond, 75 005 Paris, France
(Received 15 June 2004; published 24 February 2005)
We report an experimental study on the effect of an external phase noise on the parametric amplification
of surface waves. We observe that both the instability growth rate and the wave amplitude above the
instability onset are decreased in the presence of noise. We show that all the results can be understood with
a deterministic amplitude equation for the wave in which the effect of noise is just to change the forcing
term. All the data for the growth rate (respectively the wave amplitude), obtained for different forcing
amplitudes and different intensities of the noise, can be collapsed on a single curve using this
renormalized forcing in the presence of noise.
DOI: 10.1103/PhysRevLett.94.070603 PACS numbers: 05.40.­a, 47.20.Ky
Introduction.--Parametric resonance occurs when the
natural frequency of an oscillator or a wave is modulated
in time or space. Since the early observation of parametri-
cally amplified standing waves on the surface of a verti-
cally vibrated layer of fluid by Faraday [1], it has been
recognized that parametric resonance is involved in most
areas of physics: Bragg scattering of a wave by a spatially
periodic medium or by another wave, energy bands in


Source: Aumaître, Sébastien - Laboratoire de Physique Statistique, Département de Physique, École Normale Supérieure


Collections: Physics