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Effect of phase noise on parametric instabilities
F Pétrélis1, S Aumaître, S Fauve
1Laboratoire de Physique Statistique, Ecole Normale Supérieure, UMR 8550, 24, rue Lhomond, 75 005 Paris, France.
Physical Review Letters
|March 24, 2005
Summary
External phase noise reduces surface wave amplification. This study demonstrates noise modifies the forcing term in wave amplitude equations, unifying experimental data on growth rates and amplitudes under varying noise levels.
Area of Science:
- Experimental physics
- Wave phenomena
- Nonlinear dynamics
Background:
- Parametric amplification is a key process in wave dynamics.
- External noise can significantly influence nonlinear systems.
- Understanding noise effects on surface wave amplification is crucial.
Purpose of the Study:
- To experimentally investigate the impact of external phase noise on surface wave parametric amplification.
- To analyze how noise affects instability growth rates and wave amplitudes.
- To develop a theoretical framework explaining the observed phenomena.
Main Methods:
- Conducted experimental studies on surface waves.
- Introduced controlled external phase noise.
- Measured instability growth rates and wave amplitudes.
- Developed and applied a deterministic amplitude equation model.
Main Results:
- Observed a decrease in both instability growth rate and wave amplitude with increasing phase noise.
- Demonstrated that noise effectively modifies the forcing term in the amplitude equation.
- Successfully collapsed experimental data for growth rate and wave amplitude onto a single curve using a renormalized forcing term.
Conclusions:
- External phase noise plays a significant role in suppressing surface wave parametric amplification.
- A modified amplitude equation accurately describes the experimental observations, highlighting the renormalized forcing effect.
- The findings provide a unified understanding of noise-induced modifications in nonlinear wave systems.
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