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Parametric autoresonance in Faraday waves.

Michael Assaf1, Baruch Meerson

  • 1Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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Using a negative chirp, researchers excited gravity waves via parametric autoresonance. This method offers a way to control wave growth, with capture into resonance occurring at small chirp rates.

Area of Science:

  • Fluid dynamics
  • Nonlinear dynamics
  • Wave phenomena

Background:

  • Parametric excitation is a key mechanism for generating waves.
  • Standing gravity waves are fundamental in fluid mechanics.
  • Nonlinear effects and time-dependent forcing introduce complex dynamics.

Purpose of the Study:

  • To theoretically investigate parametric excitation of weakly nonlinear standing gravity waves.
  • To explore the role of a time-dependent ("chirped") vibration frequency.
  • To analyze the phenomenon of parametric autoresonance.

Main Methods:

  • Development of a theoretical framework for parametric excitation.
  • Application of the method of averaging to derive governing equations.
  • Analytical and numerical solutions for inviscid and viscous fluids.

Related Experiment Videos

  • Investigation of different initial conditions and chirp rates.

    • Main Results:

    • A negative chirp can excite steadily growing waves through parametric autoresonance.
    • Resonance capture is consistently observed for sufficiently small chirp rates.
    • A critical chirp rate is identified, beyond which autoresonance breaks down.
    • Autoresonance is predicted to cease at large amplitudes due to system stability changes.

    Conclusions:

    • Parametric autoresonance offers a controllable method for exciting gravity waves.
    • The chirp rate is a critical parameter determining the success and breakdown of autoresonance.
    • Fluid viscosity and initial conditions influence resonance capture and autoresonance stability.