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Coupled mean flow-amplitude equations for nearly inviscid parametrically driven surface waves.

Edgar Knobloch1, Carlos Martel, José M Vega

  • 1Department of Physics, University of California, Berkeley, California 94720, USA. knobloch@physics.berkeley.edu

Annals of the New York Academy of Sciences
|November 26, 2002
PubMed
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Parametrically excited surface waves in finite depth domains exhibit complex behaviors. Mean flow, driven by boundary layers, causes instabilities and pattern drift even with low viscosity.

Area of Science:

  • Fluid dynamics
  • Wave phenomena
  • Nonlinear physics

Background:

  • Surface gravity-capillary waves are fundamental in fluid mechanics.
  • Parametric excitation can lead to complex wave dynamics.
  • Interactions between waves and mean flow are crucial for understanding stability.

Purpose of the Study:

  • To investigate nearly inviscid surface gravity-capillary waves in 2D periodic domains.
  • To derive coupled equations for wave amplitudes and mean flow interaction.
  • To establish conditions for the validity of these derived equations.

Main Methods:

  • Derivation of coupled equations for resonant wave amplitudes.
  • Analysis of mean flow, including inviscid and viscous streaming components.

Related Experiment Videos

  • Investigation of boundary layer effects on mean flow.

    • Main Results:

    • Coupled equations were derived for left- and right-traveling waves.
    • Mean flow includes inviscid and viscous streaming parts driven by boundary layers.
    • These forcing mechanisms are significant even at vanishing viscosity.

    Conclusions:

    • The derived model captures essential dynamics of surface waves and mean flow.
    • Viscous streaming flow, driven by boundary layers, is responsible for instabilities.
    • Pattern drift is a key instability arising from the interaction of waves and mean flow.