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Grid states and nonlinear selection in parametrically excited surface waves.

T Epstein1, J Fineberg

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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 29, 2006
PubMed
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Parametrically excited surface waves form complex nonlinear states. Introducing a third frequency allows selective control over these interactions, leading to specific "grid" states.

Area of Science:

  • Nonlinear dynamics
  • Fluid mechanics
  • Wave phenomena

Background:

  • Parametrically excited surface waves, known as Faraday waves, arise from two commensurate frequencies.
  • These waves exhibit complex nonlinear states due to three-wave resonant interactions.
  • Understanding pattern selection in such systems is crucial for nonlinear physics.

Purpose of the Study:

  • To investigate the influence of a third driving frequency on nonlinear surface wave interactions.
  • To identify and characterize the resulting nonlinear states, particularly "grid" states.
  • To explore the role of quadratic nonlinearities and driving phase in pattern selection.

Main Methods:

  • Numerical simulations of interacting surface waves under parametric excitation.

Related Experiment Videos

  • Perturbation analysis by introducing a third driving frequency.
  • Analysis of wave vector interactions and stability of resulting patterns.

    • Main Results:

    • Selective favoring of different nonlinear wave interactions by the third frequency.
    • Observation of "grid" states as the dominant pattern when quadratic nonlinearities are prevalent.
    • Identification of specific driving phase combinations that govern the selection of different grid states.

    Conclusions:

    • A third driving frequency provides a mechanism to control nonlinear surface wave interactions.
    • "Grid" states represent a significant class of nonlinear patterns selected by quadratic nonlinearities.
    • Driving phase is a critical parameter for selecting specific grid states in Faraday wave systems.