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Weak turbulent Kolmogorov spectrum for surface gravity waves.

A I Dyachenko1, A O Korotkevich, V E Zakharov

  • 1Landau Institute for Theoretical Physics, 2, Kosygin Street, Moscow, 119334, Russian Federation.

Physical Review Letters
|April 20, 2004
PubMed
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Researchers explored surface gravity waves using numerical simulations. They found that nonlinear interactions create a stationary spectrum, resembling a weak-turbulent Kolmogorov spectrum for energy cascade.

Area of Science:

  • Fluid dynamics
  • Wave physics
  • Nonlinear dynamics

Background:

  • Surface gravity waves are fundamental phenomena in fluid mechanics.
  • Understanding their long-time evolution under external forcing is crucial.
  • Nonlinear interactions significantly influence wave dynamics.

Purpose of the Study:

  • Investigate the long-time evolution of surface gravity waves on deep water.
  • Analyze the impact of stochastic external forcing on wave spectra.
  • Characterize the resulting wave spectrum and its relation to turbulence theory.

Main Methods:

  • Numerical implementation of primitive Euler equations for potential flow.
  • Utilized Hamiltonian canonical variables and Hamiltonian expansion up to fourth-order nonlinearity.

Related Experiment Videos

  • Analyzed surface elevation using Fourier spectrum analysis.

    • Main Results:

    • Formation of a stationary Fourier spectrum for surface elevation.
    • Observed spectrum closely approximates <|eta(k)|(2)> ~ k(-7/2).
    • This spectrum is consistent with a weak-turbulent Kolmogorov spectrum.

    Conclusions:

    • Nonlinear interaction processes drive the formation of the observed spectrum.
    • The results support the interpretation of a direct energy cascade in a weak-turbulent regime.
    • This study provides insights into the statistical behavior of surface gravity waves.