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Modulated periodic stokes waves in deep water

Ablowitz1, Hammack, Henderson

  • 1Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA.

Physical Review Letters
|October 4, 2000
PubMed
Summary

Controlled deep-water Stokes waves were studied. Experiments showed reproducible wave maker data diverging downstream, while theory revealed chaotic evolution under nonlinear Schrodinger equation dynamics.

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Area of Science:

  • Fluid dynamics
  • Nonlinear wave phenomena

Background:

  • Deep-water Stokes waves are fundamental in fluid mechanics.
  • Understanding their stability and evolution is crucial for predicting complex wave behaviors.

Purpose of the Study:

  • To experimentally and theoretically investigate the dynamics of modulated deep-water 1D Stokes waves.
  • To analyze the conditions leading to chaotic evolution in these wave trains.

Main Methods:

  • Controlled modulation of wave trains in laboratory experiments.
  • Numerical integration of a perturbed nonlinear Schrodinger equation.
  • Analysis of associated linear spectral problems.

Main Results:

  • Experimental data showed reproducibility near the wave maker, but divergence downstream.
  • Numerical simulations indicated chaotic evolution of modulated periodic Stokes waves under specific conditions.
  • Sensitive spectral evolution was observed near homoclinic manifolds of the unperturbed nonlinear Schrodinger equation.

Conclusions:

  • Modulated deep-water Stokes waves can exhibit chaotic dynamics.
  • The nonlinear Schrodinger equation accurately models this chaotic behavior.
  • Experimental results highlight the sensitivity of wave evolution to initial conditions and downstream effects.

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