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Alexey Tikan1,2, Félicien Bonnefoy3, Guillaume Ducrozet3

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Researchers measured the nonlinear dispersion relation (NDR) of water waves, revealing soliton impacts and deviations from integrable turbulence. This work advances understanding of complex wave dynamics in oceanic environments.

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Area of Science:

  • Fluid dynamics
  • Wave propagation
  • Nonlinear physics

Background:

  • Partially coherent waves exhibit complex behaviors influenced by nonlinear effects.
  • Integrable turbulence, characterized by solitons, is a key framework for understanding random wave dynamics.
  • The nonlinear dispersion relation (NDR) is crucial for characterizing wave properties.

Purpose of the Study:

  • To numerically and experimentally investigate the nonlinear dispersion relation (NDR) of nonlinear random waves.
  • To characterize frequency shifts and NDR broadening in deep-water waves.
  • To identify signatures of deviation from integrable turbulence due to higher-order effects.

Main Methods:

  • Numerical simulations based on the nonlinear Schrödinger equation.
  • Experimental measurements using a limited number of wave gauges in a one-dimensional water tank.
  • Comparison of experimental data with numerical simulations of Dysthe and Euler equations.

Main Results:

  • Accurate measurement of the NDR for the slowly varying envelope of deep-water waves.
  • Precise characterization of frequency shift and NDR broadening.
  • Identification of solitons and their role in wave dynamics.
  • Experimental signatures of deviations from integrable turbulence due to higher-order effects were observed.

Conclusions:

  • The study successfully measured and characterized the NDR of nonlinear random waves.
  • Solitons play a significant role in the observed wave dynamics.
  • The NDR shape and broadening serve as indicators of deviations from integrable turbulence caused by higher-order effects in experimental settings.