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Area of Science:

  • Fluid Dynamics
  • Nonlinear Physics
  • Surface Wave Phenomena

Background:

  • Resonant wave interactions are fundamental to energy transfer across scales in wave systems.
  • Three- and four-wave interactions are classical nonlinear mechanisms driving these energy exchanges.
  • Gravity-capillary waves, influenced by both gravity and surface tension, exhibit complex nonlinear behaviors.

Purpose of the Study:

  • To experimentally investigate three-wave resonant interactions in crossing gravity-capillary surface waves.
  • To verify the resonance conditions (frequency and wave number matching) for generated waves.
  • To quantify the growth rate of resonant modes and compare it with theoretical predictions.

Main Methods:

  • Generation of two crossing wave trains in a laboratory tank.
  • Utilization of laser Doppler vibrometry for local measurements.
  • Application of diffusive light photography for spatiotemporal wave analysis.
  • Focus on the stationary regime with consideration of viscous dissipation.

Main Results:

  • Detection of a third resonant wave, confirming three-wave interaction.
  • Experimental verification of frequency and wave number resonance conditions.
  • Direct estimation of the resonant mode's growth rate.
  • Qualitative confirmation and extension of previous experimental findings for collinear waves.

Conclusions:

  • The experimental results qualitatively confirm and extend previous findings on three-wave interactions.
  • The study validates the predictions of weakly nonlinear triadic resonance interaction theory for non-collinear waves.
  • Highlights the relevance of three-wave interactions in the context of gravity-capillary turbulence.