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While deriving the Doppler formula for the observed frequency of a sound wave, it is assumed that the speed of sound in the medium is greater than the source's speed through it. When this condition is breached, a shock wave occurs.
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Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
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Hydrodynamic X Waves.

James N Steer1, Alistair G L Borthwick1, Miguel Onorato2

  • 1School of Engineering, University of Edinburgh, Edinburgh EH9 3FB, United Kingdom.

Physical Review Letters
|November 26, 2019
PubMed
Summary
This summary is machine-generated.

Researchers observed stable, X-shaped surface gravity waves that maintain their form over long distances. This finding advances understanding of nonlinear wave phenomena in fluid dynamics and related fields.

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Area of Science:

  • Fluid dynamics
  • Nonlinear physics
  • Wave phenomena

Background:

  • Stationary wave groups are observed in various nonlinear dispersive media.
  • These include optics, Bose-Einstein condensates, plasma, and hydrodynamics.

Purpose of the Study:

  • To experimentally observe nonlinear surface gravity X waves.
  • To characterize their propagation and constant form.

Main Methods:

  • Experimental observation of surface gravity waves.
  • Analysis of wave envelope propagation and form.
  • Comparison with theoretical models, specifically the 2D+1 nonlinear Schrödinger equation.

Main Results:

  • Experimental confirmation of nonlinear surface gravity X waves.
  • Observation of X-shaped wave envelopes propagating with constant form over long distances.
  • Validation of the theoretical prediction of a balance between dispersion and diffraction at specific angles (±35.26°).

Conclusions:

  • The study provides experimental evidence for stable, self-localized nonlinear wave structures (X waves) in surface gravity water waves.
  • Findings contribute to understanding extreme wave events in directional seas.
  • Results encourage further investigation of X waves in other nonlinear dispersive systems.