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Observing a focused weak shock wave perform a Hilbert transform.

Miguel A Alonso1,2, Pedro A Quinto-Su3

  • 1Institut Fresnel, Centrale Med, CNRS, Aix Marseille Univ, UMR 7249, 13397 Marseille Cedex 20, France.

Physical Review. E
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PubMed
Summary
This summary is machine-generated.

Researchers imaged focusing shock waves in liquids. Their profiles before and after focusing form a Hilbert transform pair, explained by the Gouy phase shift.

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Area of Science:

  • Fluid dynamics
  • Wave phenomena
  • Optics

Background:

  • Focusing shock waves are crucial in various physical phenomena.
  • Understanding their spatial profiles is key to predicting wave behavior.
  • Previous studies explored wave focusing but lacked detailed spatial imaging in liquid media.

Purpose of the Study:

  • To image the spatial profiles of focusing two-dimensional shock waves.
  • To investigate the relationship between shock wave profiles before and after focusing.
  • To explain the observed spatial profile transformation using optical principles.

Main Methods:

  • Utilized shadowgraphy with strobe photography for imaging.
  • Created focusing shock waves in a thin liquid gap.
  • Analyzed shock wave profiles at different focusing conditions and angles.

Main Results:

  • Observed that shock wave profiles before and after focusing approximate a Hilbert transform pair.
  • This relationship holds irrespective of focusing geometry (single point or caustic).
  • The Hilbert transform behavior is consistent across various directional angles.

Conclusions:

  • The spatial profiles of focusing shock waves exhibit a Hilbert transform relationship.
  • This phenomenon is attributable to the π/2 Gouy phase shift in two-dimensional focused waves.
  • The findings offer insights into wave propagation and focusing in liquid environments.