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Nonlinear Fresnel diffraction of weak shock waves.

François Coulouvrat1, Régis Marchiano

  • 1Laboratoire de Modélisation en Mécanique, Université Pierre et Marie Curie & CNRS (UMR 7607), 4 place Jussieu, 75252 Paris 05, France. coulouvr@ccr.jussieu.fr

The Journal of the Acoustical Society of America
|November 1, 2003
PubMed
Summary

Weak shock waves in nonlinear acoustics diffract differently than linear waves, penetrating deeper into shadow zones. The penumbra thickness grows with propagation distance, offering new insights into nonlinear diffraction phenomena.

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Area of Science:

  • Nonlinear acoustics
  • Wave propagation
  • Diffraction phenomena

Background:

  • Fresnel diffraction is typically analyzed for linear acoustics.
  • The behavior of shock waves in the penumbra region of diffraction is not well understood.
  • Existing models often do not account for nonlinear effects in diffraction.

Purpose of the Study:

  • To investigate Fresnel diffraction for nonlinear acoustic waves.
  • To establish similarity laws for shock wave diffraction at a straight edge.
  • To compare nonlinear diffraction with the linear acoustic case.

Main Methods:

  • Utilizing the KZ equation and its jump relations for shock analysis.
  • Developing similarity laws for various shock wave types (step shock, N wave, sawtooth wave).

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  • Performing direct numerical simulations of the KZ equation.

    • Main Results:

    • Weak shock waves penetrate deeper into the shadow zone compared to linear waves.
    • Penumbra thickness increases with propagation distance following distinct power laws (1 for step shock, 3/4 for N wave).
    • Nonlinear evolution of the frequency spectrum explains the observed diffraction patterns.

    Conclusions:

    • Nonlinear acoustics significantly alters diffraction patterns at a straight edge.
    • The study provides new formulas for Rayleigh/Fresnel distance in nonlinear diffraction.
    • Findings offer a deeper understanding of weak shock wave behavior in diffraction boundary layers.