Shock wave stability in steep density gradients

Re'em Sari, Eli Waxman, Dov Shvarts

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


The stability of spherical accelerating shock waves is discussed via the examination of the stability of the new Waxman-Shvarts self-similar solutions to the strong explosion problem with a density profile ρ ∝ r with ω > 3. We show that accelerating shock waves that diverge in finite time (obtained for ω larger than a critical value ωc : ω > ωc) are unstable for small and intermediate wavenumbers, in accordance with the conclusions of Chevalier, who studied the stability of planar shock wave propagating in an exponentially decaying density profile. However, accelerating shock waves that diverge in infinite time (obtained for ω < ωc) are stable for most wavenumbers. We find that perturbation of small wavenumber grow or decay monotonically in time, while perturbations of intermediate and high wavenumber oscillate in time.

Original languageEnglish
Pages (from-to)475-479
Number of pages5
JournalAstrophysical Journal, Supplement Series
Issue number2
StatePublished - 1 Apr 2000
Externally publishedYes


  • Hydrodynamics
  • Instabilities
  • Shock waves

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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