The stability of decelerating shocks revisited

Doron Kushnir, Eli Waxman, Dov Shvarts

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We present a new method for analyzing the global stability of the Sedov-von Neumann-Taylor self-similar solutions, describing the asymptotic behavior of spherical decelerating shock waves expanding into ideal gas with density ∝r. Our method allows one to overcome the difficulties associated with the nonphysical divergences of the solutions at the origin. We show that while the growth rates of global modes derived by previous analyses are accurate in the large-wavenumber (small-wavelength) limit, they do not correctly describe the small-wavenumber behavior for small values of the adiabatic index γ. Our method furthermore allows one to analyze the stability properties of the flow at early times, when the flow deviates significantly from the asymptotic self-similar behavior. We find that at this stage the perturbation growth rates are larger than those obtained for unstable asymptotic solutions at similar γ, ω. Our results reduce the discrepancy that exists between theoretical predictions and experimental results.

Original languageEnglish
Pages (from-to)407-418
Number of pages12
JournalAstrophysical Journal
Issue number1 I
StatePublished - 20 Nov 2005


  • Hydrodynamics
  • Instabilities
  • Shock waves

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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