Stability of planar flames as gasdynamic discontinuities

Andreas G. Class*, B. J. Matkowsky, A. Y. Klimenko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


The stability of a steadily propagating planar premixed flame has been the subject of numerous studies since Darrieus and Landau showed that in their model flames are unstable to perturbations of any wavelength. Moreover, the instability was shown to persist even for very small wavelengths, i.e. there was no high-wavenumber cutoff of the instability. In addition to the Darrieus-Landau instability, which results from thermal expansion, analysis of the diffusional thermal model indicates that premixed flames may exhibit cellular and pulsating instabilities as a consequence of preferential diffusion. However, no previous theory captured all the instabilities including a high-wavenumber cutoff for each. In Class, Matkowsky & Klimenko (2003) a unified theory is proposed which, in appropriate limits and under appropriate assumptions, recovers all the relevant previous theories. It also includes additional new terms, not present in previous theories. In the present paper we consider the stability of a uniformly propagating planar flame as a solution of the unified model. The results are then compared to those based on the models of Darrieus-Landau, Sivashinsky and Matalon-Matkowsky. In particular, it is shown that the unified model is the only model to capture the Darrieus-Landau, cellular and pulsating instabilities including a high-wavenumber cutoff for each.

Original languageEnglish (US)
Pages (from-to)51-63
Number of pages13
JournalJournal of fluid Mechanics
StatePublished - Sep 25 2003
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


Dive into the research topics of 'Stability of planar flames as gasdynamic discontinuities'. Together they form a unique fingerprint.

Cite this