Flame front propagation V: Stability Analysis of Flame Fronts: Dynamical Systems Approach in the Complex Plane

Abstract

We consider flame front propagation in channel geometries. The steady state solution in this problem is space dependent, and therefore the linear stability analysis is described by a partial integro-differential equation with a space dependent coefficient. Accordingly it involves complicated eigenfunctions. We show that the analysis can be performed to required detail using a finite order dynamical system in terms of the dynamics of singularities in the complex plane, yielding detailed understanding of the physics of the eigenfunctions and eigenvalues.

17 pages 7 figures

References in corpus (2)

• Flame front propagation I: The Geometry of Developing Flame Fronts: Analysis with Pole Decomposition
• Flame front propagation VI: Dynamics and Wrinkling of Radially Propagating Fronts Inferred from Scaling Laws in Channel Geometries

Cited by in corpus (5)

• Front propagation into unstable states
• Flame front propagation IV: Random Noise and Pole-Dynamics in Unstable Front Propagation II
• The Sivashinsky equation for corrugated flames in the large-wrinkle limit
• Laplacian Growth II: Saffman - Taylor Problem Without Surface Tension in Filtration Combustion: Formation of One Finger with Half of the Channel Width
• Premixed flame shapes and polynomials