Flame front propagation IV: Random Noise and Pole-Dynamics in Unstable Front Propagation II

Abstract

The current paper is a corrected version of our previous paper arXiv:adap-org/9608001. Similarly to previous version we investigate the problem of flame propagation. This problem is studied as an example of unstable fronts that wrinkle on many scales. The analytic tool of pole expansion in the complex plane is employed to address the interaction of the unstable growth process with random initial conditions and perturbations. We argue that the effect of random noise is immense and that it can never be neglected in sufficiently large systems. We present simulations that lead to scaling laws for the velocity and acceleration of the front as a function of the system size and the level of noise, and analytic arguments that explain these results in terms of the noisy pole dynamics.This version corrects some very critical errors made in arXiv:adap-org/9608001 and makes more detailed description of excess number of poles in system, number of poles that appear in the system in unit of time, life time of pole. It allows us to understand more correctly dependence of the system parameters on noise than in arXiv:adap-org/9608001

23 pages, 4 figures,revised, version accepted for publication in journal "Combustion, Explosion and Shock Waves". arXiv admin note: substantial text overlap with arXiv:nlin/0302021, arXiv:adap-org/9608001, arXiv:nlin/0302017

References in corpus (7)

• Flame front propagation I: The Geometry of Developing Flame Fronts: Analysis with Pole Decomposition
• The Rate of Expansion of Spherical Flames
• Flame front propagation VI: Dynamics and Wrinkling of Radially Propagating Fronts Inferred from Scaling Laws in Channel Geometries
• Flame front propagation V: Stability Analysis of Flame Fronts: Dynamical Systems Approach in the Complex Plane
• Flame front propagation IV: Random Noise and Pole-Dynamics in Unstable Front Propagation II
• Pole solutions in the case of problems of flame front propagation and Saffman-Teylor "finger" formation without surface tension: open problems and possible ways of their solutions
• Flame front propagation III: Random Noise and Pole-Dynamics in Unstable Front Propagation (new version)

Cited by in corpus (2)

• Flame front propagation IV: Random Noise and Pole-Dynamics in Unstable Front Propagation II
• Laplacian Growth II: Saffman - Taylor Problem Without Surface Tension in Filtration Combustion: Formation of One Finger with Half of the Channel Width