Fronts in reactive convection: Bounds, stability, and instability

✍ Scribed by Peter Constantin; Alexander Kiselev; Lenya Ryzhik

• Book ID: 102116955
• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 208 KB
• Volume: 56
• Category: Article
• ISSN: 0010-3640
• DOI: 10.1002/cpa.10110

✦ Synopsis

Abstract

This paper examines a simplified active combustion model in which the reaction influences the flow. We consider front propagation in a reactive Boussinesq system in an infinite vertical strip. Nonlinear stability of planar fronts is established for narrow domains when the Rayleigh number is not too large. Planar fronts are shown to be linearly unstable with respect to long‐wavelength perturbations if the Rayleigh number is sufficiently large. We also prove uniform bounds on the bulk burning rate and the Nusselt number in the KPP reaction case. © 2003 Wiley Periodicals, Inc.