Fronts in reactive convection: bounds, stability and instability

2002/11/22 by Peter Constantin, Constantin, Peter, Alexander Kiselev +3
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Nonlinear Dynamics and Pattern Formation #Stochastic processes and statistical mechanics #nlin.CD

paper · pdf · doi:10.48550/arxiv.nlin/0211042

arxiv created 2002/11/22 · openalex publication_date 2002/11/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider front propagation in a reactive Boussinesq system in an infinite vertical strip. We establish nonlinear stability of planar fronts 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.

Citations

• Variational Principles for Propagation Speeds in Inhomogeneous Media

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