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Fronts in reactive convection: Bounds, stability, and instability
Author(s) -
Constantin Peter,
Kiselev Alexander,
Ryzhik Lenya
Publication year - 2003
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.10110
Subject(s) - planar , nusselt number , instability , convection , mathematics , nonlinear system , mechanics , front (military) , stability (learning theory) , rayleigh scattering , rayleigh number , wavelength , mathematical analysis , physics , meteorology , natural convection , computer science , optics , computer graphics (images) , quantum mechanics , machine learning , reynolds number , turbulence
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.