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Fronts in reactive convection: Bounds, stability, and instability. (English) Zbl 1072.76068
Summary: 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.

MSC:
76V05 Reaction effects in flows
76E06 Convection in hydrodynamic stability
35Q35 PDEs in connection with fluid mechanics
80A25 Combustion
76E30 Nonlinear effects in hydrodynamic stability
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