ATTRACTOR DIMENSION FOR A SIMPLE PREMIXED FLAME PROPAGATION MODEL

A premixed two-dimensional flame propagating from below in the vertical plane generates a convective motion, which is treated here in the Boussinescq approximation. A simple one-step chemical reaction model is assumed. Recently developed methods of functional analysis are used to estimate the dimension of the attractor (essentially the number of degrees of freedom) characterizing the time asymptotic behavior of the flame propagation and the accompanying fluid motion. The attractor dimension is found to depend on four characteristic lengths intrinsic to the model of the combustion process and to the fluid motion. In particular, for a laminar flame the estimate of the attractor dimension is dominated by the flame diffusion length and the thickness of the reaction zone.