Comparison of experiments and a nonlinear model equation for spatially developing flame instability

We extend the Michelson-Sivashinsky equation, for arbitrary gas density rat io, to model the dynamics of an inclined anchored flame front. A flow veloc ity component tangential to the flame front transforms temporally developin g structures into spatially developing ones. Closer investigation shows tha t a transition from absolute to convective instability should occur for a f inite flow velocity. Using pole decomposition, we give a particular solutio n to this equation in the limit of high flow velocity compared to laminar f lame speed. The analytical results are compared to measurements on a two-di mensional laminar flame. The growth rate, shape, and amplitude of the satur ated structures, as well as the width of the crossover region are all well described. However, we experimentally observe the presence of a large scale transverse gas circulation not predicted by the analysis. We attribute thi s effect to the streamwise variation of the pressure jump across the flame brush. (C) 2001 American Institute of Physics.