A Note on Ordering Perturbations and the Insignificance of Linear Coupling in Combustion Instabilities

Abstract

Formal analysis of combusion instabilities has been based on expansion of the equations of motion in two small parameters, March numbers characterizing the average and fluctuating flows. The procedure is reviewed and extended in this note explain how new terms involving nonlinear mean flow/acoustic interactions may be incorporated. As a further example of the ordering procedure, the reasoning is given to show why coupling of modes, linear in the average March number, cannot legitimately be ratained when the equations have been expanted only to first order in Mach number