Combustion Science and Technology, Vol.126, No.1-6, 359-379, 1997
A note on ordering perturbations and the insignificance of linear coupling in combustion instabilities
Formal analysis of combustion instabilities has been based on expansion of the equations of motion in two small parameters, Mach numbers characterizing the average and fluctuating flows. The procedure is reviewed and extended in this note to 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 Mach number, cannot legitimately be retained when the equations have been expanded only to first order in Mach number.