Abstract
The leading-order fluid motions and frequencies in resonance tubes coupled to a combustion-driven flow source, such as occurs in various types of pulse combustors, are usually strongly related to those predicted by linear acoustics. However, in order to determine the amplitudes of the infinite number of classical acoustic modes predicted by linear theory alone, and hence the complete solution, a nonlinear analysis is required. In the present work, we adopt a formal perturbation approach based on the smallness of the mean-flow Mach number which, as a consequence of solvability conditions at higher orders in the analysis, results in an infinitely coupled system of nonlinear evolution equations for the amplitudes of the linear acoustic modes
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