The coupling leads to separate families of modes, driven by compressibility or by the swirl, which must be treated separately. We consider the practically important case in which the swirl Mach numbers are comparable to those of the steady axial flow. WKB analysis is applied using É›, the mean axial gradient of the cylinder walls, as the small parameter. At O(1) we determine local wave numbers according to the parallel-flow theory of Atassi, while at O(É›) a secularity condition yields the variaition of the modal amplitudes along the axis. We demonstrate that the presence of swirl can significantly reduce the amplitude of acoustic modes in the pipe. This is of practical significnance for the prediction of noise generation by turbomachinery, since rotating blade rows can produce significant mean swirl downstream.
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