Nonlinear propagation of arbitrary plane waves in ducts carrying plug flows

An analysis is presented of the propagation of high intensity plane waves in uniform ducts carrying uniform mean flows. The method of renormalization is used to determine a uniformly valid first-order expansion for running waves in the shock free regions. This expansion is combined with weak-shock theory to describe the wave propagation in the ducts. The effects of viscosity near the duct walls (mean and acoustic boundary layers) can be accounted for by decomposing the wave over short distances into its harmonic content and correcting each component independently. The mean boundary layer distorts the waves by dispersion, while the acoustic boundary layer distorts the waves by both dispersion and attenuation.