Guided acoustic wave propagation in a shear flow

The present work deals with the propagation of sound within a shear flow that takes place inside a two-dimensional rigid duct. Two kinds of hows are considered: a constant gradient shear flow and a shear flow with turbulent effects. A new analytical method based upon stratification that consists of dividing the guide into a number of uniform flow layers is proposed. This method enables the determination of the modal solutions for the complex potential in each layer for the upstream, downstream, propagative, and evanescent modes. Once these solutions have been calculated, the pressure profiles can be plotted for the duct section. The downstream "quasi-plane" mode is compared with results obtained by various authors. The second part of the study consists of, using the previous results, estimating the effects of frequency and speed on the pressure profiles on the upper side of the duct in the presence of a source located in front of the duct.