Analytical solution of multimodal acoustic propagation in circular ducts with laminar mean flow profile

In this paper, an analytical solution for the propagation of sound in circular ducts in the presence of Poiseuille mean flow is derived. This solution uses Kummer's functions and it generalizes the results found by Gogate and Munjal. Links between this solution and already-known solutions for more specific cases (no mean flow, uniform flow) are made. Results for calculation of the propagation constant and pressure profiles are presented and compared with the literature. The effect of shear on multimodal acoustic propagation, including modes of higher radial order is discussed.