The influence of a stationary uniform axial flow on the propagation of acoustic modes of vibration in a cylindrical duct

The propagation, in a cylindrical duct, of acoustic modes of vibration whose wavelength is smaller than the damping length, is studied in the presence of a stationary uniform axial flow. The conditions for propagation are investigated and the space-time structure of the direct (νφνg > 0) downstream (νφ > 0) mode and upstream (νφ < 0) mode and of the inverse modes (νφνg < 0) are determined as functions of the flow velocity V0 and of the duct wall impedance Z. (νφ is the phase velocity and νg the group velocity.) The damping and the energy ratio of the modes are also studied as functions of V0 and Z.