Acoustic–vorticity Waves in Swirling Flows

The propagation of small disturbances in an annular duct with a mean vortical swirling flow is studied. The disturbance velocity is split into a nearly-convected part and a nearly-sonic part, obeying weakly coupled equations. A normal mode analysis shows that the eigenvalues are segregated into a finite number of propagating pressure-dominated nearly-sonic waves and a cluster of infinite number of vorticity-dominated nearly-convected modes. A generalized gust can then be identified with the vorticity-dominated nearly-convected eigensolutions. The nearly-convected eigenvalues form two branches on either side of a critical layer which corresponds to purely convected modes. An asymptotic analysis is used to investigate the stability of the nearly-convected eigensolutions in the vicinity of the critical layer.