Near-neutral centre-modes as inviscid perturbations to a trailing line vortex

Inviscid linear perturbations to a columnar trailing line vortex are found in the form of center-modes. These near-neutral modes, occurring at moderate values of the azimuthal wavenumber n, are the analogue of the ring modes for large n discussed by Stewartson and Capell (1985). The appearance and disappearance of these modes as the swirl parameter varies may partly explain the difficulties encountered by numerical analysts in the computation of such modes. In addition, instabilities are found at higher values of the swirl parameter than have previously been reported.