Viscous instabilities in trailing vortices at large swirl numbers

This paper deals with the temporal stability of the q-vortex trailing line vortex model. We describe a family of viscous instabilities existing in a range of parameters which is usually assumed to be stable, namely large swirl parameters (q > 1.5) and large Reynolds numbers. These instabilities affect negative azimuthal wavenumbers (in < 0) and take the form of centre-modes (i.e. with a structure concentrated along the vortex centreline). They are related to a family of viscous modes described by Stewartson, Ng and Brown (1988) in swirling Poiseuille flow, and are the temporal counterparts of weakly amplified spatial modes recently computed by Olendraru and Sellier (2002). These instabilities are studied numerically using an original and highly accurate Chebyshev collocation method, which allows a mapping of the unstable regions up to Re ≈ 10⁶ and q ≈ 7. Our results indicate that in the limit of very large Reynolds numbers, trailing vortices are affected by this kind of instability whatever the value of the swirl number.