Study of a Rankine vortex with axial velocity discontinuity in an infinite tube

Abstract

In this work it is shown that a Rankine vortex with uniform axial flow, has only neutral modes even though the axial velocity be discontinuous at the rotational-irrotational interface. This discontinuity produces a bending of the dispersión curve branches in such a way of crossing the wave number axes with negative slope that is to say with negative group velocity. This result supports the initial idea about that the vortex breakdown phenomenon would be explained as a result of stationary waves of finite length by transporting the perturbation upstream in the frame of a stable flow. The dimensions of the bubble, considerably greater than the vortex core radius, could be explained by the condition of Beltrami perturbations that lets the formation of finite amplitude waves.