Axisymmetric vortex rings with swirl in an inviscid incompressible fluid are considered and it is demonstrated how the geometrical optics method can be used for investigating their stability. The evolution of rapidly oscillating initial data is studied and it is shown that the corresponding rings are unstable if the transport equations associated with the wave which is advected by the flow have unbounded solutions. It is shown that unbounded solutions grow either exponentially or algebraically. By means of the analysis of the corresponding transport equations effective stability conditions for general vortex rings with swirl are obtained. © 1993 John Wiley & Sons, Inc.
ASJC Scopus subject areas
- Applied Mathematics