Stability of a Pair of Counterrotating and Corotating Vortices of Different Strengths

Abstract

The stability of a pair of line vortices is considered. The two line vortices are different in strength of circulation and can be counter- or corotating. This work is a generalization reported by Crow in 1970 and Jimenez in 1975. We find that the most unstable wave number and the maximum growth rate of instability are influenced by the circulation difference between the vortices for a pair of counterrotating vortices. For a pair of corotating vortices, we find that their stability properties are not significantly influenced by their circulation difference. Although the physically most-amplified wave number is not apparent based on linear stability analysis, a pair of corotating vortices is unstable irrespective of the circulation difference.