Behavior of asymmetric unstable modes of a trailing line vortex near the upper neutral curve

The linear stability of a trailing line vortex subjected to disturbances having azimuthal wave number n = -1 is considered. In the limit of large Reynolds numbers, the corresponding inviscid solution for this wave number is obtained. It is found that near the upper neutral curve, there exists mode crossing and mode switching between the primary and secondary modes. It is also found that viscous forces have both stabilizing and destabilizing effects on inviscid modes, which result in the appearance of a second peak in the growth rate curves.