Importance of Antisymmetric Modes of the Crow Instability

The antisymmetric mode was neglected in the original Crow instability. In this study, a general-instability-analysis method was used to obtain the upper bounds of the instability growth rates, which are independent of the cutoff parameter in the self-induction integral. This result suggests that, not only do the antisymmetric modes exist, but also they are most amplified. These antisymmetric modes can occur in both the long- and short-wave modes. An example of the growth histories of the symmetric and antisymmetric modes for an aircraft wake is given. It is shown that the presence of the antisymmetric modes can cause the time of linking of the wake vortices to be shortened, which could lead to the reduction of the wake-vortex hazard to following aircraft.