Destabilizing Neutrally Stable Wake Vortices Using Degenerate Eigenmodes

We demonstrate a method to de-stabilize linearly, neutrally stable q-vortices and other columnar vortices in a manner that has the potential to mitigate hazards of aircraft trailing wake vortices. Due to the symmetries of the vortices, in general, it is impossible to destabilize a neutral eigenmode by linearly perturbing the flow. Rather, it is necessary to simultaneously perturb a pair of degenerate eigenmodes such that one grows while the other decays. To quickly "tune" the flow to create degenerate eigenmodes from non-degenerate eigenmodes, non-degenerate perturbation theory is used. Then, to determine the required linear resonant perturbation to cause one of the eigenmodes of the degenerate pair to go unstable with a fast growth rate, degenerate perturbation theory is used. The resulting perturbation is then used in an initial-value calculation to determine the nonlinear evolution and growth of the instability. The special role of eigenmodes with critical layers is examined.