  Designing effective control for complex three-dimensional flow fields proves
to be non-trivial. Oftentimes, intuitive control strategies lead to suboptimal
control. To navigate the control space, we utilize a linear parabolized
stability analysis to guide the design of a control scheme for a trailing
vortex flow field aft of a NACA0012 half-wing at an angle of attack $\alpha =
5^\circ$ and a chord-based Reynolds number $Re = 1000$. The stability results
show that the unstable mode with the smallest growth rate (fifth wake mode)
provides a pathway to excite a vortex instability, whereas the principal
unstable mode remains in the wake of the wing. Inspired by this finding, we
perform direct numerical simulations that excite each mode with body forces
matching the shape function from the stability analysis. Relative to the
baseline uncontrolled case, the principal wake mode reduces the vortex length,
while the fifth wake mode further shortens the tip vortex. Analogously, the
streamwise circulation of the trailing vortex is found to be significantly
reduced. From these results, we conclude that a rudimentary linear stability
analysis can provide key insight into the underlying physics and help engineers
design more effective control.
