Stability Analysis of a Cylinder Wake With applied Harmonic Forcing

We apply localized forcing with harmonic frequencies and study the effect on the secondary instabilities present in cylinder wakes. The main forcing frequency of interest fm is equal to 2f0, where f0 is the vortex shedding frequency. The blowing ratio Br is set to 0.8, where this parameter corresponds to the strength of the harmonic forcing. Our recent research suggests that the secondary instabilities become attenuated at Re = 1000. This conjecture arises from the isosurface plots of vorticity and observing the suppression of streamwise vorticities. Using Nektar++ we conduct direct numerical simulations (DNS) in order to recreate the secondary instabilities and subsequently apply harmonic forcing. From these results, we definitively show the suppression of the streamwise vortices and confirm the suppression of the secondary instabilities using the growth rates obtained from Floquet Stability Analysis. Applying harmonic forcing leads to spanwise uniformity in the wake, otherwise the wake is defined by spanwise kinks in shed vortices for the unforced flows.