On the role of modal phase interference in the formation of asymmetric wakes over a finite-span wing

We analyze the formation of spanwise-asymmetric wake downstream of a finite-span wing by disentangling asymmetric flow structures into symmetric and anti-symmetric ones. Here, the wing has a NACA 0012 section with an aspect-ratio of 2.5, and chord-based Reynolds number is set to be 1000. Our focus is placed upon the phase dynamics of the unsteady wake structures, which is distilled from a spatial-temporal harmonic resolvent analysis performed over a symmetry-enforced and an asymmetrically perturbed wakes downstream of the wing. We show that the resolvent modes obtained from the asymmetric base flow lie closely in span of the symmetric and anti-symmetric modes obtained from the symmetric base flow. More than 90% of the modal energy of asymmetric modes is captured by the symmetric and anti-symmetric modes obtained from the symmetric base flow. This indicates that the formation of asymmetric wake structures can be understood as the result of the phase interference between symmetric and anti-symmetric modes that underly in symmetric base flows. The current study paves a way towards the prediction of asymmetric wake structures via analyzing the canonically symmetric counterparts.