Resolvent analysis of a counter rotating vortex pair in the far wake of a finite aspect-ratio wing

We perform resolvent analysis over a streamwise slice of the far-wake flowfield downstream a finite-span wing of an aspect-ratio of 2.5 and at 5 degree angle of attack. At the chosen Reynolds number of 1000 and the free-stream Mach number of 0.3, the flow exhibits no unsteadiness. The flowfield over the streamwise slice, characterized by a pair of counter-rotating tip vortices and a wake deficit in the streamwise velocity component, is considered as the base flow in the resolvent analysis. The analysis is performed in a parallel-flow setting where the streamwise wavenumber is parametrized. At a low-frequency range, we observe that the dominant response modes are associated with the long-wave Crow instability. Over this range, both the forcing and response modes show symmetric structures in the streamwise and transverse velocity components and anti-symmetric in the spanwise component. According to the forcing mode structures, the Crow instability can be effectively triggered by introducing streamwise perturbation at the mid-span (symmetry) plane. Over the high-frequency range, we do not observed the manifestion of Widnall instability. This can be attributed to the low ellipticity in the shapes of the tip vortices. Comparing these results to those from Lamb-Oseen vortex pairs, we also suspect the absence of Widnall structures from the dominant modes are likely due to the stabilizing effects of the streamwise velocity component in the wake.