Disentangling spanwise asymmetries in unsteady wing wakes: global mode sensitivity and spatio-temporal harmonic resolvent analyses
We investigate the emergence of long-time spanwise asymmetries in an unsteady wake downstream of a finite-span wing by disentangling flow asymmetries into symmetric and anti-symmetric components using global mode (structural) sensitivity and spatio-temporal harmonic resolvent analysis. The global mode sensitivity analysis shows that asymmetric modes emerge when symmetric and anti-symmetric eigenmodes appear as pairs and exhibit high levels of modal non-normality. The modal non-normality renders the eigenmodes susceptible to asymmetric disturbances, which results in phase interference between the paired symmetric and anti-symmetric modes and unfolds them into highly asymmetric modes. Such interferences further motivate the development of a spatio-temporal harmonic resolvent analysis to examine the cross-frequency phase coupling between modes of different phase velocities. We observe that the flow asymmetries are primarily driven by elliptic vortex instability and its interaction with the wake shear layers. Moreover, we show that, even with a large-amplitude departure in the base flow from the symmetric state, the asymmetric modes obtained from the asymmetric wake can be accurately reconstructed by the symmetric and anti-symmetric modes from the symmetric base flow. This important finding suggests that flow asymmetries can be understood as a superposition of symmetric and anti-symmetric structures that lie under the symmetric base flow, and their phase interference serves as a potential mechanism for the emergence of long-time flow asymmetries. We believe that the present study provides a promising path towards understanding and controlling the emergence of asymmetric flow structures over finite-span wings.