Transient perturbation dynamics of vortex-airfoil interaction

Analyzing the perturbation dynamics is challenging for unsteady base flows due to their transient dynamics and the high degree of freedom. We leverage a linear reduced-order method based on the optimally time-dependent (OTD) bases to trace the dominant amplified directions of vortex-airfoil interaction. We consider complex transient dynamics with a positive vortical gust advecting over a NACA 0012 airfoil at the angle of incidence of 12 degrees. The flow around the airfoil is at a chord-length-based Reynolds number of 400. This gust incites vortex shedding above the airfoil and wake fluctuations behind the airfoil trailing edge (TE). We reveal the transitions of the most amplified region from the leading edge region to the negative leading-edge vortex, with a secondary amplified direction due to the wake deformation behind the airfoil TE. This study provides physical insights into the time-evolving perturbation amplification of transient, non-periodic, and nonlinear flows.