Hysteresis of two-dimensional flows around a NACA0012 airfoil at Re=5000 and linear analyses of their mean flow

Two-dimensional numerical simulations of the flow around a NACA0012 profile at Reynolds number Re = 5000 show that unsteady periodic flows reach different saturated states when increasing or decreasing the angle of attack between 7 degrees and 8(degrees). Within this range, the lift signal shows co-existing periodic states and period-doubling, as the wake undergoes a substantial change in character from the standard von-Karma n vortex street. Results of experiments in a water channel also indicate a change of the flow topology but at slightly lower angles of attack alpha = 6 degrees. A discussion of the discrepancy between numerical and experimental results is proposed in light of results about the three-dimensional transition of wake flows behind bluff bodies and airfoils. Finally, eigenvalue and resolvent analyses of time-averaged flows are used to investigate the two-dimensional transitions further. While a peak of energetic amplification is obtained at the frequency of a single periodic state, a double peak is observed for co-existing periodic states, the second one being at the frequency of the periodic state not used to compute the time-averaged flow. This behaviour also characterizes the resolvent analysis of the period-doubled states, although less pronounced.