Resolvent analysis of co-existing periodic-flow solutions for a NACA0012 airfoil

At Re = 5000, both experiments and two-dimensional simulations of a NACA0012 airfoil wake show that, as the angle-of-attack is increased, there is a steep rise in lift beyond approximately 5^◦ as vortex shedding begins to occur. Simulations show that the unsteady flow displays different frequencies in its saturated state between 7^◦ and 8^◦, although periodic at higher and lower Reynolds numbers. Indeed, within this range, the lift signal shows multiple states and period-doubling, as the wake undergoes a substantial change in character from the standard vonKármán vortex street. Direct simulations and resolvent analysis are used to investigate the transitions further, with the latter well predicting the observed wake frequencies and co-existing periodic states.