From low-frequency oscillations to Markovian bistable stall dynamics

We study the dynamics of a fixed wing at stall in a wind tunnel by measuring the aerodynamic forces. We report experimental evidence of a critical Reynolds number from which low-frequency oscillations in the force are replaced by random bistable dynamics. In this new regime, the flow explores each state intermittently with long residence times. This stochastic process can be modeled as a continuous Markov chain, and equivalently, it shows a superexponential scaling for the mean residence times. Furthermore, the probability density function of the lift coefficient exhibits the characteristic heavy tail of extreme events. Extreme minima and maxima are at the origin of the transitions. We analyzed the evolution of these tails using extreme-value theory to identify the bifurcation points of the associated dynamical system. The results are in good agreement with a user-defined threshold method, the advantage being the unambiguity in the computation.