Statistical properties of the low-frequency flow oscillations over an airfoil near stall

We investigate the stochastic behavior of the aerodynamic force fluctuations on an LRN(1)-1007 airfoil operating at a chord-based Reynolds number of 10⁵. Our focus is on angles of attack near stall conditions, where low-frequency flow oscillations can occur. We find that the conditional probability distribution of the lift fluctuations obeys the Chapman–Kolmogorov equation. We confirm through a three-point joint probability check that the lift fluctuations follow a Markov process, and we estimate the Markov time scale using the chi-squared test. The Kramers–Moyal coefficients of the master equation indicate that only the drift and diffusion terms contribute significantly to the stochastic processes in this system, implying that the Fokker–Planck equation governs the evolution of the probability density functions. Our results show that the stationary solution of the Fokker–Planck equation can accurately predict the empirical probability density functions. These findings provide insight into the stochastic behavior of airfoil systems and may have practical implications for the design and optimization of aircraft.