On the relation between linear stability analysis and mean flow properties in wakes

Abstract: In recent studies on wake stability, it has been observed that a simple linear stability analysis applied to the mean flow instead of the basic flow, could give an accurate prediction of the global mode selected frequency, although these phenomena are strongly non-linear. In this letter, we study the transient regime between the stationary (so called basic state) and unstationary solutions of the wake of a circular cylinder at Re=150. We show that the shift of the global frequency as a function of time due to strong non-linear effects, can be interpreted by a continuous mean flow correction induced by the growth of the instability. We show that during this transient regime, the mean state as a function of time plays the role of an instantaneous basic state on which the global frequency can be determined linearly.