Mechanism of sustained oscillations in a fluid flowing past a circular cylinder obstacle

The mechanism of sustained oscillation in the flow past a circular cylinder is investigated numerically, in which impulsive force is given at a certain point in the flow and subsequent spatiotemporal development of induced disturbance is observed. The impulsive force generates an intense localized disturbance at the point of forcing, which is transmitted immediately up to a region just behind the cylinder, and there it yields an transient and eigen modes of disturbance having a packet form. Extending the conventional notions of convective and absolute modes of instability established on the parallel flow approximation to nonparallel flows, we define "passive" and "active" modes of instability, respectively, and evaluate the growth rate of each mode. It was found that the entire flow field is stable to active mode below the critical Reynolds number for the global instability though some extent of the flow behind the cylinder is unstable to passive mode, while the flow becomes unstable to active mode everywhere simultaneously when the Reynolds number exceeds the critical value. The numerical analysis brought us a conclusion that the oscillation is sustained by superiority of the growth of disturbance due to instability over the decrease due to advection of the packet.