At the Upper Transition of Subcritical Regime of a Circular Cylinder

The present study establishes the transition between the lower and upper subcritical regime of flow over a circular cylinder at $7×103<Re<2×104.$ Based on a new sampling technique, it is shown that the small-scale secondary vortices, especially those of high energy, play an important role in the transition. Within a primary vortex shedding period, the secondary vortices appear in groups. In a group, the streamwise velocity of secondary vortices exhibits the increase, peak, and decrease pattern associated with the formation of Strouhal vortices. In the lower subcritical regime, the Group I of singular group occurs most frequently, while in the upper subcritical regime, the Group III of three groups is the most frequent. Pairings of successive secondary vortices are found, and the paired vortices also appear in groups. The present model of transition involves the excitation of the separated shear layer at the most amplified mode by the disturbances associated with the secondary and paired vortices. Due to their mutual interference, the higher-energy small-scale vortices affect the primary vortex sheet, which in turn amplifies the former. These higher-energy vortices have enhanced pairings, which also play a dominant role in the later stage of transition.