ON THE SYMMETRY-BREAKING INSTABILITY LEADING TO VORTEX SHEDDING

It is well known that at early stages an impulsively started flow past a circular cylinder consists of twin vortices which are images of one another by reflection through the mid-plane. While the twin vortices are stable for Reynolds numbers below the critical Reynolds number val ue (Re-c similar or equal to 48), they become unstable above the criti cal Reynolds number. At Re>Re-c, the flow keeps its symmetric recircul ating bubble structure for a short time, undergoes a symmetry-breaking instability, and develops into a Karman vortex street. Foppl's vortex model is studied here as a low-dimensional model for the symmetric bu bble. The stability analysis of a fixed bubble in the model shows that there are two asymmetric eigenmodes, a stable mode and an unstable on e. In this paper, we show by two-dimensional direct numerical simulati ons (DNS) of the impulsively started flow past a circular cylinder how the instability properties of the model qualitatively mimic those of the re-al flow. (C) 1997 American Institute of Physics.