The Physical Mechanism of Transition in Bluff Body Wakes

The physical nature of the initial transition to three-dimensionality of #ow past a circular cylinder has been the subject of considerable debate in the literature. Of several proposed mechanisms, the possibility of classi"cation as an elliptical instability is re-examined in this article. Detailed Floquet analysis of the transition shows clear evidence of the growth of an elliptic instability in the forming vortex cores followed by ampli"cation by the strong strain "eld in the hyperbolic region between the forming and shed vortices. In fact, it appears that the wake immediately behind the cylinder shows distinct signs of a cooperative elliptic instability as found previously for interacting counter-rotating vortices. Further downstream, after the vortices have been shed into the wake, the instability again grows in the cores. Threedimensional simulations provide a semi-quantitative estimate of the &&elliptic content'' of instability, and con"rm that elliptic instability seems to be dominant in the initiation and maintenance of the 3-D perturbation. ( 2001 Academic Press