Absolute instability in the near-wake of two-dimensional bluff bodies

The linear inviscid instability of a family of mean velocity profiles which is representative of the near wake of two-dimensional bluff bodies is studied on a locally parallel basis. Restricting attention to the incompressible case, both the influence of the centerline velocity and the ratio of wake width to individual mixing layer thickness are explored. The parameters are identified for which the flow is absolutely unstable locally, i.e. for which instability waves amplifying in the upstream direction exist. This feature plays an important role when the attempt is made to explain the selection of a particular vortex shedding mode, i.e. to predict the shedding frequency, for instance. Different possibilities of feedback loops, such as the one proposed by Koch, as well as other mode selection criteria, notably the one used by Pierrehumbert, and their relevance to particular types of wakes are discussed. For top-hat wakes bounded by thin mixing layers a new criterion is proposed which properly accounts for the influence of the initial mixing layer thickness. In addition, the effects of a recirculating region near the body and of initial mixing layer curvature on the near-wake stability are considered qualitatively. Finally, the possible bearing of these concepts on the observed mode competition between the Karman and the varicose mode is examined.