3-DIMENSIONAL INSTABILITIES IN WAKE TRANSITION

It is now well-known that the wake transition regime for a circular cy linder involves two modes of small-scale three-dimensional instability , modes ''A'' and ''B'', occurring in different Reynolds number ranges . These modes are quite distinct in spanwise lengthscale and in symmet ry, and they are found to scale on different physical features of the how. Mode A has a large spanwise wavelength of around 3-4 cylinder dia meters, and scales on the larger physical structure in the flow, namel y the core of the primary Karman vortices. The feedback from one vorte x to the next gives an out-of-phase streamwise vortex pattern for this mode. In contrast, the mode B instability has a distinctly smaller sp anwise wevelength (1 diameter) which scales on the smaller physical st ructure in the flow, namely the braid shear layer. The symmetry of mod e B is determined by the reverse flow behind the bluff cylinder, leadi ng to a system of streamwise vortices which are in phase between succe ssive half cycles. The symmetries of both modes are the same as the on es found in the vortex system evolving from perturbed plane wakes stud ied by Meiburg and Lasheras (1988) and Lasheras and Meiburg (1990). Fu rthermore, the question of the physical origin of these three-dimensio nal instabilities is addressed. We present evidence that they are link ed to general instability mechanisms found in two-dimensional linear f lows. In particular, mode A seems to be a result of an elliptic instab ility of the near-wake vortex cores; predictions based on elliptic ins tability theory concerning the initial perturbation shape and the span wise wevelength are in good agreement with experimental observations. For the mode B instability,it is suggested that it is a manifestation of a hyperbolic instability of the stagnation point flow found in the braid shear layer linking the primary vortices. (C) Elsevier, Paris.