Journal of Fluid Mechanics

The natural and forced formation of spot-like ‘vortex dislocations’ in the transition of a wake

C. H. K.  Williamson a1
a1 Mechanical and Aerospace Engineering, Upson Hall, Cornell University, Ithaca, NY 14853, USA

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The three-dimensional transition of the flow behind a bluff body is studied, with an emphasis placed on the evolution of large-scale structures in the wake. It has previously been found that there are two fundamental modes of three-dimensional vortex shedding in the wake of a circular cylinder (each mode being dependent on the range of Reynolds number), with a spanwise lengthscale of the same order as the primary streamwise wavelength of the vortex street. However. it is shown in the present study that the wake transition also involves the appearance of large-scale spot-like ‘vortex dislocations’, that grow downstream to a size of the order of 10–20 primary wavelengths. Vortex dislocations are generated between spanwise vortex-shedding cells of different frequency. The presence of these dislocations explains the large intermittent velocity irregularities that were originally found by Roshko (1954) and later by Bloor (1964) to characterize transition. The presence of these vortex dislocations in wake transition is largely responsible for the break-up to turbulence of the wake as it travels downstream.

In order to study their evolution in detail, dislocations have been (passively) forced to occur at a local spanwise position with the use of a small ring disturbance. It is found that ‘two-sided’ dislocations are stable in a symmetric in-phase configuration, and that they induce quasi-periodic velocity spectra and (beat) dislocation-frequency oscillations in the near wake. Intrinsic to these dislocations is a mechanism by which they spread rapidly in the spanwise direction, involving helical twisting of the vortices and axial core flows. This is felt to be a fundamental mechanism by which vortices develop large-scale distortions in natural transition. As the wake travels downstream, the energy at the low dislocation frequency decays slowly (in contrast to the rapid decay of other frequencies), leaving the downstream wake dominated by the large dislocation structures. Distinct similarities are found between the periodic forced dislocations and the intermittent dislocations that occur in natural transition. Further similarities of dislocations in different types of flow suggest that vortex or phase dislocations could conceivably be a generic feature of transition in all shear flows.

(Published Online April 26 2006)
(Received August 29 1991)
(Revised February 14 1992)