Three-dimensional vortex dynamics in bluff body wakes

Abstract

Over the last few years, there has been a surge of activity concerning wake flows, in particular regarding 3-D aspects of flows that are nominally two-dimensional. In the laminar shedding regime, it has become evident that end boundary conditions can control the three-dimensional wake pattern over long spans. These end conditions can be manipulated to produce oblique shedding, chevron patterns, parallel shedding, cellular shedding, and vortex dislocations. Transient patterns known as phase shocks and phase expansions can be induced by temporal control of end conditions by using variable suction. These experimental patterns may be modeled analytically using Guinzburg-Landau equations. The long-standing controversy regarding discontinuities in the Strouhal-Reynolds number relationship is caused by the phenomenon of oblique shedding, in turn dependent on end conditions. The original scatter of around 20% in the measurement of this relationship between different laboratories, up to 1988, has been reduced to 1% when parallel shedding is induced. In the wake transition regime, the large discrepancy in reported critical Reynolds numbers (Re = 140–190) over the last 40 years has been found to be due to contamination from end conditions. Indeed, remarkably “clean” end conditions can extend the laminar regime to Re = 194. The wake transition is shown to involve two successive stages, each corresponding to a discontinuity in both the character of wake formation and the S-Re relationship. The first discontinuity (Re = 180–194) is associated with the inception of vortex loops and is hysteretic. The second discontinuity (Re = 230–260) corresponds to a change to a finer scale streamwise vortex structure. The wake can exhibit enormous vortical structures, “vortex dislocations,” which explain the origin of the low-frequency velocity irregularities first observed by Roshko in 1954. Such dislocations, which cause surprisingly large fluctuation energy downstream, are conceivably an intrinsic feature of transition of shear flows in general. In the far wake, the honeycomb-like three-dimensional pattern first observed by Cimbala et al. in 1988, is found to be due to interactions between oblique shedding waves formed upstream with growing 2D waves amplified in the far wake from free-stream disturbances. Previous observations may now be explained in terms of these wave interactions. With these deductions as the starting point, we have gone on to discover a new mechanism of “oblique wave resonance,” whereby the two wave systems above interact nonlinearly to produce a third “oblique resonance wave,” which is then preferentially amplified (by up to two orders of magnitude over the 2-D waves). This single oblique wave resonance can be visualized remarkably clearly and is distinctly different from themodels hitherto proposed for the far wake.