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Show spiraling up into the furnace, while the vorticity associated with the vortex sheet is depicted by the diverging conic section with negative helical vortex lines embedded in it. The chain-dashed lines depict mean streamtubes near the centerline of the furnace which are consistent with the presence of the positive helical vortex lines and the concomitant internal recirculation zone. This feature is similar to that pointed out by Chen et al. (1990) based on arguments put forth by Batchelor (1967). In this figure we show the vortex sheet as having penetrated only a small distance into the furnace. In the region near the inlet, the sheet bows outward slightly (consistent with centrifugal effects) and exhibits Kelvin-Helmholtz type instabilities similar to that of the two-dimensional shear layer. (See, in particular, the small scale structures on the right side of Fig. 7). Past this location, the sheet experiences significant deformation as large scale structures begin to appear. The reason for the abrupt transition to these structures is not known, but we suspect that they may be necessary to accomplish the transition between the upstream flow, where the vorticity is well organized and Biot-Savart effects are strong, and the downstream flow, where (we propose that) vorticity has dispersed and the Biot-Savart effects (which might otherwise stabilize the jet) are diminished. The formation of these structures along the vortex sheet denotes the concentration of vorticity at discrete locations along the sheet (Fig. 17). This concentration occurs at the expense of the adjacent locations in the sheet in the same fashion that the structures in a two-dimensional shear layer deplete the vorticity in the braid region. We speculate that the large scale structures are formed by a systematic pulling together of the vortex lines as the flow proceeds downstream. Since the vortex lines within the sheet form left-handed helixes, this would require that any connections between the structures appearing in Figs. 6 - 9 take the form of a left-handed helix. Meiberg and Martin (1990) have shown that such large scale structures can result from a helical perturbation to a cylindrical vortex sheet where the vorticity is initially perpendicular to the axis of the cylinder. We speculate that, in a similar fashion, the helically-wound vortex sheet is unstable to this perturbation and note that this is the only structure consistent with the clockwise tails observed in cross-stream photographs such as Fig. 10. Concentration of the negative helical vorticity in these structures has the effect of clustering that vorticity as the flow proceeds in the streamwise direction. Two consequences of this clustering may be observed. The first is that the large scale structures so formed begin to dominate the flow. Up until the point where these structures are formed there is a discernable mean flow to which a fluctuating component might be added. Once these structures have formed however, there is no longer a distinct mean flow -- the flow simply alternates between the presence and absence of the structures. Stated another way, the scales of the fluctuations exceed the scales of the mean flow. The second consequence of this clustering is that it creates a local imbalance between the positive and negative helical vorticity in the flow. Since the negative vorticity has become concentrated, it begins to pull more strongly on the adjacent positive vorticity fluid through the action of the Biot-Savart law. The result is that the positive vorticity fluid begins to experience a rotation around, and then entrainment into, the negative vorticity fluid. Figure 18 shows how this might occur and illustrates how in doing so, it causes the positive vorticity to be drawn out of the central region of the flow towards the outer wall. This convection of the positive vorticity - 7 - |
