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The principal feature in the roll-up of the ligament is that the only stable configuration is that of a sphere.
These data suggest that the growth of the instability and the resulting vortex roll-up is considerably stronger in the circular jet.
The calculation proceeds smoothly until roll-up begins; inevitably the sheet crosses itself.
To obtain a regular roll-up the vortices are uniformly spaced and given a sinusoidal perturbation of the appropriate wavelength.
The result is the roll-up of the shear layer into vortical lumps one wavelength apart, connected by thin braids.
In actual physical flows, a nonlinear roll-up of the vortex sheets occurs and the wake configuration is not known in advance.
Both the roll-up and the coalescence of the vortices take place in a region, not at a single point.
These data show that both the vortices accelerate after roll-up, then vortex 1 continues to accelerate but vortex 2 starts decelerating.
The motion of the point vortices becomes chaotic in the region of the vortex sheet roll-up.
This difference between the maximally unstable and the natural roll-up frequencies is being further investigated in our laboratory.
We include in figure 2 a sequence of pictures showing the initial regular stages of roll-up of a vortex sheet.
Two plateaus, one at the roll-up region and the other at the vortex merging region, existed.
The apparent 'roll-up' of the streaklines is followed by their distortion and segregation during impingement upon the edge.
It is available in a roll-up stick form.
The roll-up of the shear layer is a mechanism for accumulation of vorticity in lumps.
