A numerical study of the roll-up of a finite vortex sheet
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A point-vortex representation is used to study numerically the evolution of an initially plane vortex sheet. By introducing a tip vortex to represent the tightly rolled portion of the vortex sheet, the chaotic motion which was a feature of some earlier studies is eliminated and the details of the outer portion of the spiral are calculated. The rate of rolling up is calculated and is shown to be governed by the analytically predicted similarity law of Kaden during the initial stages of the rolling up. The calculations are continued until 99% of the vorticity has been rolled up, at which stage the spiral displays a marked ellipticity.
[1] H. Kaden. Aufwicklung einer unstabilen Unstetigkeitsfläche , 1931 .
[2] J. H. B. Smith,et al. Improved calculations of leading-edge separation from slender, thin, delta wings , 1968, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.
[3] K. Kuwahara,et al. Numerical Studies of Two-Dimensional Vortex Motion by a System of Point Vortices , 1973 .
[4] R. Clements,et al. The rolling up of a trailing vortex sheet , 1973, The Aeronautical Journal (1968).