On the Point Vortex Method

The discretization of the integrodifferential equation governing the evolution of a vortex sheet leads to a representation of the sheet by point vortices. It is shown, by examination of the special case of a uniform circular vortex sheet, that the chaotic motion which often arises when the point vortex representation is used is due to the amplification of numerically introduced disturbances. The mechanism is a discrete form of Helmholtz instability. The linear smoothing method of Longuet-Higgins and Cokelet (1976) and the repositioning method of Fink and Soh (1978) are shown to reduce the instability.

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