Abstract
Vortex dynamics is a powerful tool for theoretical investigation of flows in which vorticity is confined within narrow regions and viscosity plays no essential role. Two cases have been investigated extensively: an ensemble of two dimensional point vortices, motions of which are governed by the Hamiltonian dynamics [1], and a single or several vortex filaments in three-dimensional motion which is determined uniquely by Biot-Savart’s law. The motion of a single vortex filament is analysed by Hama [2], Betchov [3], Hasimoto [4] and Takaki [5]. Interactions of two vortex filaments are treated by Crow [6], Moffatt [7], Hopfinger et al. [8] and Takaki & Hussain [9]. The short wave instability on a single vortex ring, investigated by Widnall et al. [10] and Saffman [11], also causes interaction between parts of a vortex filament.
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