Vortex dynamics simulation of interacting vortex rings and filaments

Abstract
Interaction between a vortex ring and a vortex filament of the same strength has been simulated by a three-dimensional vortex method which employs vortex arrows with the Rosenhead-Moore core structure. The power spectrum of the velocity field and the enstrophy spectrum are obtained in a closed form whose limit of the core radius tending to zero is equivalent to that given be Aksman et al. (1985) Phys. Rev. Lett. 54 2410. Four basic modes of the interaction are shown to exist. Temporal evolution of the spectrum during the interaction is also obtained for the basic modes: the energy of the velocity field is generally transferred to the high-wavenumber range as the interaction proceeds.

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