Dynamics of Nearly Circular Vortex Filaments
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Date
2014-08-25
Authors
Nelson, Sybil Prince
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Abstract
We derive a model for the dynamics of a pair of nearly-circular vortex filaments, and obtain a system of coupled partial differential equations that incorporate both the self-induced dynamics due to the vorticity of each filament and the interaction of the two filaments. Our derivation follows the one by Klein, Majda, and Damodaran [1] for the case of nearly-parallel vortex filaments. The evolution equations for nearly circular vortex filaments contain a curvature dependent term in the self-induction component of the vector field. Such component is obtained by linearizing the Vortex Filament Equation around a circle. We discuss special time-independent solutions using perturbation methods and Fourier-series methods for the associated partial differential equations.
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Keywords
Vortex-motion; Differential equations, Partial.