Sybil Nelson, College of Charleston


Dynamics of nearly circular vortex filaments

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 vectorfield. Such component is obtained by linearizing the Vortex Filament Equation around a circle. We are currently studying special solutions of our model and their stability.

Mentor: Annalisa Calini (College of Charleston)

References:R. Klein, A. J. Majda, amd K. Damodaran. Simplified equations for the interaction of nearly parallel vortex filaments. Journal of Fluid Mechanics (1995) vol. 288 pp. 201-248.