Dynamics of Nearly Circular Vortex Filaments

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dc.contributor.advisorCalini, Annalisa
dc.contributor.committeeMemberLaFortune, Stephane
dc.contributor.committeeMemberDougherty, Martha
dc.contributor.committeeMemberMitchener, Garrett
dc.creatorNelson, Sybil Prince
dc.date.accessioned2016-10-18T16:13:10Z
dc.date.available2016-10-18T16:13:10Z
dc.date.issued2014-08-25
dc.description.abstractWe 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.en_US
dc.description.sponsorshipCollege of Charleston. Graduate School; College of Charleston. Department of Mathematics.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/3004
dc.language.isoen_USen_US
dc.subjectVortex-motion; Differential equations, Partial.en_US
dc.titleDynamics of Nearly Circular Vortex Filamentsen_US
dc.typeThesisen_US
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