We introduce variable thickness, viscous vortex filaments. These can model such varied phenomena as underwater bubble rings or the intricate "chandeliers" formed by ink dropping into fluid. Treating the evolution of such filaments as an instance of Newtonian dynamics on a Riemannian configuration manifold we are able to extend classical work in the dynamics of vortex filaments through inclusion of viscous drag forces. The latter must be accounted for in low Reynolds number flows where they lead to significant variations in filament thickness and form an essential part of the observed dynamics. We develop and document both the underlying theory and associated practical numerical algorithms.
This work was supported in part by the DFG Collaborative Research Center TRR 109 "Discretization in Geometry and Dynamics," the Caltech Center for Information Science and Technology, and the Einstein Foundation Berlin. Additional support was provided by SideFX software.