Kinetic energy of vortex knots and unknots

Details Kinetic energy of vortex knots and unknots Kinetic energy of vortex knots and unknots

2009-04-23

arxiv.org/abs/0904.3658v1

Physics

Fluid Dynamics

14 pages, 5 figures

Scientific paper

New results on the kinetic energy of ideal vortex filaments in the shape of torus knots and unknots are presented. These knots are given by small-amplitude torus knot solutions (Ricca, 1993) to the Localized Induction Approximation (LIA) law. The kinetic energy of different knot and unknot types is calculated and presented for comparison. These results provide new information on relationships between geometry, topology and dynamics of complex vortex systems and help to establish possible connections between aspects of structural complexity of dynamical systems and vortical flows.

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