Kinetic energy of vortex knots and unknots

TL;DR

This paper investigates the kinetic energy of ideal vortex filaments shaped as torus knots and unknots, revealing relationships between their geometry, topology, and dynamics, thus advancing understanding of complex vortex systems.

Contribution

It provides new calculations of kinetic energy for various vortex knot types using the LIA law, linking structural complexity with vortex dynamics.

Findings

Kinetic energy varies with knot topology and geometry.

Results establish connections between vortex structure and flow dynamics.

Provides a basis for further studies on vortex complexity.

Abstract

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.