  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.

Fluid Dynamics