Evolution of vortex knots

For the first time since Lord Kelvin's original conjectures of 1875 we addr ess and study the time evolution of vortex knots in the context of the Eule r equations. The vortex knot is given by a thin vortex filament in the shap e of a torus knot T-p,T-q (p > 1, q > 1; p, q co-prime integers). The time evolution is studied numerically by using the Biot-Savart (BS) induction la w and the localized induction approximation (LIA) equation. Results obtaine d using the two methods are compared to each other and to the analytic stab ility analysis of Ricca (1993, 1995). The most interesting finding is that thin vortex knots which are unstable under the LIA have a greatly extended lifetime when the BS law is used. These results provide useful information for modelling complex structures by using elementary vortex knots.