For the first time since Lord Kelvin's original conjectures of 1875 we address and study the time evolution of vortex knots in the context of the Euler equations. The vortex knot is given by a thin vortex filament in the shape of a torus knot T(p,q) (p > 1, q > 1; p, q co-prime integers). The time evolution is studied numerically by using the Biot-Savart (BS) induction law and the localized induction approximation (LIA) equation. Results obtained using the two methods are compared to each other and to the analytic stability 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

Ricca, R., Samuels, D., Barenghi, C. (1999). Evolution of vortex knots. JOURNAL OF FLUID MECHANICS, 391, 29-44 [10.1017/S0022112099005224].

Evolution of vortex knots

Ricca, R;
1999

Abstract

For the first time since Lord Kelvin's original conjectures of 1875 we address and study the time evolution of vortex knots in the context of the Euler equations. The vortex knot is given by a thin vortex filament in the shape of a torus knot T(p,q) (p > 1, q > 1; p, q co-prime integers). The time evolution is studied numerically by using the Biot-Savart (BS) induction law and the localized induction approximation (LIA) equation. Results obtained using the two methods are compared to each other and to the analytic stability 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
Articolo in rivista - Articolo scientifico
Biot-Savard induction law; Vortex knots; Euler equations; Thin vortex filament; Torus knot; Localized induction approximation
English
1999
391
29
44
none
Ricca, R., Samuels, D., Barenghi, C. (1999). Evolution of vortex knots. JOURNAL OF FLUID MECHANICS, 391, 29-44 [10.1017/S0022112099005224].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/20231
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