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Velocity, energy, and helicity of vortex knots and unknots

Lookup NU author(s): Sultan Alamri, Professor Carlo Barenghi


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In this paper we determine the velocity, the energy, and estimate writhe and twist helicity contributions of vortex filaments in the shape of torus knots and unknots (as toroidal and poloidal coils) in a perfect fluid. Calculations are performed by numerical integration of the Biot-Savart law. Vortex complexity is parametrized by the winding number w given by the ratio of the number of meridian wraps to that of longitudinal wraps. We find that for w < 1 vortex knots and toroidal coils move faster and carry more energy than a reference vortex ring of same size and circulation, whereas for w > 1 knots and poloidal coils have approximately same speed and energy of the reference vortex ring. Helicity is dominated by writhe contributions. Finally, we confirm the stabilizing effect of the Biot-Savart law for all knots and unknots tested, found to be structurally stable over a distance of several diameters. Our results also apply to quantized vortices in superfluid He-4.

Publication metadata

Author(s): Maggioni F, Alamri S, Barenghi CF, Ricca RL

Publication type: Article

Publication status: Published

Journal: Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

Year: 2010

Volume: 82

Issue: 2

Print publication date: 17/08/2010

ISSN (print): 1539-3755

ISSN (electronic): 1550-2376

Publisher: American Physical Society


DOI: 10.1103/PhysRevE.82.026309


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