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Influence of winding number on vortex knots dynamics
Chiara Oberti1, Renzo L Ricca2,3
1Department of Mathematics & Applications, University of Milano-Bicocca, Via Cozzi 55, 20125, Milano, Italy.
Scientific Reports
|November 23, 2019
Summary
The winding number significantly impacts vortex torus knot dynamics in ideal fluids. Increasing toroidal coils generally speed up motion, but poloidal coils can reverse it, revealing crucial 3D flow features.
Area of Science:
- Fluid Mechanics
- Topology
- Mathematical Physics
Background:
- Vortex dynamics are fundamental to fluid mechanics.
- Topological invariants like winding number offer insights into complex flow structures.
- Previous studies suggested numerical results for vortex torus knots.
Purpose of the Study:
- To determine the effects of winding number on vortex torus knot and unknot dynamics.
- To analyze the influence of winding number on induced velocity components.
- To investigate the role of toroidal and poloidal coils in vortex motion.
Main Methods:
- Applied the Moore-Saffman desingularization technique.
- Utilized the full Biot-Savart induction law.
- Analyzed 56 knots and unknots up to 51 crossings.
Main Results:
- Proved winding number is a primary factor in vortex motion.
- Showed propagation speed generally increases with toroidal coils.
- Demonstrated poloidal coils and aspect ratio can reverse vortex motion.
Conclusions:
- Winding number is crucial for understanding vortex torus knot dynamics.
- Three-dimensional features significantly influence vortex motion.
- Results aid in understanding helicity and energy transfer in vortical flows.
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