A Study on Topological Vortex Ring Interactions Based on Möbius Loop and Hopf Link Concepts (5)
- Călugăreanu, G. (1959). L'intégrale de Gauss et l'analyse des nœuds tridimensionnels [The Gauss Integral and the Analysis of Three-Dimensional Knots]. Revue de mathématiques pures et appliquées, 4, 5-20.
- Faddeev, L. D., & Niemi, A. J. (1997). Stable knot-like structures in classical field theory. Nature, 387(6628), 58-61.
- Hopf, H. (1931). Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche [On the Mappings of the Three-Dimensional Sphere onto the Spherical Surface]. Mathematische Annalen, 104(1), 637-665.
- Kleckner, D., & Irvine, W. T. M. (2013). Creation and dynamics of knotted vortices. Nature Physics, 9(4), 253-258.
- Möbius, A. F. (1858). Über die Bestimmung des Inhaltes eines Polyëders [On the Determination of the Volume of a Polyhedron]. Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften, Mathematisch-Physische Klasse, 17, 31-68.
- Moffatt, H. K. (1969). The degree of knottedness of tangled vortex lines. Journal of Fluid Mechanics, 35(1), 117-129.
- Ricca, R. L., & Berger, M. A. (1996). Topological ideas and fluid mechanics. Physics Today, 49(12), 28-34.
- White, J. H. (1969). Self-linking and the Gauss integral in higher dimensions. American Journal of Mathematics, 91(3), 693-728.
- Yao, J., & Hussain, F. (2020). A physical model of turbulence cascade via vortex reconnection sequence and avalanche. Journal of Fluid Mechanics, 883, DOI:10.1017/jfm.2019.905.
- This document presents a draft theoretical framework conceived to explore the application of topological concepts in fluid mechanics. The models, analogies, and inferences discussed herein are based on established mathematical principles and physical laws, aiming to propose a novel analytical perspective rather than report specific experimental or computational results.
- The referenced concepts, such as the Möbius loop and Hopf link, serve as metaphorical descriptions and formal analogies for the complex topological properties of vortex rings, with the purpose of constructing an illustrative theoretical model. The physical processes discussed, such as vortex reconnection and knot formation, have been observed in numerous prior experiments and numerical simulations.
- The author confirms that this text is solely an exposition of preliminary ideas intended to stimulate academic discussion and collaboration. It is hereby solemnly declared that the content of this document has not been published or presented in any form in any academic journal or conference. Any subsequent in-depth research based on the ideas herein should through standard academic citation practices. Relevant theories, concepts, and data referenced in this paper have been sourced to the best of author's ability, respecting the intellectual property rights of the original authors. Author welcome corrections for any omissions.
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