Topological fluid mechanics is a crucial area of classical mechanics, with remarkable theoretical significance and wide applications in practice. In this paper, we expect to present an introductory review of the direction, for the purpose of attracting more domestic researchers of China to enter into this important area. Our emphasis is placed on the topological essence of fluid helicity. We will give the relationship between helicity and mathematical knotted field theory (i.e., that between helicity and the mutual- and self-linking numbers, as well as the fluid knot polynomial topological invariants constructed in terms of helicity recently discovered by the authors), and give an introduction to the international research on energy-structural complexity relationship for a fluid vortex knot ensemble. Moreover, typical numerical methods are also demonstrated through examples of reconnections occurring in superfluid vortex knots/links. Expectedly, a combination of the theoretical framework and numerical techniques may contribute to the reader a comprehensive understanding of the main target, research methodology and potential technical difficulties in practice in this interdisciplinary field of cutting-edge research world-wide.

Guan, H., Zuccher, S., Ricca, R., Liu, X. (2020). Topological fluid mechanics and its new developments. DIQIU XUEBAO, 50(5), 054701 [10.1360/SSPMA-2019-0101].

Topological fluid mechanics and its new developments

Renzo Ricca
Penultimo
;
2020

Abstract

Topological fluid mechanics is a crucial area of classical mechanics, with remarkable theoretical significance and wide applications in practice. In this paper, we expect to present an introductory review of the direction, for the purpose of attracting more domestic researchers of China to enter into this important area. Our emphasis is placed on the topological essence of fluid helicity. We will give the relationship between helicity and mathematical knotted field theory (i.e., that between helicity and the mutual- and self-linking numbers, as well as the fluid knot polynomial topological invariants constructed in terms of helicity recently discovered by the authors), and give an introduction to the international research on energy-structural complexity relationship for a fluid vortex knot ensemble. Moreover, typical numerical methods are also demonstrated through examples of reconnections occurring in superfluid vortex knots/links. Expectedly, a combination of the theoretical framework and numerical techniques may contribute to the reader a comprehensive understanding of the main target, research methodology and potential technical difficulties in practice in this interdisciplinary field of cutting-edge research world-wide.
Articolo in rivista - Articolo scientifico
mathematical methods in theoretical fluid mechanics; topological fluid mechanics; fluid helicity; topological invariants of fluid knots; energy-structural complexity relationship; numerical simulations; reconnections of quantum vortices in superfluid flows;
English
2020
50
5
054701
052008
open
Guan, H., Zuccher, S., Ricca, R., Liu, X. (2020). Topological fluid mechanics and its new developments. DIQIU XUEBAO, 50(5), 054701 [10.1360/SSPMA-2019-0101].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/271949
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