The process of vortex cascade through continuous reduction of topological complexity by stepwise unlinking, that has been observed experimentally in the production of vortex knots (Kleckner & Irvine, 2013), is shown to be reproduced in the branching of the skein relations of knot polynomials (Liu & Ricca, 2015) used to identify topological complexity of vortex systems. This observation can be usefully exploited for predictions of energy-complexity estimates for fluid flows.
Ricca, R. (2016). Vortex knot cascade in polynomial skein relations. In T.E. Simos, T.E. Simos, C. Tsitouras, T.E. Simos (a cura di), International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015; Rodos Palace HotelRhodes; Greece; 23-29 September 2015. American Institute of Physics Inc. [10.1063/1.4951930].
Vortex knot cascade in polynomial skein relations
Ricca, R
2016
Abstract
The process of vortex cascade through continuous reduction of topological complexity by stepwise unlinking, that has been observed experimentally in the production of vortex knots (Kleckner & Irvine, 2013), is shown to be reproduced in the branching of the skein relations of knot polynomials (Liu & Ricca, 2015) used to identify topological complexity of vortex systems. This observation can be usefully exploited for predictions of energy-complexity estimates for fluid flows.
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