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Lookup NU author(s): Dr David Samuels,
Professor Carlo Barenghi
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For the first time since Lord Kelvin's original conjectures of 1875 we address and study the time evolution of vortex knots in the context of the Euler equations. The vortex knot is given by a thin vortex filament in the shape of a torus knot Jp,q (p > 1, q > 1; p, q co-prime integers). The time evolution is studied numerically by using the Biot-Savart (BS) induction law and the localized induction approximation (LIA) equation. Results obtained using the two methods are compared to each other and to the analytic stability analysis of Ricca (1993, 1995). The most interesting finding is that thin vortex knots which are unstable under the LIA have a greatly extended lifetime when the BS law is used. These results provide useful information for modelling complex structures by using elementary vortex knots.
Author(s): Ricca RL, Samuels DC, Barenghi CF
Publication type: Article
Publication status: Published
Journal: Journal of Fluid Mechanics
Print publication date: 25/07/1999
ISSN (print): 0022-1120
ISSN (electronic): 1469-7645
Publisher: Cambridge University Press
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