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Evolution of vortex knots

Lookup NU author(s): Dr David Samuels, Professor Carlo Barenghi

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Abstract

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.


Publication metadata

Author(s): Ricca RL, Samuels DC, Barenghi CF

Publication type: Article

Publication status: Published

Journal: Journal of Fluid Mechanics

Year: 1999

Volume: 391

Pages: 29-44

Print publication date: 25/07/1999

ISSN (print): 0022-1120

ISSN (electronic): 1469-7645

Publisher: Cambridge University Press

URL: http://dx.doi.org/10.1017/S0022112099005224

DOI: 10.1017/S0022112099005224


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