Evolution of vortex knots

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 [Tscr ]p,q (p>1, q>1; p, q co-prime integers)....

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Bibliographic Details
Published in:Journal of fluid mechanics 1999-07, Vol.391, p.29-44
Main Authors: RICCA, RENZO L., SAMUELS, DAVID C., BARENGHI, CARLO F.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Inviscid flows with vorticity
Laminar flows
Physics
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Summary: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 [Tscr ]p,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.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112099005224