Abstract
The method of magnetic relaxation for the determination of solutions of the Euler equations representing steadily propagating vortical structures is reviewed, and compared with alternative artificial relaxation procedures that conserve the topology of the vorticity field. Attention is focussed first on axisymmetric vortex ring configurations, for which such relaxation techniques provide simple proofs of the existence of vortex rings of prescribed ‘signature’, the imprint of conserved topology. Relaxation of knotted and linked configurations are briefly considered, from which the concept of an energy spectrum of knots and links emerges in a natural way. Attention is drawn to recent work of Buniy & Kephart (2005), which seeks to identify such energy spectra with the spectrum of excitations (glueballs) in the quark-gluon plasma, in a spirit reminiscent of Kelvin’s ‘vortex theory of atoms’ but here at the elementary particle level of quantum chromodynamics.
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Moffatt, H.K. (2013). Relaxation to Steady Vortical Flows – And Knots in the Quark-Gluon Plasma. In: Denier, J., Finn, M. (eds) Mechanics Down Under. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5968-8_10
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DOI: https://doi.org/10.1007/978-94-007-5968-8_10
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