Short wavelength spectrum and Hamiltonian stability of vortex rings

Uwe R. Fischer and Nils Schopohl
Phys. Rev. E 64, 016306 – Published 18 June 2001
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Abstract

We compare dynamical and energetical stability criteria for vortex rings. It is argued that vortex rings will be intrinsically unstable against perturbations with short wavelengths below a critical wavelength because the canonical vortex Hamiltonian is unbounded from below for these modes. To explicitly demonstrate this behavior, we derive the oscillation spectrum of vortex rings in incompressible, inviscid fluids within a geometrical cutoff procedure for the core. The spectrum develops an anomalous branch of negative group velocity and approaches the zero of energy for wavelengths that are about six times the core diameter. We show the consequences of this dispersion relation for the thermodynamics of vortex rings in superfluid 4He at low temperatures.

  • Received 6 December 2000

DOI:https://doi.org/10.1103/PhysRevE.64.016306

©2001 American Physical Society

Authors & Affiliations

Uwe R. Fischer and Nils Schopohl

  • Eberhard-Karls-Universität Tübingen, Institut für Theoretische Physik, Auf der Morgenstelle 14, D-72076 Tübingen, Germany

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Vol. 64, Iss. 1 — July 2001

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