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Waves on a vortex filament: exact solutions of dynamical equations

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Abstract

In this paper, we take into account the dynamical equations of a vortex filament in superfluid helium at finite temperature (1 K < T < 2.17 K) and at very low temperature, which is called Biot–Savart law. The last equation is also valid for a vortex tube in a frictionless, unbounded, and incompressible fluid. Both the equations are approximated by the Local Induction Approximation (LIA) and Fukumoto’s approximation. The obtained equations are then considered in the extrinsic frame of reference, where exact solutions (Kelvin waves) are shown. These waves are then compared one to each other in terms of their dispersion relations in the frictionless case. The same equations are then investigated for a quantized vortex line in superfluid helium at higher temperature, where friction terms are needed for a full description of the motion.

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Authors and Affiliations

  1. Dipartimento di Energia, ingegneria dell’Informazione e modelli Matematici, Università di Palermo, Palermo, Italy

    Tommaso Brugarino

  2. Dipartimento di Ingegneria Chimica, Gestionale, Informatica, Meccanica, Università di Palermo, Palermo, Italy

    Maria Stella Mongiovi

  3. Dipartimento di Scienze Agrarie e Forestali, Università di Palermo, Palermo, Italy

    Michele Sciacca

Authors
  1. Tommaso Brugarino
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  2. Maria Stella Mongiovi
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  3. Michele Sciacca
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Correspondence to Michele Sciacca.

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Brugarino, T., Mongiovi, M.S. & Sciacca, M. Waves on a vortex filament: exact solutions of dynamical equations. Z. Angew. Math. Phys. 66, 1081–1094 (2015). https://doi.org/10.1007/s00033-014-0450-5

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  • DOI: https://doi.org/10.1007/s00033-014-0450-5

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