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Self-similar vortex filament motion under the non-local Biot–Savart model

Published online by Cambridge University Press:  10 August 2016

Robert A. Van Gorder
Robert A. Van Gorder*
Affiliation:
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
*
†Email address for correspondence: Robert.VanGorder@maths.ox.ac.uk
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Abstract

One type of thin vortex filament structure that has attracted interest in recent years is that which obeys self-similar scaling. Among various applications, these filaments have been used to model the motion of quantized vortex filaments in superfluid helium after reconnection events. While similarity solutions have been described analytically and numerically using the local induction approximation (LIA), they have not been studied (or even shown to exist) under the non-local Biot–Savart model. In this present paper, we show not only that self-similar vortex filament solutions exist for the non-local Biot–Savart model, but that such solutions are qualitatively similar to their LIA counterparts. This suggests that the various LIA solutions found previously should be valid physically (at least in the small amplitude regime), since they agree well with the more accurate Biot–Savart model.

JFM classification

Mathematical Foundations: Computational methods Mathematical Foundations: Mathematical Foundations Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 802 , 10 September 2016 , pp. 760 - 774
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Copyright
© 2016 Cambridge University Press 

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