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- Title
Self-similar vortex filament motion under the non-local Biot–Savart model.
- Authors
Van Gorder, Robert A.
- 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.
- Subjects
VORTEX motion; BIOT-Savart law
- Publication
Journal of Fluid Mechanics, 2016, Vol 802, p760
- ISSN
0022-1120
- Publication type
Article
- DOI
10.1017/jfm.2016.502