Dynamics of quantized vortex filaments under a local induction approximation with second-order correction

2019 ◽  
Vol 31 (6) ◽  
pp. 065103
Author(s):  
Christopher L. Horner ◽  
Robert A. Van Gorder
Keyword(s):  
Second Order ◽  
Quantized Vortex ◽  
Order Correction ◽  
Vortex Filaments ◽  
Local Induction Approximation

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

2016 ◽  
Vol 802 ◽  
pp. 760-774 ◽  
Author(s):  
Robert A. Van Gorder
Keyword(s):  
Superfluid Helium ◽  
Small Amplitude ◽  
Similarity Solutions ◽  
Vortex Filament ◽  
Quantized Vortex ◽  
Vortex Filaments ◽  
Filament Structure ◽  
Non Local ◽  
Self Similar ◽  
Local Induction Approximation

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.

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