Title

Motion Of A Vortex Filament In The Local Induction Approximation: A Perturbative Approach

Keywords

Local induction approximation; Perturbation method; Vortex dynamics; Vortex filament

Abstract

Very recently, Shivamoggi and van Heijst (Phys Lett A 374:1742, 2010) reformulated the Da Rios-Betchov equations in the extrinsic vortex filament coordinate space andwere able to find an exact solution to an approximate equation governing a localized stationary solution. The approximation in the governing equation was due to the author's consideration of a first-order approximation of dx ds = 1/1 + y2 x + z2x ; previously, an order-zero approximation was considered by Dmitriyev (Am J Phys 73:563, 2005). Such approximations result in exact solutions, but these solutions may break down outside of specific parameter regimes. Presently, we avoid making the simplifying assumption on dx ds , which results in a much more difficult governing equation to solve. However, we are able to obtain perturbation solutions, by way of the ?-expansion method, which cast light on this more general problem. We find that such solutions more readily agree with the numerical solutions, while our solutions also match those exact solutions present in the literature for certain values of the parameters (corresponding to y2 x + z2x 1). © Springer-Verlag 2011.

Publication Date

1-1-2012

Publication Title

Theoretical and Computational Fluid Dynamics

Volume

26

Issue

1-4

Number of Pages

161-171

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00162-010-0218-2

Socpus ID

84859701595 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84859701595

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