Abstract
Three-dimensional motion of a slender vortex tube, embedded in an inviscid incompressible fluid, is investigated based on the Euler equations. Using the method of matched asymptotic expansions in a small parameter ∈, the ratio of core radius to curvature radius, the velocity of a vortex filament is derived to O(∈ 3), whereby the influence of elliptical deformation of the core due to the self-induced strain is taken into account. In the localized induction approximation, this is reducible to a completely integrable evolution equation among the localized induction hierarchy.
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Fukumoto, Y. (2001). Motion of a Curved Vortex Filament: Higher-Order Asymptotics. In: Kambe, T., Nakano, T., Miyauchi, T. (eds) IUTAM Symposium on Geometry and Statistics of Turbulence. Fluid Mechanics and Its Applications, vol 59. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9638-1_25
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DOI: https://doi.org/10.1007/978-94-015-9638-1_25
Publisher Name: Springer, Dordrecht
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