@inproceedings{f8b3a875afe14953be52a22356f1ee26,
title = "A counter-rotating vortex pair in inviscid fluid",
abstract = "We study the motion of a counter-rotating vortex pair with the circulations ±Γ move in incompressible fluid. The assumption is made that the core is very thin, that is the core radius σ is much smaller than the vortex radius d such that ϵ = σ/d ≤ 1. With this condition, the method of matched asymptotic expansion is employed. The solutions of the Navier-Stokes equations and the Biot-Savart law, regarding the inner and outer solutions respectively, are constructed in the form of a small parameter. An asymptotic expansion of the Biot-Savart law near the vortex core provides with the matching condition for an asymptotic expansion for limiting the Navier-Stokes equations for large radius r. The general formula of an anti-parallel vortex pair is established. At leading order O(ϵ), we apply the special case in inviscid fluid, the Rankine vortex, a circular vortex of uniform vorticity. Furthermore at leading order O(ϵ5) we show the traveling speed of a vortex pair.",
keywords = "Finite-thickness effect, Matched asymptotic expansions, Rankine vortex, Vortex pair",
author = "Ummu Habibah and Yasuhide Fukumoto",
note = "Publisher Copyright: {\textcopyright} 2017 Author(s).; International Conference and Workshop on Mathematical Analysis and its Applications, ICWOMAA 2017 ; Conference date: 02-08-2017 Through 03-08-2017",
year = "2017",
month = dec,
day = "5",
doi = "10.1063/1.5016656",
language = "English",
series = "AIP Conference Proceedings",
publisher = "American Institute of Physics Inc.",
editor = "Adem Kilicman and Marjono and Wibowo, \{Ratno Bagus Edy\} and Imron, \{Moch. Aruman\}",
booktitle = "International Conference and Workshop on Mathematical Analysis and its Applications, ICWOMAA 2017",
}