A counter-rotating vortex pair in inviscid fluid

Ummu Habibah, Yasuhide Fukumoto

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

抄録

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.

本文言語英語
ホスト出版物のタイトルInternational Conference and Workshop on Mathematical Analysis and its Applications, ICWOMAA 2017
編集者Adem Kilicman, Marjono, Ratno Bagus Edy Wibowo, Moch. Aruman Imron
出版社American Institute of Physics Inc.
ISBN(電子版)9780735416055
DOI
出版ステータス出版済み - 12 5 2017
イベントInternational Conference and Workshop on Mathematical Analysis and its Applications, ICWOMAA 2017 - Malang, インドネシア
継続期間: 8 2 20178 3 2017

出版物シリーズ

名前AIP Conference Proceedings
1913
ISSN(印刷版)0094-243X
ISSN(電子版)1551-7616

その他

その他International Conference and Workshop on Mathematical Analysis and its Applications, ICWOMAA 2017
Countryインドネシア
CityMalang
Period8/2/178/3/17

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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