A counter-rotating vortex pair in inviscid fluid

Ummu Habibah, Yasuhide Fukumoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish
Title of host publicationInternational Conference and Workshop on Mathematical Analysis and its Applications, ICWOMAA 2017
EditorsAdem Kilicman, Marjono, Ratno Bagus Edy Wibowo, Moch. Aruman Imron
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735416055
DOIs
Publication statusPublished - Dec 5 2017
EventInternational Conference and Workshop on Mathematical Analysis and its Applications, ICWOMAA 2017 - Malang, Indonesia
Duration: Aug 2 2017Aug 3 2017

Publication series

NameAIP Conference Proceedings
Volume1913
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

OtherInternational Conference and Workshop on Mathematical Analysis and its Applications, ICWOMAA 2017
CountryIndonesia
CityMalang
Period8/2/178/3/17

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All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Habibah, U., & Fukumoto, Y. (2017). A counter-rotating vortex pair in inviscid fluid. In A. Kilicman, Marjono, R. B. E. Wibowo, & M. A. Imron (Eds.), International Conference and Workshop on Mathematical Analysis and its Applications, ICWOMAA 2017 [020022] (AIP Conference Proceedings; Vol. 1913). American Institute of Physics Inc.. https://doi.org/10.1063/1.5016656