TY - GEN

T1 - A counter-rotating vortex pair in inviscid fluid

AU - Habibah, Ummu

AU - Fukumoto, Yasuhide

PY - 2017/12/5

Y1 - 2017/12/5

N2 - 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.

AB - 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.

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U2 - 10.1063/1.5016656

DO - 10.1063/1.5016656

M3 - Conference contribution

AN - SCOPUS:85037826797

T3 - AIP Conference Proceedings

BT - International Conference and Workshop on Mathematical Analysis and its Applications, ICWOMAA 2017

A2 - Kilicman, Adem

A2 - Marjono, null

A2 - Wibowo, Ratno Bagus Edy

A2 - Imron, Moch. Aruman

PB - American Institute of Physics Inc.

T2 - International Conference and Workshop on Mathematical Analysis and its Applications, ICWOMAA 2017

Y2 - 2 August 2017 through 3 August 2017

ER -