000014769 001__ 14769
000014769 005__ 20161115100201.0
000014769 04107 $$aeng
000014769 046__ $$k2016-08-21
000014769 100__ $$aFukumoto, Yasuhide
000014769 24500 $$aMotion of a vortex pair at high and low Reynolds numbers

000014769 24630 $$n24.$$p24th International Congress of Theoretical and Applied Mechanics - Book of Papers
000014769 260__ $$bInternational Union of Theoretical and Applied Mechanics, 2016
000014769 506__ $$arestricted
000014769 520__ $$2eng$$aWe establish a high- and a low-Reynolds-number asymptotics for the speed of a counter-rotating vortex pair, traveling in a viscous incompressible fluid. At a high Reynolds number, the solution of the Navier-Stokes equation is constructed by use of the matched asymptotic expansions in a small parameter, a measure of the core radius to the half distance between the vortices. The correction to the traveling speed, originating from finite-thickness effect, arises at fifth order. We drastically simplify it in a form including solely strength of the quadrupole field of second order. We derive a two-dimensional analogue, applicable in the entire range of the Reynolds number, of the Helmholtz-Lamb formula for an axisymmetric vortex ring. At a low Reynolds number, the vorticity field obeying the Stokes equation is substituted into this formula. Thereby we describe the whole life of the motion a vortex pair.

000014769 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000014769 653__ $$a

000014769 7112_ $$a24th International Congress of Theoretical and Applied Mechanics$$cMontreal (CA)$$d2016-08-21 / 2016-08-26$$gICTAM2016
000014769 720__ $$aFukumoto, Yasuhide
000014769 8560_ $$ffischerc@itam.cas.cz
000014769 8564_ $$s106369$$uhttps://invenio.itam.cas.cz/record/14769/files/TS.FM15-3.03.pdf$$yOriginal version of the author's contribution as presented on CD,  page 1530, code TS.FM15-3.03
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000014769 962__ $$r13812
000014769 980__ $$aPAPER