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$$yOriginal version of the author's contribution as presented on CD, page 1530, code TS.FM15-3.03 . 000014769 962__ $$r13812 000014769 980__ $$aPAPER