Abstract

GONZALEZ, Jeasson F.. Determination of translational velocity of the ring vortex using multipolar expansion. Rev. acad. colomb. cienc. exact. fis. nat. [online]. 2019, vol.43, n.166, pp.31-37. ISSN 0370-3908.  https://doi.org/10.18257/raccefyn.000.

The velocity field of a vortex ring is established considering a small aspect ratio (r 1 /r 0, where r 0 is the radius of the vortex central line and r 1 is the radius of cross section), for the purpose of finding the translation velocity, Г/4πr 0[log(8r 0 /r 1) − 1/4], of the ring vortex with circulation . The induced field is calculated through the Biot-Savart law using a multipole expansion; thus the translation velocity is determined by means of the comparison between the derived field and the substantial condition on the vortex surface. The formulation presented in this work is an alternative to the conventional methods in vortex dynamics. However, it offers an advantage related to the study of more complex vortical structures. The achieved results show that the translation velocity corresponds to the first order solution of the multipole expansion; which concerns curvature effects on the vorticity distribution of the cross section.. © 2019. Acad. Colomb. Cienc. Ex. Fis. Nat.

Keywords : Translational velocity; Ring vortex; Multipolar expansion.

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