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Calculation of Travelling Velocity of an Axisymmetric Vortex Ring

Corresponding Author : T. K. Sheel (tarunbd@gmail.com)

Keywords : Axisymmetric vortex ring, travelling velocity, MDGRAPE-2, Low Reynolds number

Abstract :

An initial value problem of the Navier-Stokes equation is solved, at low Reynolds numbers, for evolution of an axisymmetric vortex ring. The travelling velocity is written down in closed form over the whole time range, in term of the generalized hyper geometric functions, for a vortex ring starting with infinitely thin core. We show how the ideas of topology and variation principle, opened up by Euler, facilitate the calculation of motion of vortex rings. We consider finiteamplitude Kelvin waves on an inviscid vortex assuming that the vortex core has infinitesimal thickness. By numerically solving the governing Biot-Savart equation of motion, we study how the frequency of the Kelvin waves and the velocity of the perturbed ring depend on the Kelvin wave amplitude. Finally the simulated results are compared with the analytical and experimental results to validate our numerical scheme. 

Published on June 30th, 2014 in Volume 21, Issue 1, Applied Sciences and Technology