Journal of Applied Mathematics
Volume 2008 (2008), Article ID 586567, 40 pages
Research Article

Velocity Induced by a Plane Uniform Vortex Having the Schwarz Function of Its Boundary with Two Simple Poles

G. Riccardi and D. Durante

Department of Aerospace and Mechanical Engineering, Second University of Naples, Via Roma 29, Aversa, 81031 Caserta, Italy

Received 6 June 2008; Accepted 8 September 2008

Academic Editor: Bernard Geurts

Copyright © 2008 G. Riccardi and D. Durante. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The velocity induced by a plane, uniform vortex is investigated through the use of an integral relation between Schwarz function of the vortex boundary and conjugate of the velocity. The analysis is restricted to a certain class of vortices, the boundaries of which are described through conformal maps onto the unit circle and the corresponding Schwarz functions possess two poles in the plane of the circle. The dependence of the velocity field on the vortex shape is investigated by comparing velocity and streamfunction with the ones of the equivalent Rankine vortex (which has the same vorticity, area, and center of vorticity). By changing the parameters of the Schwarz function (poles and corresponding residues), rather complicated vortex shapes can be easily analyzed, some of them mimicing an incipient filamentation of the vortex boundary.