Articolo in rivista, 2008, ENG, 10.1155/2008/586567

Velocity induced by a plane uniform vortex having the Schwarz function of its boundary with two simple poles

Riccardi G.; Durante D.

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

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.

Journal of applied mathematics (Internet) 2008

Keywords

Schwarz function, Complex analysis, Vortex dynamics

CNR authors

Durante Danilo

CNR institutes