Velocity induced by a plane uniform vortex having the Schwarz function of its boundary with two simple poles. (English) Zbl 1162.30008

Summary: The velocity induced by a plane, uniform vortex is investigated through the use of an integral relation between the Schwarz function of the vortex boundary and the 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. 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 the velocity and the 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.


30C20 Conformal mappings of special domains
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