Velocity induced by a plane uniform vortex having the Schwarz function of its boundary with two simple poles
type: Item
instance of: scholarly article
title: Velocity induced by a plane uniform vortex having the Schwarz function of its boundary with two simple poles
zbMATH Open document ID: 1162.30008
DOI: 10.1155/2008/586567
author: J. Martínez
published in: Journal of Applied Mathematics
publication date: 2009-03-31T00:00:00Z
full work available at URL: https://eudml.org/doc/55446
review text: 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.
Mathematics Subject Classification ID: 30C20
zbMATH DE Number: 5538036
zbMATH Keywords: Schwarz function
zbMATH Keywords: velocity
MaRDI profile type: Publication
OpenAlex ID: W2029697543
Wikidata QID: Q58645963
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description: scientific article; zbMATH DE number 5538036