Velocity Induced by a Plane Uniform Vortex Having the Schwarz Function of Its Boundary with Two Simple Poles
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 ma...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2008/586567 |
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| _version_ | 1850231588757962752 |
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| author | G. Riccardi D. Durante |
| author_facet | G. Riccardi D. Durante |
| author_sort | G. Riccardi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0b8ed2b92dc94811868c0162d2d0bcbc |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-0b8ed2b92dc94811868c0162d2d0bcbc2025-08-20T02:03:28ZengWileyJournal of Applied Mathematics1110-757X1687-00422008-01-01200810.1155/2008/586567586567Velocity Induced by a Plane Uniform Vortex Having the Schwarz Function of Its Boundary with Two Simple PolesG. Riccardi0D. Durante1Department of Aerospace and Mechanical Engineering, Second University of Naples, Via Roma 29, Aversa, 81031 Caserta, ItalyDepartment of Aerospace and Mechanical Engineering, Second University of Naples, Via Roma 29, Aversa, 81031 Caserta, ItalyThe 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.http://dx.doi.org/10.1155/2008/586567 |
| spellingShingle | G. Riccardi D. Durante Velocity Induced by a Plane Uniform Vortex Having the Schwarz Function of Its Boundary with Two Simple Poles Journal of Applied Mathematics |
| title | Velocity Induced by a Plane Uniform Vortex Having the Schwarz Function of Its Boundary with Two Simple Poles |
| title_full | Velocity Induced by a Plane Uniform Vortex Having the Schwarz Function of Its Boundary with Two Simple Poles |
| title_fullStr | Velocity Induced by a Plane Uniform Vortex Having the Schwarz Function of Its Boundary with Two Simple Poles |
| title_full_unstemmed | Velocity Induced by a Plane Uniform Vortex Having the Schwarz Function of Its Boundary with Two Simple Poles |
| title_short | Velocity Induced by a Plane Uniform Vortex Having the Schwarz Function of Its Boundary with Two Simple Poles |
| title_sort | velocity induced by a plane uniform vortex having the schwarz function of its boundary with two simple poles |
| url | http://dx.doi.org/10.1155/2008/586567 |
| work_keys_str_mv | AT griccardi velocityinducedbyaplaneuniformvortexhavingtheschwarzfunctionofitsboundarywithtwosimplepoles AT ddurante velocityinducedbyaplaneuniformvortexhavingtheschwarzfunctionofitsboundarywithtwosimplepoles |