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Application of the Biot–Savart law to parabolic vortex segments using elliptic integrals

The Biot–Savart law is used in aerodynamic theory to calculate the velocity induced by curved vortex lines. Explicit formulas are developed, using multivariate Appell hypergeometric functions, for the velocity induced by a general parabolic vortex segment. The formulas are derived by constructing a...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2020-08, Vol.71 (4), Article 104
Main Authors: Malmendier, Andreas, Reid, Jackson T.
Format: Article
Language:English
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Summary:The Biot–Savart law is used in aerodynamic theory to calculate the velocity induced by curved vortex lines. Explicit formulas are developed, using multivariate Appell hypergeometric functions, for the velocity induced by a general parabolic vortex segment. The formulas are derived by constructing a particular pencil of elliptic curves whose period integrals provide the solution to the induced velocity. We use numerical integration and a perturbation expansion to evaluate the validity of our formulas.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-020-01319-3