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Application of the Biot-Savart Law to Parabolic Vortex Segments using Elliptic Integrals
- Source :
- Z. Angew. Math. Phys. 71 (2020), no. 4, Paper No. 104, 20 pp
- Publication Year :
- 2019
-
Abstract
- 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.<br />Comment: 18 pages, 5 figures; minor typos corrected in version 2
- Subjects :
- Physics - Fluid Dynamics
76G25, 33E05
Subjects
Details
- Database :
- arXiv
- Journal :
- Z. Angew. Math. Phys. 71 (2020), no. 4, Paper No. 104, 20 pp
- Publication Type :
- Report
- Accession number :
- edsarx.1907.10131
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00033-020-01319-3