Application of the Biot-Savart Law to Parabolic Vortex Segments using Elliptic Integrals
arXiv:1907.10131 · doi:10.1007/s00033-020-01319-3
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.
18 pages, 5 figures; minor typos corrected in version 2