Application of the Biot-Savart Law to Parabolic Vortex Segments using Elliptic Integrals
Fluid Dynamics
2022-06-01 v2
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.
Keywords
Cite
@article{arxiv.1907.10131,
title = {Application of the Biot-Savart Law to Parabolic Vortex Segments using Elliptic Integrals},
author = {Andreas Malmendier and Jackson T. Reid},
journal= {arXiv preprint arXiv:1907.10131},
year = {2022}
}
Comments
18 pages, 5 figures; minor typos corrected in version 2