Point vortices and classical orthogonal polynomials
arXiv:1201.3481 · doi:10.1134/S1560354712050012
Abstract
Stationary equilibria of point vortices with arbitrary choice of circulations in a background flow are studied. Differential equations satisfied by generating polynomials of vortex configurations are derived. It is shown that these equations can be reduced to a single one. It is found that polynomials that are Wronskians of classical orthogonal polynomials solve the latter equation. As a consequence vortex equilibria at a certain choice of background flows can be described with the help of Wronskians of classical orthogonal polynomials.
20 pages, 12 figures