2 research outputs found
Point vortices and classical orthogonal polynomials
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.Comment: 20 pages, 12 figure