Dariya Safonova
Kashirskoe sh. 31, Moscow, 115409 Russia
National Research Nuclear University MEPhI
Publications:
Safonova D. V., Demina M. V., Kudryashov N. A.
Stationary Configurations of Point Vortices on a Cylinder
2018, vol. 23, no. 5, pp. 569579
Abstract
In this paper we study the problem of constructing and classifying stationary
equilibria of point vortices on a cylindrical surface. Introducing polynomials with roots at vortex
positions, we derive an ordinary differential equation satisfied by the polynomials. We prove
that this equation can be used to find any stationary configuration. The multivortex systems
containing point vortices with circulation $\Gamma_1$ and $\Gamma_2$ $(\Gamma_2 = \mu\Gamma_1)$ are considered in detail.
All stationary configurations with the number of point vortices less than five are constructed.
Several theorems on existence of polynomial solutions of the ordinary differential equation under
consideration are proved. The values of the parameters of the mathematical model for which
there exists an infinite number of nonequivalent vortex configurations on a cylindrical surface
are found. New point vortex configurations are obtained.
