0
2013
Impact Factor

# 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.  569-579 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. Keywords: point vortices, stagnation points, stationary configuration, vortices on a cylinder, polynomial solution of differential equation Citation: Safonova D. V., Demina M. V., Kudryashov N. A.,  Stationary Configurations of Point Vortices on a Cylinder, Regular and Chaotic Dynamics, 2018, vol. 23, no. 5, pp. 569-579 DOI:10.1134/S1560354718050064