Bifurcation Analysis of the Problem of Two Vortices on a Finite Flat Cylinder
Received 22 November 2023; accepted 20 December 2023; published 27 December 2023
2024, Vol. 20, no. 1, pp. 95-111
Author(s): Kilin A. A., Artemova E. M.
This paper addresses the problem of the motion of two point vortices of arbitrary strengths
in an ideal incompressible fluid on a finite flat cylinder. A procedure of reduction to the level set
of an additional first integral is presented. It is shown that, depending on the parameter values,
three types of bifurcation diagrams are possible in the system. A complete bifurcation analysis of
the system is carried out for each of them. Conditions for the orbital stability of generalizations
of von Kármán streets for the problem under study are obtained.
Download File PDF, 1.11 Mb |
This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License