Dynamics of a few vortices in an ideal fluid and in a Bose-Einstein condensate

TL;DR

This paper analyzes the dynamics of two vortices in ideal fluids and Bose-Einstein condensates, revealing new bifurcation diagrams and classifying vortex behaviors within an integrable Hamiltonian framework.

Contribution

It introduces a new bifurcation diagram for vortex dynamics and provides explicit reduction to a one-degree-of-freedom system for arbitrary vortex intensities.

Findings

New bifurcation diagram discovered for vortex configurations.

Explicit reduction to a single degree of freedom system.

Classification of vortex dynamics within bifurcation chambers.

Abstract

Completely Liouville integrable Hamiltonian system with two degrees of freedom is considered. This Hamiltonian system describes the dynamics of two vortex filaments in a Bose-Einstein condensate enclosed in a cylindrical trap and dynamics of two vortices in the ideal fluid contained in a domain with the form of a circular cylinder, generatrix of which is parallel to vortices. An explicit reduction to a system with one degree of freedom for the case of arbitrary signs of the vortex intensities is derived from the original system under consideration. Along with the fact that in the case of two vortices with intensities of opposite signs, a bifurcation diagram was obtained for a generalized two-parameter integrable family, similar to that obtained earlier for the case of a Bose-Einstein condensate, a new bifurcation diagram was found that had not been encountered before. Various types of vortex dynamics corresponding to points inside chambers of bifurcation diagrams are presented.