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It is shown that based on the concept of a toroidal self-gravitating ring vortex with a swirl (with an orbital motion along the torus generatrix), it is possible to explain all the main morphological features of the famous Hoag ring galaxy, including the still unexplained rotation of the central elliptical galaxy. The astronomical observations can be used, thus, to study complex vortex motions [The article based on the authors' reports Bannikova et al., XIII International Conference to 100 years of Illia Mikhailovich Lifshitz, Kharkiv, KhNU (2017) and Kontorovich et al., XIV International Science Conference "Physical phenomena in solids", Kharkiv, KhNU (2019) at the Conferences on condensed matter physics at Kharkiv National University, the first of which was dedicated to the 100th anniversary of the birth of Ilya Mikhailovich Lifshitz, a teacher and friend of Mark Azbel.]. [ABSTRACT FROM AUTHOR]

The orbital motion along the directrix of ring vortices (vortex with swirl) regulated by helicity can exert a significant influence on the vortex collapse and motion in a convergent (accretion) flow. The solutions for both single and dipole toroidal vortices in Hamiltonian representation have been obtained. The phenomenon considered can have applications in the astrophysics of active galactic nuclei and the dynamics of atmospheric vortices. [ABSTRACT FROM AUTHOR]

Exact solutions are obtained for the two-dimensional hydrodynamic equations for symmetric configurations of two and four vortices in the presence of an arbitrary flow with a point singularity. These solutions describe the dynamics of a dipole toroidal vortex in accretion and wind flows within the active nuclei of galaxies. It is shown that in a converging (accretion) flow, as they are compressed along their major radius, toroidal vortices are ejected with acceleration along the axis of symmetry of the active nucleus, to form the components of a bilateral jet. For a symmetric flow, the increase in the velocity of the vortices is determined by the monopole component of the flow, and, when there is an asymmetry in the flow, also by the dipole component of the flow, which controls the asymmetry of the ejection. [ABSTRACT FROM AUTHOR]

The problem of vortex pair motion in two-dimensional radial flow is solved. Under certain conditions for flow parameters, the vortex pair can reverse its motion within a bounded region. The vortex-pair translational velocity decreases or increases after passing through the source/sink region, depending on whether the flow is diverging or converging, respectively. The rotational motion of a corotating vortex pair in a quiescent environment transforms into motion along a logarithmic spiral in radial flow. The problem may have applications in astrophysics and geophysics. [ABSTRACT FROM AUTHOR]