VORTEX RINGS: HISTORY AND STATE OF THE ART

摘要

In the present paper, we describe the fascinating 150-year history of vortex dynamics, which started from the classical work by H. Helmholtz (1858). This work contains not only the general theorems on vortex motion, but also a special section devoted to axisymmetric circular vortex filaments and, in particular, to vortex rings. The aim of our investigation is both to clarify some purely mathematical questions connected with the Dyson model for coaxial vortex rings with a small circular cross-section in an ideal incompressible fluid and to provide a historical overview of the achievements in experimental, analytical, and numerical studies of the interaction of vortex rings. The model is illustrated by several examples of the motion of vortex rings. Finally, we present a complete classification of the interactions of two coaxial vortex rings in an ideal fluid.