The motion of a system of vortex rings in an incompressible fluid

Theory of Concentrated Vortices

“…Various techniques have been proposed in order to overcome such a problem: according to Brutyan and Krapivskii (1984) the self-induced velocity is excluded from consideration and only the velocity induced by the system of surrounding vortices is considered. Various techniques have been proposed in order to overcome such a problem: according to Brutyan and Krapivskii (1984) the self-induced velocity is excluded from consideration and only the velocity induced by the system of surrounding vortices is considered.…”

“…As a result we obtain the model of thin vortex rings with the excluded core (Acton 1980;Brutyan and Krapivskii 1984). As a result we obtain the model of thin vortex rings with the excluded core (Acton 1980;Brutyan and Krapivskii 1984).…”

The dynamics of vortex rings: leapfrogging in an ideal and viscous fluid

“…The general problem of description of the motion of two axisymmetric vortices and, in particular, their leapfrogging motion, was considered in several publications (see Boyarintsev et al 1985, Brutyan and Krapivskii 1984, Gurzhii et al 1988, Lamb 1932. A more detailed list of references and historical comments can be found in Meleshko (2010).…”