  In a companion paper [Pitrou, Phys. Rev. E 97, 043115 (2018)], a formalism
allowing to describe viscous fibers as one-dimensional objects was developed.
We apply it to the special case of a viscous fluid torus. This allows to
highlight the differences with the basic viscous string model and with its
viscous rod model extension. In particular, an elliptic deformation of the
torus section appears because of surface tension effects, and this cannot be
described by viscous string nor viscous rod models. Furthermore, we study the
Rayleigh-Plateau instability for periodic deformations around the perfect
torus, and we show that the instability is not sufficient to lead to the torus
breakup in several droplets before it collapses to a single spherical drop.
Conversely, a rotating torus is dynamically attracted toward a stationary
solution, around which the instability can develop freely and split the torus
in multiple droplets.
