  The paper is studying the dynamics of twisted vortex bundles, which were
detected in experimental investigations of superfluid turbulence in superfluid
3He-B. The analysis shows that a linear torsion oscillation of a vortex bundle
is a particular case of the slow vortex mode related with the inertial wave,
which was already investigated in the past in connection with observation of
the Tkachenko waves in superfluid 4He and the experiments on the slow vortex
relaxation in superfluid 3He-B. The paper addresses also a twisted vortex
bundle terminating at a lateral wall of a container starting from the
elementary case when the bundle reduces to a single vortex. The theory
considers the laminar regime of the vortex-bundle evolution and investigates
the Glaberson-Johnson-Ostermeier instability of the laminar regime, which is a
precursor for the transition to the turbulent regime at strong twist of the
bundle. The propagation and the rotation velocities of the vortex front (the
segment of the vortex bundle diverging to the wall) can be found from the
equations of balance for the linear and the angular momenta, and the energy. It
is demonstrated that the vortex front can move with finite velocity even in the
absence of mutual friction (the T = 0 limit). The theory is compared with
experimental results on vortex-front propagation in superfluid 3He-B.
