  A trapped Bose--Einstein-condensed mixture of two types of cold atoms with
significantly different masses has been simulated numerically within the
coupled Gross--Pitaevskii equations. A configuration consisting of a
vortex-free core and a shell penetrated by quantum vortices is possible in the
phase separation regime. The dynamic properties of vortices in the shell are
determined by several parameters. Physically implementable parametric domains
corresponding to long-lived strongly nonstationary systems of several vortices
attached to the core have been sought. A number of realistic numerical examples
of three vortex pairs existing for many hundreds of characteristic times have
been presented.
