  Specific topological excitations of energetically stable "core-and-mantle"
configurations of trapped two-component immiscible Bose-Einstein condensates
are studied numerically within the coupled Gross-Pitaevskii equations.
Non-stationary long-lived coherent structures, that consist of several quantum
vortex filaments penetrating the "mantle" from outside to inside and vice-versa
and demonstrate quite nontrivial dynamics, are observed in simulations for the
first time. The ends of filaments can remain attached to the interface between
the "mantle" and the "core" if the latter is large enough while the surface
tension is not small. The shapes of such "bubbles" are strongly affected by the
vortices and sometimes are far from being spherical.
