Abstract
Vortex dynamics is used to consider the following problems concerning vortices in the space between concentric spheres: the equilibrium shape of vortices (they are almost rectilinear if their number is large), the metastable clusters with nonequilibrium number of vortices, the processes of vortex breaking and connection in the vicinity of the inner sphere equator, the annihilation in the vicinity of the outer sphere equator, and the behavior of an almost freely rotating double-sphere device during the variation of the superfluid angular momentum caused by the changes of vortex configuration (similar phenomena are among the possible reasons of pulsars self-acceleration).
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