  Confinement can be used to systematically tame turbulent dynamics occurring
in active fluids. Although periodic channels are the simplest geometries to
study confinement numerically, the corresponding experimental realizations
require closed racetracks. Here, we computationally study 2D active nematics
confined to such a geometry -- an annulus. By systematically varying the
annulus inner radius and channel width, we bridge the behaviors observed in the
previously studied asymptotic limits of the annulus geometry: a disk and an
infinite channel. We identify new steady-state behaviors, which reveal the
influence of boundary curvature and its interplay with confinement. We also
show that, below a threshold inner radius, the dynamics are insensitive to
topological constraints imposed by boundary conditions. We explain this
insensitivity through a simple scaling analysis. Our work sheds further light
on design principles for using confinement to control the dynamics of active
nematics.
