  Annular Couette flow is the flow between two coaxial cylinders driven by the
axial translation of the inner cylinder. It is investigated using direct
numerical simulation in long domains, with an emphasis on the laminar-turbulent
coexistence regime found for marginally low values of the Reynolds number.
Three distinct flow regimes are demonstrated as the radius ratio $\eta$ is
decreased from 0.8 to 0.5 and finally to 0.1. The high-$\eta$ regime features
helically-shaped turbulent patches coexisting with laminar flow, as in planar
shear flows. The moderate-$\eta$ regime does not feature any marked
laminar-turbulent coexistence. In an effort to discard confinement effects,
proper patterning is however recovered by artificially extending the azimuthal
span beyond 2$\pi$. Eventually, the low-$\eta$ regime features localised
turbulent structures different from the puffs commonly encountered in
transitional pipe flow. In this new coexistence regime, turbulent fluctuations
are surprisingly short-ranged. Implications are discussed in terms of phase
transition and critical scaling.
