 Plug-flow criterion for a column in a low-viscosity annulus

A column of viscosity $\mu$ in an annulus of viscosity $\lambda \mu$ and gap $h\ll a$ drives return flow of speed $O(a|w|/h)$ in a closed container. Annular shear scales as $\lambda \mu a|w|/h^2$, inducing relative core-velocity variation $O(\lambda a^2/h^2)$. Thus the extensional equations for a slender Newtonian column admit a leading plug-like axial velocity when $\lambda \ll h^2/a^2$. The small viscosity ratio alone is insufficient when the gap is very narrow.