  We deal with the problem of separation of time-scales and filamentation in a
linear drift-diffusion problem posed on the whole space $\mathbb{R}^2$. The
passive scalar considered is stirred by an incompressible flow with radial
symmetry. We identify a time-scale, much faster than the diffusive one, at
which mixing happens along the streamlines, as a result of the interaction
between transport and diffusion. This effect is also known as enhanced
dissipation. For power-law circular flows, this time-scale only depends on the
behavior of the flow at the origin. The proofs are based on an adaptation of a
hypocoercivity scheme and yield a linear semigroup estimate in a suitable
weighted $L^2$-based space.
