  Mixing in open incompressible flows is studied in a model problem with
inhomogeneous passive scalar injection on an inlet boundary. As a measure of
the efficiency of stirring, the bulk scalar concentration variance is bounded
and the bound is shown to be sharp at low Peclet number. Although no specific
flow saturating the bound at high Peclet number is produced here, the estimate
is conjectured to be approached for flows possessing sufficiently sustained
chaotic regions.
