  In this article we are interested in the geometric and analytic mixing scales
of solutions to passive scalar problems. Here, we show that both notions are
comparable after possibly removing large scale projections. In order to discuss
our techniques in a transparent way, we further introduce a dyadic model
problem.
  In a second part of our article we consider the question of sharp decay rates
for both scales for Sobolev regular initial data when evolving under the
transport equation and related active and passive scalar equations. Here, we
show that slightly faster rates than the expected algebraic decay rates are
optimal.
