  We investigate the direct enstrophy cascade of two-dimensional decaying
turbulence in a flowing soap film channel. We use a coarse-graining approach
that allows us to resolve the nonlinear dynamics and scale-coupling
simultaneously in space and in scale. From our data, we verify an exact
relation due to Eyink (1995) between traditional 3rd-order structure function
and the enstrophy flux obtained by coarse-graining. We also present
experimental evidence that enstrophy cascades to smaller (larger) scales with a
60% (40%) probability, in support of theoretical predictions by Merilees & Warn
(1975) which appear to be valid in our flow owing to the ergodic nature of
turbulence. We conjecture that their kinematic arguments break down in
quasi-laminar 2D flows. We find some support for these ideas by using an
Eulerian coherent structure identification technique, which allows us to
determine the effect of flow topology on the enstrophy cascade. A key finding
is that "centers" are inefficient at transferring enstrophy between scales, in
contrast to "saddle" regions which transfer enstrophy to small scales with high
efficiency.
