  We use the recently developed Macroscopic Forcing Method [Mani and Park,
Physical Review Fluids, 6:054607, 2021] to compute the scale-dependent eddy
diffusivity characterizing ensemble-averaged scalar and momentum transport in
incompressible homogeneous isotropic turbulence. For scales larger than the
energy containing eddies, eddy diffusivity is found to be constant and
consistent with the Boussinesq approximation. However for small scales eddy
diffusivity is found to vanish inversely proportional to the wavenumber.
Behavior at all scales is reasonably captured by a non-local eddy diffusivity
operator modeled as $D/\sqrt{\mathcal{I}-l^2\nabla^2}$, where $D$ is the eddy
diffusivity in the Boussinesq limit, and $l$ is a constant on the order of the
large-eddy length.
  These results present the first direct measurement of eddy diffusivity in
turbulence with implications in turbulence modeling.
