  This Letter introduces unexpected diffusion properties in dense granular
flows, and shows that they result from the development of partially jammed
clusters of grains, or granular vortices. Transverse diffusion coefficients $D$
and average vortex sizes $\ell$ are systematically measured in simulated plane
shear flows at differing internal numbers $I$ revealing (i) a strong deviation
from the expected scaling $D\propto d^2 \dot \gamma$ involving the grain size
$d$ and shear rate $\dot \gamma$ and (ii) an increase in average vortex size
$\ell$ at low $I$, following $\ell\propto dI^{-\frac{1}{2}}$ but limited by the
system size. A general scaling $D\propto \ell d \dot \gamma $ is introduced
that captures all the measurements and highlights the key role of vortex size.
This leads to establishing a scaling for the diffusivity in dense granular flow
as $D\propto d^2 \sqrt{\dot \gamma/ t_i}$ involving the geometric average of
shear time $1/\dot\gamma$ and inertial time $t_i$ as the relevant time scale.
Analysis of grain trajectories further evidence that this diffusion process
arises from a vortex-driven random walk.
