  Eruptive activity in the solar corona can often lead to the propagation of
shock waves. In the radio domain the primary signature of such shocks are type
II radio bursts, observed in dynamic spectra as bands of emission slowly
drifting towards lower frequencies over time. These radio bursts can sometimes
have inhomogeneous and fragmented fine structure, but the cause of this fine
structure is currently unclear. Here we observe a type II radio burst on
2019-March-20th using the New Extension in Nan\c{c}ay Upgrading LOFAR
(NenuFAR), a radio interferometer observing between 10-85 MHz. We show that the
distribution of size-scales of density perturbations associated with the type
II fine structure follows a power law with a spectral index in the range of
$\alpha=-1.7$ to -2.0, which closely matches the value of $-5/3$ expected of
fully developed turbulence. We determine this turbulence to be upstream of the
shock, in background coronal plasma at a heliocentric distance of $\sim$2
R$_{\odot}$. The observed inertial size-scales of the turbulent density
inhomogeneities range from $\sim$62 Mm to $\sim$209 km. This shows that type II
fine structure and fragmentation can be due to shock propagation through an
inhomogeneous and turbulent coronal plasma, and we discuss the implications of
this on electron acceleration in the coronal shock.
