  In this paper we perform Direct Statistical Simulations of a model of
two-dimensional flow that exhibits a transition from jets to vortices. The
model employs two-scale Kolmogorov forcing, with energy injected directly into
the zonal mean of the flow. We compare these results with those from Direct
Numerical Simulations. For square domains the solution takes the form of jets,
but as the aspect ratio is increased a transition to isolated coherent vortices
is found. We find that a truncation at second order in the equal-time but
nonlocal cumulants that employs zonal averaging (zonal CE2) is capable of
capturing the form of the jets for a range of Reynolds numbers as well as the
transition to the vortex state, but, unsurprisingly, is unable to reproduce the
correlations found for the fully nonlinear (non-zonally symmetric) vortex
state. This result continues the program of promising advances in statistical
theories of turbulence championed by Kraichnan.
