  We consider long simulations of 2D Kolmogorov turbulence body-forced by
$\sin4y \ex$ on the torus $(x,y) \in [0,2\pi]^2$ with the purpose of extracting
simple invariant sets or `exact recurrent flows' embedded in this turbulence.
Each recurrent flow represents a sustained closed cycle of dynamical processes
which underpins the turbulence. These are used to reconstruct the turbulence
statistics in the spirit of Periodic Orbit Theory derived for certain types of
low dimensional chaos. The approach is found to be reasonably successful at a
low value of the forcing where the flow is close to but not fully in its
asymptotic (strongly) turbulent regime. Here, a total of 50 recurrent flows are
found with the majority buried in the part of phase space most populated by the
turbulence giving rise to a good reproduction of the energy and dissipation
probability density functions. However, at higher forcing amplitudes now in the
asymptotic turbulent regime, the generated turbulence data set proves
insufficiently long to yield enough recurrent flows to make viable predictions.
Despite this, the general approach seems promising providing enough simulation
data is available since it is open to extensive automation and naturally
generates dynamically important exact solutions for the flow.
