  Two dimensional turbulence has a remarkable tendency to self-organize into
large, coherent structures, forming a mean flow. The purpose of this paper is
to elucidate how these structures are sustained, and what determines them and
the fluctuations around them. A recent theory for the mean flow will be
reviewed. The theory assumes turbulence is excited by a forcing supported on
small scales, and uses a linear shear model to relate the turbulent momentum
flux to the mean shear rate. Extending the theory, it will be shown here that
the relation between the momentum flux and mean shear is valid, and the
momentum flux is non-zero, for both an isotropic and an anisotropic forcing,
independent of the dissipation mechanism at small scales. This conclusion
requires taking into account that the linear shear model is an approximation to
the real system. The proportionality between the momentum flux and the inverse
of the shear can then be inferred most simply on dimensional grounds. Moreover,
for a homogeneous pumping, the proportionality constant can be determined by
symmetry considerations, recovering the result of the original theory. The
regime of applicability of the theory, its compatibility with observations from
simulations, a formula for the momentum flux for an inhomogeneous pumping, and
results for the statistics of fluctuations, will also be discussed.
