  Zonal jets and non-zonal large-scale flows are often present in
forced-dissipative barotropic turbulence on a beta-plane. The dynamics
underlying the formation of both zonal and non-zonal coherent structures is
investigated in this work within the statistical framework of Stochastic
Structural Stability Theory (S3T). Previous S3T studies have shown that the
homogeneous turbulent state undergoes a bifurcation at a critical parameter and
becomes inhomogeneous with the emergence of zonal and/or large-scale non-zonal
flows and that these statistical predictions of S3T are reflected in direct
numerical simulations. In this paper, we study the dynamics underlying the S3T
statistical instability of the homogeneous state as a function of parameters.
It is shown that for weak planetary vorticity gradient, $\beta$, both zonal
jets and non-zonal large-scale structures form from upgradient momentum fluxes
due to shearing of the eddies by the emerging infinitesimal flow. For large
$\beta$, the dynamics of the S3T instability differs for zonal and non-zonal
flows but in both the destabilizing vorticity fluxes decrease with increasing
$\beta$. Shearing of the eddies by the mean flow continues to be the mechanism
for the emergence of zonal jets while non-zonal large-scale flows emerge from
resonant and near resonant triad interactions between the large-scale flow and
the stochastically forced eddies. The relation between the formation of
large-scale structure through modulational instability and the S3T instability
of the homogeneous state is also investigated and it is shown that the
modulational instability results are subsumed by the S3T results.
