  Planetary and magnetohydrodynamic drift-wave turbulence is observed to
self-organize into large scale structures such as zonal jets and coherent
vortices. In this Letter we present a non-equilibrium statistical theory, the
Stochastic Structural Stability theory (SSST), that can make predictions for
the formation and finite amplitude equilibration of non-zonal and zonal
structures (lattice and stripe patterns) in homogeneous turbulence. This theory
reveals that the emergence of large scale structure is the result of an
instability of the interaction between the coherent flow and the associated
turbulent field. Comparison of the theory with nonlinear simulations of a
barotropic flow in a beta-plane channel with turbulence sustained by isotropic
random stirring, demonstrates that SSST predicts the threshold parameters at
which the coherent structures emerge as well as the characteristics of the
emerging structures (scale, amplitude, phase speed). It is shown that non-zonal
structures (lattice states or zonons) emerge at lower energy input rates of the
stirring compared to zonal flows (stripe states) and their emergence affects
the dynamics of jet formation.
