Zonal flow dynamics and anomalous transport

Nonlinear equations for the slow space-time evolution of the radial drift wave-ion-temperature gradient (DW-ITG) envelope and zonal flow (ZF) amplitude have been derived within a coherent four-wave drift wave-zonal flow model. In the local limit this model demonstrates spontaneous generation of zonal flow and nonlinear drift wave-zonal flow dynamics in toroidal plasmas. The model allows slow temporal and spatial variations of the DW-ITG radial envelope, incorporating the effects of equilibrium variations, i.e., turbulence spreading and size dependence of the saturated wave intensities and transport coefficients. The competition between linear drive/damping and drift wave spreading due to linear and nonlinear group velocities and nonlinear energy transfer between DW and ZF determines the saturation levels of the fluctuating fields. The turbulence intensity level exhibits a transition from Bohm scaling at small system size (Lp/ρi) to gyro-Bohm for large system size. This system exhibits chaotic behavior and intermittency, depending on system size and proximity to marginal stability