Nonlinear paradigm for drift wave–zonal flow interplay: Coherence, chaos, and turbulence

Starting from the coherent four-wave drift wave–zonal flow modulation interaction model of Chen, Lin, and White [Phys. Plasmas 7, 3129 (2000)], nonlinear equations for drift wave–zonal flow interplay are systematically derived from first principles for nonuniform toroidal plasmas. The paradigm model, presented here, is based on a hierarchy in nonlinear wave–wave couplings, which assumes that different drift wave interactions on the shortest nonlinear time scale are mediated by zonal flows. The resulting coherent model demonstrates turbulence spreading to be the cause of transport scaling with system size. The nonlinear saturated state can be either coherent, with limit cycles, or chaotic, depending on the proximity to marginal stability.