Self-consistent theory of zonal flows in ion temperature gradient turbulence

A self-consistent theory of nonlinear zonal flows amidst complex background of ion temperature gradient (ITG) turbulence is presented. Starting with a reactive fluid model, a set of coupled nonlinear equations has been obtained in the form of Zakharov-like equations using the reductive perturbation method. These equations represent dynamical evolution of nonlinearly excited zonal flows and potential fluctuations of ITG turbulence. The derived equations have the potential to provide a qualitative explanation of the evolution of zonal flows and drift wave turbulence and their mutual interaction, which have been observed in recent gyrokinetic simulations [A. Dimits et al., Phys. Plasmas 7, 969 (2000)]. The nonlinear coupling coefficients are studied and show that the excitation of zonal flows is due to a resonance in the energy nonlinearity. The resonance turns out to be sensitive to fluid closure