Non-perturbative statistical theory of intermittency in ITG drift wave turbulence with zonal flows

The probability distribution functions (PDFs) of momentum flux and zonal flow formation in ion-temperature-gradient (ITG) turbulence are investigated in two different models. The first is a general five-field model (ni, , Ti, Te, vi) where a reductive perturbation method is used to derive dynamical equations for drift waves and a zonal flow. The second is a reduced two-field model (, Ti) that has an exact non-linear solution (bipolar vortex soliton). In both models the exponential tails of the zonal flow PDFs are found with the same scaling ( ), but with different coefficients cZF. The PDFs of momentum flux is, however, found to be qualitatively different with the scaling (PDF ~ exp{−cMRs}), where s = 2 and s = 3/2 in the five and two-field models, respectively.