We review some recent results that have been obtained in the investigation of zonal flow emergence, by means of a gyrokinetic trapped ion model, in the regime of ion temperature gradient instabilities for tokamak plasmas. We show that an analogous formulation of the zonal flow dynamics in terms of the Reynolds tensor applies in the fluid and kinetic regimes, where polarization effects play a major role. The kinetic regime leads to the emergence of a resonant mode at a frequency close to the drift frequency. With the objective of modeling both separate fluid and kinetic regimes of zonal flows, we used in this paper a methodology for deriving both Charney–Hasegawa–Mima (CHM) and Hasegawa–Wakatani models. This methodology is based on the trapped ion model and is analogous to the hierarchy leading from the Vlasov equation to the macroscopic fluid equations. The nature of zonal flows in the hierarchy of the Mima, Hasegawa and Wakatani models is investigated and discussed through comparisons with global kinetic simulations. Applications to the CHM equation are discussed, which applies to a broad variety of hydrodynamical systems, ranging from large-scale processes met in magnetically confined plasma to the so-called zonostrophy turbulence emerging in the case of small-scale forced, two-dimensional barotropic turbulence (Sukoriansky et al. Phys. Rev. Letters, 101, 178501, 2008).
Sarto, D., & Ghizzo, A. (2017). Hasegawa–Wakatani and Modified Hasegawa–Wakatani Turbulence Induced by Ion-Temperature-Gradient Instabilities. Fluids, 2(4), 65. https://doi.org/10.3390/fluids2040065