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

Abstract

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 (n i , φ, T i , T e , v i ) 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 (φ, T i ) 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 (P DF ∼ exp{−c ZF φ 3 ZF }), but with different coefficients c ZF .The PDFs of momentum flux is however found to be qualitatively

Statistical properties of Charney-Hasegawa-Mima zonal flows

“…However, in many cases for the CHM zonal flows we find Gaussian PDFs in similarity to what was seen from the theoretical model in Ref. 39, whereas for some mid radial points the system exhibit sub-exponential PDFs ∼ exp − const |φ| α with α < 1, where the dynamics is strongly influenced by the zonal flow resulting in strong intermittency.…”

Statistical analysis of Hasegawa-Wakatani turbulence

“…However, when the nonlinear interactions are weak, as well as in the case of an imposed zonal flow, we find Gaussian statistics where χ = 2 as is elucidated in Ref. 35. In the analysis we will make use of different types of distributions to retro-fit the PDFs of simulation results mainly using the Laplace distribution (χ = 1.0) and the Gaussian distribution (χ = 2.0).…”

“…We have observed that similar values of kurtosis of the potential and vorticity are recovered by the ARIMA model however the original time traces seem to have sub-Gaussian distributions, indicative of sub-diffusive behaviour where kurtosis is below three. It has previously been predicted that a diffusive character of the transport is to be expected as a result of the influence of zonal flow driven by micro-scale turbulence 35 . We note that there seems to be a relation between the statistics of the potential and the vorticity indication that the modon assumption in Eq.…”

Gyrokinetic Study of the Local Entropy Dynamics in Turbulent Plasmas with Zonal Flow

“…A statistical approach is one way to identify such turbulent plasmas. The non-diffusive nature of turbulent transport in the presence of zonal flows has been studied using probability density functions [4,5]. Alternatively, based on a thermodynamics approach, entropy has been introduced, which has the advantage of connecting micro-scale phase space structure to macro-scale thermodynamic quantities.…”