Analytical theory of the probability distribution function of structure formation

Abstract

The probability distribution function (PDF) tails of the zonal flow structure formation and the PDF tails of momentum flux by incorporating effect of a shear flow in ion-temperature-gradient (ITG) turbulence are computed in the present paper. The bipolar vortex soliton (modon) is assumed to be the coherent structure responsible for bursty and intermittent events driving the PDF tails. It is found that stronger zonal flows are generated in ITG turbulence than Hasegawa-Mima (HM) turbulence as well as further from marginal stability. This suggests that although ITG turbulence has a higher level of heat flux, it also more likely generates stronger zonal flows, leading to a selfregulating system. It is also shown that shear flows can significantly

Coherent structures in ion temperature gradient turbulence-zonal flow

“…However, numerical simulations and experiments show that drift wave turbulence exhibits several non-Gaussian features like intermittency, bursty transport, etc. [8][9][10][11][12][13][14][15][16][17][18][19][20] These characteristics are related to the presence of coherent structures in drift-wave turbulence [21][22][23] and cannot be described by renormalized weak turbulence theories. Nonlinear coherent structure formation in the zonal flow envelope in simple drift wave zonal flow system has been studied in Refs.…”

Statistical properties of Charney-Hasegawa-Mima zonal flows

“…We utilize analytical results from nonperturbative stochastic theory, the so-called instanton method [31][32][33][34][35][36][37] for computing PDFs in turbulence as a comparison to the numerical data. The analytically derived PDFs are rather insensitive to the details of the linear physics of the system 36 and thus display salient features of the nonlinear interactions.…”

Statistical Theory of Plasmas Turbulence

“…Note that, for the same reason, a similar exp (−cR 3 ) scaling was found in the tails of the PDFs of positive velocity gradients in Burgers turbulence [18]. While the exponential scaling is robust, the amplitude of the PDFs rather sensitively depends on parameter values in the model through the value of the constant c 2 [30,33]. Similar exponential PDFs are thus expected when the effect of toroidal coupling is incorporated, with the same (quadratic) highest nonlinearity in Eq.…”

“…On the other hand, the constant c 1 depends on the spatial profile of the coherent structure (modons), U − V 0 , and other physical parameters (η i , τ, etc. ), which is investigated in detail in [30].…”

“…The PDFs of the local Reynolds stress in Hasagawa-Mima [25,26] and toroidal ITG turbulence models were investigated by Kim et al [27,28]. In the following, we consider a slightly different ITG model and compute the PDFs of (global) momentum flux and zonal flow formation [29,30]. Specifically, we model ITG turbulence using the continuity and temperature equation for the ions, assuming Boltzmann electrons, and ignoring the effects of parallel ion motion, magnetic shear, trapped particles, and finite beta on the ITG modes [31].…”