Analytical theory of the probability distribution function of structure formation

TL;DR

This paper develops an analytical framework to understand the probability distribution tails of structure formation and momentum flux in turbulence, highlighting the role of shear flows and coherent structures like bipolar vortices.

Contribution

It introduces an analytical method to compute PDF tails considering shear flow effects and the influence of bipolar vortex solitons in ITG turbulence.

Findings

Stronger zonal flows are generated in ITG turbulence compared to HM turbulence.

Shear flows can significantly suppress the PDF tails of Reynolds stress.

ITG turbulence more likely produces stronger zonal flows despite higher heat flux.

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 self-regulating system. It is also shown that shear flows can significantly reduce the PDF tails of Reynolds stress and structure formation.