# Statistical analysis of Hasegawa - Wakatani turbulence

## TL;DR

This paper analyzes the statistical properties of turbulence in the Hasegawa-Wakatani model, revealing super-diffusive behavior of small-scale eddies and the influence of zonal flows on transport dynamics.

## Contribution

It provides a theoretical interpretation of PDFs of intermittent events in Hasegawa-Wakatani turbulence, highlighting super-diffusive statistics and the role of zonal flows.

## Key findings

- Small-scale turbulent eddies exhibit super-diffusive statistics.
- Large events follow a Laplace distribution, small events are Gaussian.
- Zonal flows influence flux behavior, causing sub-diffusive transport.

## Abstract

Resistive drift wave turbulence is a multipurpose paradigm that can be used to understand transport at the edge of fusion devices. The Hasegawa-Wakatani model captures the essential physics of drift turbulence while retaining the simplicity needed to gain a qualitative understanding of this process. We provide a theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent events in Hasegawa-Wakatani turbulence with enforced equipartition of energy in large scale zonal flows and small scale drift turbulence. We find that for a wide range of adiabatic index values the stochastic component representing the small scale turbulent eddies of the flow, obtained from the ARIMA model, exhibits super-diffusive statistics, consistent with intermittent transport. The PDFs of large events (above one standard deviation) are well approximated by the Laplace distribution, while small events often exhibit a Gaussian character. Furthermore there exist a strong influence of zonal flows for example, via shearing and then viscous dissipation maintaining a sub-diffusive character of the fluxes.