Anisotropic truncation for turbulent transport in the Hasegawa-Wakatani system

TL;DR

This paper develops anisotropic Fourier truncation models for the Hasegawa-Wakatani system, demonstrating their effectiveness in capturing turbulent transport and zonal flow dynamics compared to direct numerical simulations.

Contribution

It introduces reduced anisotropic Fourier models that accurately reproduce turbulence and zonal flow behaviors in the Hasegawa-Wakatani system, highlighting the importance of poloidal mode selection.

Findings

At least 4 poloidal modes are needed to match DNS results.

Approximately 10 modes are required in flux-driven models to replicate particle flux distribution.

Inverse energy cascade occurs at large poloidal scales, while forward enstrophy cascade occurs at smaller scales.

Abstract

Reduced models based on an anisotropic truncation of the Fourier space, retaining only a few poloidal wave-numbers while keeping the full radial resolution, are developed and applied to the Hasegawa-Wakatani system. The impact of the truncation is studied first by considering the fixed-gradient formulation, and by comparing to direct numerical simulations (DNS). The turbulent particle flux, and the transition from the quasi-two dimensional turbulence to the zonal flow (ZF) dominated state, are used as the main criteria for validation. Then, similar reduced models are developed in a flux-driven formulation and compared to the DNS, focusing on two cases far from the non-linear threshold of the transition from turbulence to zonal dominated states of the fixed gradient formulation. In both fixed gradient and flux driven cases, it is found that at least 4 poloidal modes, distributed around the most unstable mode, are needed to reproduce the DNS results reasonably. In the flux-driven case, about 10 modes are needed to recover the probability distribution function of the particle flux of the DNS. Considering the role played by different poloidal scales in the turbulent cascade, it is observed that in the turbulent state, an inverse energy cascade in radial wave-numbers takes place at large poloidal scales, while a forward enstrophy cascade in radial wave-numbers is observed to occur at smaller poloidal scales. Moreover, when they form, ZFs feed on poloidal scales that are around and slightly smaller than the injection scale, while giving their energy to the larger poloidal scales. In that case, there is an anisotropic inverse energy transfer, akin to inverse cascade, from the energy injection to the large poloidal scales through ZFs, while the forward enstrophy cascade seems to stay isotropic.