# The effect of background flow shear on gyrokinetic turbulence in the cold ion limit

## TL;DR

This paper derives a fluid model from gyrokinetics in the cold ion limit, analyzing how background flow shear influences turbulence stability and nonlinear mode interactions, with results validated against gyrokinetic simulations.

## Contribution

It introduces a fluid system including flow shear derived from gyrokinetics without closure, providing analytic solutions and benchmarks for turbulence studies.

## Key findings

- Flow shear affects PVG mode stability.
- Differences in nonlinear coupling between zonal and non-zonal modes.
- Analytic results match gyrokinetic simulations.

## Abstract

The cold ion limit of the local gyrokinetic model is rigorously taken to produce a nonlinear system of fluid equations that includes background flow shear. No fluid closure is required. By considering a simple slab geometry with magnetic drifts, but no magnetic shear, these fluid equations reduce to the Charney-Hasegawa-Mima model in the presence of flow shear. Analytic solutions to this model are found to study the impact of ExB flow shear on the stability of a single Parallel Velocity Gradient (PVG) driven mode. Additionally, the model is used to investigate the effect of background ExB flow shear on the basic three-mode nonlinear coupling, which reveals differences between zonal and non-zonal modes. These analytic results agree with gyrokinetic simulations and can serve to benchmark the numerical implementation of flow shear and nonlinear coupling.