Role of stable modes in driven shear-flow turbulence

TL;DR

This paper investigates the role of stable modes in driven shear-flow turbulence within a gyrokinetic framework, revealing their significant impact on turbulence saturation and momentum transport, especially under certain damping conditions.

Contribution

It demonstrates the importance of stable modes in turbulent shear flows and introduces a fluid model that improves predictions by including these modes.

Findings

Stable modes are present at every unstable wavenumber.

Stable modes significantly influence turbulence saturation and momentum transport.

Including stable modes improves model accuracy except at high radiative damping.

Abstract

A linearly unstable, sinusoidal $E \times B$ shear flow is examined in the gyrokinetic framework in both the linear and nonlinear regimes. In the linear regime, it is shown that the eigenmode spectrum is nearly identical to hydrodynamic shear flows, with a conjugate stable mode found at every unstable wavenumber. In the nonlinear regime, turbulent saturation of the instability is examined with and without the inclusion of a driving term that prevents nonlinear flattening of the mean flow, and a scale-independent radiative damping term that suppresses the excitation of conjugate stable modes. A simple fluid model for how momentum transport and partial flattening of the mean flow scale with the driving term is constructed, from which it is shown that, except at high radiative damping, stable modes play an important role in the turbulent state and yield significantly improved quantitative predictions when compared with corresponding models neglecting stable modes.