Role of Stable Modes in Driven Shear-Flow Turbulence*

Unstable shear flows are found in a variety of fusion and astrophysical systems, where they may become turbulent, and have recently been shown to nonlinearly drive large-scale damped modes [Fraser et al. PoP (2017)]. These previously-neglected stable modes remove energy from the fluctuations before it cascades to small scales, suggesting they are a key component of shear-driven turbulence, where typical models assume that the largest scales take the form of the most unstable modes. Here we compare gyrokinetic simulations of forced, shear-driven turbulence where fluctuations are subject to scale-independent radiative damping, which suppresses the impact of stable modes relative to unstable ones in a manner consistent with the expected effect of a flow-aligned magnetic field in a free shear layer. We construct a simple model for how Reynolds stress scales with driving, showing that the inclusion of stable modes yields significant improvements to the model except at high radiative damping. Informed by these results, we then compare to the free shear layer system, and investigate how the turbulence scales with the flow-aligned magnetic field.