Role of stable modes in driven shear-flow turbulence

A linearly unstable, sinusoidal E × 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. From a variety of analyses, the nonlinear state is found to have a significant component associated with stable modes. The role of these modes is investigated through a simple fluid model that tracks how momentum transport and partial flattening of the mean flow scale with the driving term. From this model, 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.