Zonal flows in gyrofluid simulations of slab electron temperature gradient turbulence

Zonal flows can be generated by drift wave turbulence through the nonlinear interactions. Three-dimensional gyrofluid simulations show that in a turbulent system driven by electrostatic sheared slab electron temperature gradient (ETG) modes, the excitation of zonal flows is a slower process, which indicates the amplitudes grow up approximately proportionally to time. The zonal flows are very weak compared with the background turbulence and hardly work for suppressing the turbulent electron heat transport. The dynamics of zonal flows is numerically explored by starting the zonal flow component in the quasi-steady state. Meanwhile, the basic modulation processes between zonal flows and the pump waves as well as the sidebands in an ETG turbulence–zonal flows system are theoretically analyzed using a four-wave or five-wave (including two pump waves) coupling model. Through comparing the spectral evolution of both ETG turbulence and zonal flows in the simulations with the modulational instability analysis based on a five-wave model, it is identified that the zonal flows may originate from the beating of any two pump waves in the ETG turbulence, the evolution of zonal flows is determined by a modulational instability that strongly depends on the spectra of the turbulence, usually a marginal instability observed in ETG turbulence simulations. The saturation of zonal flows is testified to be subject to the same modulation process that becomes stable. Afterwards, the zonal flows enter a periodic oscillation phase.