In order to better understand the feature of turbulent transport in tokamak plasmas dominated by zonal flows and nonlinearly excited tertiary (Kelvin–Helmholtz-like) waves, the radial dependency of the turbulent structure in the back of steady-state zonal flows was analyzed based on gyrofluid simulation of the electron temperature gradient turbulence in a sheared-slab configuration. The zonal flows change the characteristics of plasma turbulence from homogeneous to inhomogeneous. Thus, it is found that turbulent vortices are regulated by a radially alternative potential pattern where the spatiotemporal characteristic scales with respect to local fluctuations change radially. From the cross spectrum analysis between the poloidal electric field and the pressure perturbation, it was found that, in plasmas dominated by zonal flows, the restriction of heat flux is conducted by two mechanisms, i.e. the reduction of coherence and the phase synchronization.