The Eulerian gyrokinetic turbulence code GENE has recently been extended to a full torus code. Moreover, it now provides Krook-type sources for gradient-driven simulations where the profiles are maintained on average as well as localized heat sources for a flux-driven type of operation. Careful verification studies and benchmarks are performed successfully. This setup is applied to address three related transport issues concerning nonlocal effects. First, it is confirmed that in gradient-driven simulations, the local limit can be reproduced-provided that finite aspect ratio effects in the geometry are treated carefully. In this context, it also becomes clear that the profile widths (not the device width) may constitute a more appropriate measure for finite-size effects. Second, the nature and role of heat flux avalanches are discussed in the framework of both local and global, flux-and gradient-driven simulations. Third, simulations dedicated to discharges with electron internal barriers are addressed. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3567484]