Turbulent transport close to marginal instability: role of the source driving the system out of equilibrium

When modeling plasma turbulence, two different means of driving the system out of equilibrium are considered. On one hand, flux driven (FD) approaches are based on the idea that no scale separation can be assumed in a turbulent system. On the other hand, gradient driven (GD) approaches rely on the idea that the back-reaction of fluctuations on the mean profiles is not a critical ingredient for turbulence self-organization and saturation. We find that FD and GD systems strongly differ in regimes close to marginal stability. The characteristic non linear upshift is recovered in GD simulations but no comparable behavior is possible in FD case. Discrepancy between the various analysis in terms of diffusion and pinch velocities and between the models is also discussed.