Turbulence self-organization is studied in the flux driven regime by means of the reduced model Tokam1D. Derived in the electrostatic and isothermal limit but keeping finite electron and ion temperatures, it features two instabilities that are suspected to dominate turbulent transport at the edge of L-mode tokamak plasmas: interchange (a reduced version of the resistive ballooning modes) and collisional drift waves, governed respectively by an effective gravity parameter g and the adiabaticity parameter C. The usual properties of these two instabilities are recovered in the linear regime. The nonlinear study focuses on the self-organization of collisional drift wave turbulence at g = 0. It is found that the energy stored in zonal flows (ZFs) decreases smoothly at small C due to the reduction of both electric and diamagnetic stresses. Conversely to gradient driven simulations, no sharp collapse is observed due to the self-consistent evolution of the equilibrium density profile. ZFs are found to structure into staircases at small and large C. These structures exhibit a rich variety of dynamics but are found robust to large perturbations. Their nucleation is found to be critically governed by the phase dynamics. Last, staircase structures are lost in the gradient driven regime, when the system is prevented to store turbulent energy into the equilibrium density (pressure) profile.