Cross-field transport, that controls the energy confinement time in tokamaks, is mainly driven by turbulence. In L-mode edge plasmas, the interchange and drift waves instabilities are expected to be dominant. The first one is linked to the magnetic curvature while the second derives from the parallel conductivity [1]. It is observed that the resulting ion-scale turbulence can self-organize into zonal flows (ZFs) that participate efficiently to its saturation [2, 3]. More recently, it has been observed that ZFs can structure into staircases [4], hence producing a set of micro-barriers that can efficiently mitigate avalanche transport. In this work, the issues of ZFs generation and impact on transport are addressed by means of a reduced flux-driven nonlinear model that features both interchange and drift waves instabilities [5, 6]. The linear properties of both instabilities are controlled by two plasma parameters, the mean curvature g of the magnetic field, and the adiabaticity parameter C that scales like the square of the parallel wave vector divided by the electron-ion collision frequency. It is shown here that albeit the interchange parameter is controlling the structuration into staircases, the adiabaticity parameter controls the turbulent energy that gets stored in the flows. Moreover, the confinement time normalized to a mixing length estimate exhibits the same dependencies as the energy balance between turbulent modes and zonal flows, attesting the efficiency of nonlinearly generated flows to mitigate turbulent transport.