A new and more physical approach is investigated to study the nonlinear evolution of threshold instabilities, where the physical quantities are no longer separated into their average and fluctuating parts. This is the case where fluxes are fixed and profiles are allowed to fluctuate. These systems exhibit intermittent ballistic bursts for radial transport. Radially propagating fronts develop over a broad range of time and spatial scales. We review transport results obtained using this approach on 2D and 3D edge tokamak turbulence models. A low dimensional transport model is proposed and allows us to show the competition between diffusive and ballistic transport in this convective type turbulence.