International audienceA model of turbulence intensity spreading with self-consistent nonlinear noise is derived systematically for the simple dynamical model of resistivity gradient driven turbulence. Local effective drive, thermal conduction damping, nonlinear coupling, and spatial scattering effects are included. As a consequence of nonlinear mode coupling processes (i.e., triad mode interactions), turbulence energy can be spatially scattered, leading to turbulence propagation and spreading. However, the range of any nonlinear mode interactions of the background with a test mode is restricted to within a few mode scale widths from the test mode rational surface. The speed of a turbulent spreading front is calculated. This front speed is effectively constant on macroscopic scales. We show that the effect of self-consistent nonlinear noise on the intensity front speed is modest, as a consequence of the ordering Δc