Abstract Relaxations of localized over-density in a plane transverse to the magnetic field are numerically investigated under the effect of drift-wave and interchange drives in SOL conditions. Such a controlled departure from thermodynamic equilibrium allows the investigation of fundamental processes at play in cross-field transport. Interchange instabilities generate ballistic outward radial flux with low amplitude zonal flow patterns, whereas drift-wave instabilities result in symmetric radial flux with large amplitude zonal flow patterns. When both instabilities are considered, the combined effects tend to favor drift-waves, leading to a weaker outward flux with larger zonal flow patterns.