Several physical and astrophysical fluid and plasma systems displaying turbulent features show a 1/k (or 1/f) spectral domain at spatial (temporal) scales above the inertial range. Here, we investigate the formation of a 1/k spectral domain in fluid and MHD turbulence systems in the sub-inertial range (k < k(0), where k(0) is the injection scale) by means of shell-model simulations. The simulation results suggest that the 1/k domain emerges as a consequence of competing direct and inverse cascading processes, implying the formation and dissipation of large-scale gradients below the inertial domain. The relevance of our results for observations in space and astrophysical contexts is briefly discussed.