Self-organization of forced two-dimensional (2D) turbulence in a square no-slip domain may drive the global angular momentum to sudden peak values. This ‘spin-up’ process was observed in several direct numerical simulations (DNS) for intermediate integral-scale Reynolds numbers. The development of viscous boundary layers at the no-slip walls destabilizes the spin-up state, causing it to break-down in semi-regular intervals. After each break-down a new event of self-organization takes place, possibly with a different of rotation. If certain a priori bounds are satisfied, the evolution of the kinetic energy and the absolute angular momentum may be nearly similar in the spin-up state. Such a similarity defines a large-scale energy saturation time, which is shown to exhibit a lower bound scaling behaviour with respect to the usual turbulent time t, based upon the averaged enstrophy dissipation ¿.