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We investigate the dynamics of a closed corona cartesian reduced magnetohydrodynamic (MHD) model where photospheric vortices twist the coronal magnetic field lines. We consider two corotating or counter-rotating vortices localized at the center of the photospheric plate, and additionally more corotating vortices that fill the plate entirely. Our investigation is specifically devoted to study the fully nonlinear stage, after the linear stage during which the vortices create laminar and smoothly twisting flux tubes. Our main goal is to understand the dynamics of photospheric vortices twisting the field lines of a coronal magnetic field permeated by finite amplitude broadband fluctuations. We find that depending on the arrangement and handedness of the photospheric vortices an inverse cascade storing a significant amount of magnetic energy may occur or not. In the first case a reservoir of magnetic energy available to large events such as destabilization of a pre-CME configuration develops, while in the second case the outcome is a turbulent heated corona. Although our geometry is simplified our simulations are shown to have relevant implications for coronal dynamics and CME initiation.