Through high resolution 2D MHD simulations we analyse the formation of coherent structures induced by nonlinear interactions in turbulent flows. These coherent structures are locally (at small scales) identified by spatial intermittent behaviour and their properties are guided by the conservation of ideal quadratic (rugged) invariants of the 2D incompressible MHD equations. Different spatial regions are displayed in correspondence of the locally correlations predicted using the variational principles associated to the rugged invariants. These local correlated structures are produced rapidly, as soon as the turbulence is fully developed.