By means of the multidimensional description given by the Kolmogorov equation we study the energy transfer physics and the production mechanisms of wall-turbulent flows at moderately high Reynolds numbers. Two driving mechanisms are identified for the energy fluxes. The first stronger one, here called driving scale-range (DSR), belongs to the near-wall cycle. As expected, its topology remains unaltered with Reynolds number while its intensity is found to slightly increase with Re. The second mechanism, here called outer scale-range (OSR), takes place in the overlap layer and highlights different features in agreement with the attached eddies hypothesis usually considered to describe the overlap dynamics.