We analyze the multiscale properties of energy-conserving upwind-stabilized finite-element discretizations of the two-dimensional incompressible Euler equations. We focus our attention on two particular methods: the Lie derivative discretization introduced by Natale and Cotter and the Streamline Upwind/Petrov–Galerkin (SUPG) discretization of the vorticity advection equation. Such discretizations provide control on enstrophy by modelling different types of scale interactions. We quantify the performance of the schemes in reproducing the non-local energy backscatter that characterizes two-dimensional turbulent flows.