The Orthogonal Sub-Grid Scales-Variational Multi-Scale (OSGS-VMS) method can accurately approximate Burgers "turbulence" (a highly simplified version of the incompressible Navier–Stokes turbulence), only with the addition of purely dissipative numerical terms. The analysis of a one-dimensional Burgers equation in the Fourier space allows to clarify the scale dependence of the numerical diffusion introduced by the OSGS-VMS method. In particular, results can be contrasted with Direct Numerical Simulations (DNS) and with a spectral Large Eddy Simulation (LES).