  We present an analysis of the Navier-Stokes equations based on a spatial
filtering technique to elucidate the multi-scale nature of fully developed
turbulence. In particular, the advection of a band-pass-filtered small-scale
contribution by larger scales is considered, and rigorous upper bounds are
established for the various dynamically active scales. The analytical
predictions are confirmed with direct numerical simulation data. The results
are discussed with respect to the establishment of effective large-scale
equations valid for turbulent flows.
