For turbulence, although the two-point velocity difference u(x+r)-u(x) ateach scale r has been studied in detail, the velocity average [u(x+r)+u(x)]/2has not thus far. Theoretically or experimentally, we find interesting featuresof the velocity average. It satisfies an exact scale-by-scale energy budgetequation. The flatness factor varies with the scale r in a universal manner.These features are not consistent with the existing assumption that thevelocity average is independent of r and represents energy-containinglarge-scale motions alone. We accordingly propose that it represents motionsover scales >= r as long as the velocity difference represents motions at thescale r.
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