Non-universal scaling transition of momentum cascade in wall turbulence

As a counterpart of energy cascade, turbulent momentum cascade (TMC) in the wall-normal direction is important for understanding wall turbulence. Here, we report an analytic prediction of non-universal Reynolds number (Re-tau) scaling transition of the maximum TMC located at y(p). We show that in viscous units, y(p)(+) (and 1 + <(u'v'(+)(p))over bar>) displays a scaling transition from Re-tau(3/7) (Re-tau(-6/7)) to Re-tau(3/5)) (Re-tau(-3/5)) in turbulent boundary layer, in sharp contrast to that from Re-tau(1/3)) (Re-tau(-2/3)) to Re-tau(1/2)) (Re-tau(-1/2)) in a channel/pipe, countering the prevailing view of a single universal near-wall scaling. This scaling transition reflects different near-wall motions in the buffer layer for small Re-tau and log layer for large Re-tau, with the non-universality being ascribed to the presence/absence of mean wall-normal velocity V. Our predictions are validated by a large set of data, and a probable flow state with a full coupling between momentum and energy cascades beyond a critical Re-tau is envisaged.