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_[STIX]x1D70F ) scaling transition of the maximum TMC located at yₚ . We show that in viscous units, yₚ⁺ (and 1+uvₚ⁺ ) displays a scaling transition from Re_[STIX]x1D70F3/7 ( Re_[STIX]x1D70F-6/7 ) to Re_[STIX]x1D70F3/5 ( Re_[STIX]x1D70F-3/5 ) in turbulent boundary layer, in sharp contrast to that from Re_[STIX]x1D70F1/3 ( Re_[STIX]x1D70F-2/3 ) to Re_[STIX]x1D70F1/2 ( Re_[STIX]x1D70F-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_[STIX]x1D70F and log layer for large Re_[STIX]x1D70F , 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_[STIX]x1D70F is envisaged.