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 scaling transition of the maximum TMC located at. We show that in viscous units, (and ) displays a scaling transition from to in turbulent boundary layer, in sharp contrast to that from to 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 and log layer for large, with the non-universality being ascribed to the presence/absence of mean wall-normal velocity. 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 is envisaged.