The distribution of temporal scale-dependent streamwise velocity increments is investigated in turbulent boundary layer flows at laboratory and atmospheric Reynolds numbers, using the St. Anthony Falls Laboratory wind tunnel and the Surface Layer Turbulence and Environmental Science Test dataset, respectively. The third-order moments of velocity increments, or asymmetry index $A(a,z)$, is computed for varying wall distance $z$ and time scale separation $a$, where it was observed to leave a robust, distinct signature in the form of a hump, independent of Reynolds number and located across the inertial range. The hump is observed in wall region limited to $z^{+}<5\times 10^{3}$, with a tendency to shift towards smaller time scales as the surface is approached ($z^{+}<70$). Comparing the two datasets, the hump, and its location, are found to obey inner wall scaling and is regarded as a genuine feature of the canonical turbulent boundary layer. The magnitude cumulant analysis of the scale-dependent velocity increments further reveals that intermittency is also enhanced near the wall, in the same flow region where the asymmetry signature was observed. The combination of asymmetry and intermittency is inferred to point at non-local energy transfer and scale coupling across a range of scales. From a turbulent structure perspective, such non-local energy transfer can be seen as the result of strong scale-interaction processes between outer scale motions in the logarithmic layer impacting and distorting smaller scales at the wall, through abrupt energy transfer across scales bypassing the typical energy cascade of the inertial range.
A formal derivation of the local energy transfer (LET) theory of homogeneous turbulence
