Streamwise energy-transfer mechanisms in zero- and adverse-pressure-gradient turbulent boundary layers

The present study investigates streamwise (u²̄) energy-transfer mechanisms in the inner and outer regions of turbulent boundary layers (TBLs). Particular focus is placed on the u²̄-production, its inter-component and wall-normal transport as well as dissipation, all of which become statistically significant in the outer region with increasing friction Reynolds number (Reτ). These properties are analyzed using published data sets of zero, weak and moderately strong adverse-pressure-gradient (APG) TBLs across a decade of Reτ, revealing similarity in energy-transfer pathways for all these TBLs. It is found that both the inner and outer peaks of u²̄ are always associated with local maxima in the u²̄-production and its inter-component transport, and the regions below/above each of these peaks are always dominated by wall-ward/away-from-wall transport of u²̄, thereby classifying the u²̄-profiles into four distinct regimes. This classification reveals existence of phenomenologically similar energy-transfer mechanisms in the `inner' and `outer' regions of moderately strong APG TBLs, which meet at an intermediate location coinciding with the minimum in u²̄ profiles. Given that the wall-ward/away-from-wall transport of u²̄ is governed by the Q₄(sweeps)/Q₂(ejections) quadrants of the Reynolds shear stress, it is argued that the emergence of the u²̄ outer peak corresponds with the statistical dominance of Q₄ events in the outer region. Besides unravelling the dynamical significance of Q₂ and Q₄ events in the outer region of turbulent boundary layers, the present analysis also proposes new phenomenological arguments for testing on canonical wall-turbulence data at very high Reτ.