Production and inter-component redistribution of turbulence in adverse pressure gradient (APG) turbulent boundary layers (TBLs) with small and large velocity defects are investigated, along with the structures playing a role in these energy transfer mechanisms. We examine the wall-normal and spectral distributions of energy, production and pressure-strain in APG TBLs, and compare these distributions with those in canonical flows. It is found that the spectral distributions of production and pressure-strain are not affected profoundly by an increase of the velocity defect, although the energy spectra change drastically in the inner layer of the large-defect APG TBL. In the latter, the signature of the inner-layer streaks is absent from the energy spectra. In the outer layer, energetic, production and pressure-strain structures appear to change from wall-attached to wall-detached structures with increasing velocity defect. Despite this, the two-dimensional spectral distributions have similar shapes and wavelength aspect ratios of the peaks in all these flows. Therefore, the conclusion is that the mechanisms responsible for turbulence production and inter-component energy transfer may remain the same within each layer in all these flows. It is the intensity of these mechanisms within one layer that changes with velocity defect, because of the local mean shear variation.

Four direct numerical simulation (DNS) databases are examined to understand the effect of the wall and near-wall turbulence on the Reynolds shear-stress carrying structures in shear-driven flows. The first DNS database is of a non-equilibrium adverse-pressure-gradient (APG) turbulent boundary layer (TBL) with momentum thickness Reynolds number (Reg) reaching 8000. The second one is the same flow as the previous, but turbulence activity in the inner layer (y/S < 0.1) is artificially eliminated. The last two DNS databases are homogeneous shear turbulence (HST) with Taylor microscale Reynolds numbers (Re\) are 104 and 248. Results show that outer layer turbulence in the APG TBLs with large velocity defect is only slightly affected by the near-wall region turbulence which suggests outer layer turbulence sustains itself without necessitating near-wall turbulence. The Corrsin length scale (Lc) scales the size of the Reynolds shear-stress carrying structures in both APG TBLs and HSTs. The streamwise length of these structures is 1LC or larger in all cases. The aspect ratio of the structures behaves similarly in both APG TBLs and HSTs when the size of the structures are normalized with Lc. Sweeps and ejections tend to form side-by-side pairs in both flow types. The spatial properties of sweeps and ejections, such as aspect ratios or relative positions are not affected by near-wall turbulence activity or presence of the wall. This suggests that the structures mostly dependent on the local mean strain rates.

Two direct numerical simulation (DNS) databases are investigated to understand the effect of the outer-layer turbulence on the inner layer's structures and energy transfer mechanisms. The first DNS database is the non-equilibrium adverse-pressure-gradient (APG) turbulence boundary layer (TBL) of Gungor et al. [1]. Its Reynolds number and the inner-layer pressure gradient parameter reach above 8000 and 10, respectively. The shape factor spans between 1.4 and 3.3, which indicates the flow has various velocity defect situations. The second database is the same flow as the first one but the outer layer turbulence is artificially eliminated in this flow. Turbulence is removed above 0.15 local boundary layer thickness. For the analysis, we chose four streamwise positions with small, moderate, large, and very-large velocity defect. We compare the wall-normal distribution of Reynolds stresses, two-point correlations and spectral distributions of energy, production and pressure strain. The results show that the inner layer turbulence can sustain itself when the outer-layer turbulence does not exist regardless of the velocity defect or the pressure gradient. The two-point correlations of both cases show that outer large-scale structures affect the inner layer structures significantly. The streamwise extent of the correlation contours scales with pressure-viscous units. This shows the importance of the pressure gradient's effect on the inner-layer structures. The spectral distributions demonstrate that the energy transfer mechanisms are probably the same in the inner layer regardless of the velocity defect, which suggests the near-wall cycle may exist even in very-large defect APG TBLs where the mean shear in the inner layer is considerably lower than small-defect APG TBLs.