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This study aims to isolate the three effects of the pressure force on theinner and outer layers: the local direct impact (characterized by the pressuregradient (PG) parameter, $\beta$), the local disequilibrating effect(represented here by the normalized streamwise derivative $d\beta/dX$), and theupstream cumulative effect, while accounting for the inevitable Reynolds numberinfluence. To achieve this objective, we draw on several non-equilibrium andnear-equilibrium databases from the literature, and employ a methodology basedon the selection of PG parameters that capture the local direct impact and thelocal disequilibration effect of the PG. The pressure force impact on the innerand outer regions is represented by two parameters: the friction-viscous PGparameter, $\beta_i$, and the PG parameter based on Zagarola-Smits velocity,$\beta_{ZS}$. In the non-equilibrium flow cases, both $\beta_i$ and$\beta_{ZS}$ exhibit similar distributions, initially increasing and thendecreasing. However, the rate of change of these parameters along thestreamwise direction varies among the flows, indicating differing levels ofpressure force disequilibration. In the outer layer, it is found that both thelocal and cumulative disequilibrating effects modify the mean velocity andReynolds stress profiles at identical $\beta_{ZS}$ values. In the inner layer,which responds much faster to changes in pressure force, the localdisequilibrating effect still modifies the mean velocity profile in the viscoussublayer. Notably, when the mean velocity defect is significant, the behaviorof u-structures in the inner layer appears to be governed by how outerturbulence responds to pressure force effects. In contrast, the size ofuv-structures in the inner layer scales with the mixed pressure-frictionlength. Unlike inner u-structures, they are independent of large-scale outerstructures and flow history.

The three effects of the pressure force on turbulent boundary layers