EFFECT OF FLOW HISTORY IN TURBULENT BOUNDARY LAYERS WITH ADVERSE PRESSURE GRADIENT

The mean velocity and Reynolds stress profiles from three non-equilibrium pressure-gradient turbulent boundary layers that are generated using direct numerical simulation are examined to further understand the effect of flow history. The pressure force impact on the inner and outer regions is represented by two parameters: the friction-viscous pressure-gradient parameter, β_i, and the pressure-gradient parameter based on Zagarola-Smits velocity, β_ZS, respectively. In all three flow cases, both β_i and β_ZS exhibit similar distributions, initially increasing and then decreasing. However, the rate of change of these parameters along the streamwise direction varies among the flows, indicating differing levels of pressure force disequilibration. In addition, we employ two near-equilibrium cases with minimal variations of the pressure gradient parameters for comparisons. The study aims to isolate the three effects of the pressure force on the inner and outer layers: local direct impact (β value), local disequilibrating effect (dβ/dx value), and upstream cumulative effect, while accounting for the inevitable Reynolds number effect. In the outer layer, it is found that both the local and cumulative disequilibrating effects modify the mean velocity and Reynolds stress profiles at identical β_ZS values. The faster the variations in pressure force impact, the more delayed the response of both mean flow and turbulence. Cumulative effects prove to be significant. In the inner layer, which responds much faster to changes in pressure force, the local disequilibrating effect still modifies the mean velocity profile in the viscous sublayer. Notably, in situations where the mean velocity defect is significant, the behavior of turbulence in the inner layer appears to be dictated by how outer turbulence responds to pressure force effects.