The behaviour of turbulence production in adverse pressure gradient turbulent boundary layers

Abstract This paper investigates the behaviour of turbulence production in adverse pressure gradient (APG) turbulent boundary layers (TBLs), including the range of pressure gradients from zero-pressure-gradient (ZPG) to separation, moderate and high Reynolds numbers, and equilibrium and non-equilibrium flows. The main focus is on predicting the values and positions of turbulence production peaks. Based on the unique ability of turbulence production to describe energy exchange, the idea that the ratios of the mean flow length scales to the turbulence length scales are locally smallest near peaks is proposed. Thereby, the ratios of length scales are defined for the inner and outer regions, respectively, as well as the ratios of time scales for further consideration of local information. The ratios in the inner region are found to reach the same constant value in different APG TBLs. Like turbulence production in the ZPG TBL, turbulence production in APG TBLs is shown to have a certain invariance of the inner peak. The value and position of the inner peak can also be predicted quantitatively. In contrast, the ratios in the outer region cannot be determined with unique coefficients, which accounts for the different self-similarity properties of the inner and outer regions. The outer time scale ratios establish a link between mean flow and turbulence, thus participating in the discussion on half-power laws. The present results support the existence of a half-power-law region that is not immediately adjacent to the overlapping region.