History Effects in Adverse Pressure Gradient Turbulent Boundary Layers through Resolvent Analysis*

Adverse pressure gradient (APG) turbulent boundary layers (TBL) are paramaterized by their Reynolds number, APG strength, and APG history. Resolvent analysis identifies a decomposition of the Navier-Stokes operator, linearized about a mean flow field, that has been shown to predict key features of energetic motions in shear-driven turbulence. Biglobal resolvent analysis is leveraged to account for the nonparallel terms in the APG TBL, specifying only the temporal frequency and spanwise wavenumber. The Bobke et al. (2017) LES datasets are used to test the effect of different APG strengths and histories on the resolvent amplification. A masking technique is used to identify small and large scale structures. Similar to the energization of large scale structures in experiment, the resolvent amplification of large scale structures increases with APG strength. Domains with a larger accumulated APG have increased amplification, similar to what is observed in the streamwise fluctuations when the APG history is varied. The history effect on the resolvent amplification shares similarities with a hybrid velocity scale that mitigates APG effects of the streamwise fluctuations in the outer region. The resolvent modes are then used to reconstruct the turbulent statistics using a model-based framework.