Linear Amplification of Large Scale Structures in Adverse Pressure Gradient Turbulent Boundary Layers Through Resolvent Analysis

Incompressible adverse pressure gradient (APG) turbulent boundary layers (TBL) are characterized by their non-parallel effects due to their streamwise deceleration. A biglobal resolvent operator that accounts for the streamwise and wall-normal inhomogeneity of the mean flow field is used to study the linear response in an APG TBL. The resolvent amplification reveals increased amplification in the outer region of the flow for large-scale spanwise wavenumbers with an increase in APG strength. A rank-1 resolvent model for the streamwise fluctuations that considers the near-wall scaling is also presented. The resolvent amplification is shown to grow linearly with the APG history, measured through the streamwise averaged APG strength. This linear growth relates to a recently used hybrid velocity scale that suppresses the APG effects in the streamwise fluctuations.