Salvador Gomez

“Resolvent Amplification of Large Scale Structures in Adverse Pressure Gradient Turbulent Boundary Layers”

Advised by Prof. Parviz Moin

Abstract: Adverse pressure gradient (APG) turbulent boundary layers (TBL) experience significant streamwise variation because of the deceleration in the freestream velocity. APG TBLs are categorized by their local APG strength, their local Reynolds number, and their upstream history, here measured through the accumulated APG strength. Since the outer region of the TBL is most affected by the APG as the flow velocity matches the freestream velocity, the large-scale structures residing in the outer region are more affected by the APG than the viscous-dominated near-wall small-scales. Here, the APG effects are studied through biglobal resolvent analysis which resolves the streamwise and wall-normal inhomogeneities in the APG TBL. Resolvent analysis identifies an equation-based scale-dependent decomposition of the Navier-Stokes operator, linearized about the mean flow field, for a given spanwise wavelength and temporal frequency. The outputs of this analysis are two orthonormal bases that represent the most amplified forcing modes and their corresponding response modes, each ranked by their respective linear gain. By considering only the optimal response modes and their linear gain, it is shown that a self-similar near-wall cycle emerges while large-scale modes experience increased linear amplification in the outer region of the flow with increased Reynolds number and APG strength, consistent with experiments and simulations. Furthermore, the linear amplification is shown to grow monotonically with the history effect which is analogous to the intensification of streamwise fluctuations with the history effect. These results suggest that the linear amplification of the mean TBL flow explains many of the observations in APG TBLs.