Resolvent Analysis of Nonequilibrium Turbulent Boundary Layers

Abstract
Resolvent analysis is an equation-based, scale-dependent decomposition of the Navier Stokes equations, linearized about a known mean flow field. The decomposition identifies the optimal response and forcing modes, ranked by their linear amplification. Here, it is applied to nonequilibrium incompressible adverse pressure gradient (APG) turbulent boundary layers (TBL) and hypersonic TBLs with high-temperature real-gas effects, including chemical nonequilibrium.  To treat the nonequilibrium APG TBL, a biglobal resolvent analysis approach is used to account for the streamwise and wall-normal inhomogeneities in the streamwise developing flow, such as the pressure gradient history. An increase in APG strength is shown to increase the linear amplification of the large-scale biglobal modes in the outer region, similar to the energization of large scale modes observed in simulation. The linear amplification of these modes grows linearly with the APG history, measured as the streamwise averaged APG strength, and relates to a novel pressure-based velocity scale. For the hypersonic TBL in chemical nonequilibrium, the resolvent analysis is constructed using a parallel flow assumption, incorporating N2, O2, NO, N, and O as a mixture of chemically reacting ideal gases. Due to the chemical nonequilibrium effects, the modes can be linearly amplified through changes in chemical concentration, which have non-negligible effects on the higher order modes. Correlations in the components of the small-scale resolvent modes are shown to agree qualitatively with similar correlations in simulation data.

Speaker Bio
Salvador Rey Gomez is a Postdoctoral Fellow at the Center for Turbulence Research at Stanford University, working with Professor Moin using numerical simulations to study large and small scale interactions in compressible flows. He earned a BS in Mechanical Engineering from the University of California, Berkeley and a MS and PhD in Aeronautics from the California Institute of Technology. His PhD research, under the supervision of Professor Beverley McKeon, was focused on resolvent analysis of  nonequilibrium turbulent flows