Self Similarity in 2D Resolvent Analysis for Developing Turbulent Boundary Layer Flows

Two-dimensional resolvent analysis is applied to turbulent boundary layer flows, incorporating both the wall normal and streamwise variation of the flow, resulting in resolvent modes that evolve in the streamwise direction. Energetically relevant modes are identified from the resolvent operator, as a function of the mean flow field, spanwise wavenumber, and temporal frequency. For zero pressure gradient turbulent boundary layer flows, the self-similar scalings in different wall normal regions of the flow are well-known. Using the known mean flow scaling, as well as the analytic form of the resolvent operator, appropriate scaling is identified for the spanwise wavenumber and temporal frequency that results in a self similar resolvent operator. The resolvent modes, like the mean flow, are shown to evolve downstream in a self similar fashion. The global resolvent analysis is then used to investigate the effects of an external pressure gradient on the identified resolvent modes and their streamwise development.