Data Driven and Predictive Modal Analysis of Shock Separated Turbulent Boundary Layers

Two modal analysis methods, Spectral Proper Orthogonal Decomposition (SPOD) and Resolvent Analysis (RA), are compared in the analysis of low-frequency unsteadiness in a Mach 2.92 shock and turbulent boundary layer interaction (STBLI). RA identifies modes with the largest gains, i.e., that most strongly amplify forcing, and provides a way to decompose amplification mechanisms in a flow. The spatial and temporal correlation of the forcing must be taken into account when interpreting potential amplification mechanisms. To characterize the influence of the forcing and the presence of high-gain RA modes in high-fidelity simulations, SPOD and RA are employed alongside each other, making use of their close theoretical links [1]. Locations of high gain from [2] are examined in this framework, as well as one off-peak location at a frequency and spanwise wavelength associated with the Görtler-type vortices typical of strongly separated STBLIs. It is found that at most high-gain locations corresponding to neutrally stable global modes obtained from global stability analysis [2], the leading RA mode does not capture the features extracted by SPOD, and SPOD does not capture the energy of the flow. Instead, at these points, the leading RA mode resonates with the neutrally stable global mode. Slightly off-peak though, RA reverts back to extracting non-modal amplification mechanisms similar to the dynamics identified by SPOD, such as Görtler-type vortices at St = 0.06 and λ = 2δ, and SPOD does an excellent job at capturing the low-frequency motions present in the flow.