Data-Driven Resolvent Analysis with Residual Information

Data-driven resolvent analysis (Herrmann et al., JFM, 2021) has seen success in performing resolvent analysis in an equation-free manner, utilizing dynamic mode decomposition (DMD, Schmid, JFM, 2010) to identify the most responsive forcing and receptive states. Towards the application of data-driven resolvent analysis for turbulent flows and multiphysics problems, treatment of inherent nonlinearity and error control is necessary to capture the underlying physics. In this work, we incorporate residual dynamic mode decomposition (ResDMD, Colbrook et al., JFM, 2023) into data-driven resolvent analysis to reduce spectral pollution in the DMD-learned linear operator. The proposed approach is applied to transitional channel flow data. In addition, we investigate the connections between the learned DMD linear operator spectrum and Orr-Sommerfeld and Squire pseudospectra.