Data-driven resolvent analysis of turbulent channel flow

Resolvent analysis of a turbulent flow (McKeon & Sharma, JFM, 2010) identifies the most responsive inputs, their gains, and the most receptive outputs for the system according to the linear part of its dynamics, which is forced by nonlinearity. Data-driven resolvent analysis (Herrmann et al., JFM, 2021) performs this task on linear flows relying only on time-resolved snapshot data and Dynamic Mode Decomposition (DMD). Application of the data-driven technique to turbulent flows requires specific treatment of the nonlinearity, which may otherwise contaminate the linear operator approximated by DMD. In this work, we explore the use of recently developed data-driven methods to address this challenge in the context of high-dimensional and nonnormal nonlinear dynamical systems, such as wall-bounded turbulent flows. Specifically, we investigate the use of ResDMD (Residual DMD, Colbrook et al., JFM, 2023) to quantify the error made by DMD when producing a linear model from recordings of dynamics that are inherently nonlinear. Furthermore, we discuss the application of LANDO (Linear and Nonlinear Disambiguation Optimization, Baddoo et al., PRSA, 2022) that leverages kernel regression to simultaneously fit models to the linear and nonlinear contributions to the dynamics in a dataset. Both approaches are tested on numerical simulation data of a turbulent channel flow in a minimal box unit.