Symmetry-reduced dynamic mode decomposition of near-wall turbulence

Data-driven dimensionality reduction methods such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) have proven to be useful for exploring complex phenomena within fluid dynamics and beyond. A well-known challenge for these techniques is posed by the continuous symmetries, e.g. translations and rotations, of the system under consideration as drifts in the data dominate the modal expansions without providing an insight into the dynamics of the problem. In the present study, we address this issue for the pressure-driven flow in a rectangular channel by formulating a continuous symmetry reduction method that eliminates the translations simultaneously in the streamwise and spanwise directions. As an application, we consider turbulence in a minimal flow unit at a Reynolds number (based on the centerline velocity and half-channel height) Re = 2000 and compute the symmetry-reduced dynamic mode decomposition (SRDMD) of sliding data windows of varying durations. SRDMD of channel flow reveals episodes of turbulent time evolution that can be approximated by a low-dimensional linear expansion.