Information-theoretic machine learning for time-varying mode decomposition of separated airfoil wakes

We perform an information-theoretic mode decomposition for separated wakes around a wing. The current data-driven approach based on a neural network referred to as deep sigmoidal flow enables the extraction of an informative component from a given flow field snapshot with respect to a target variable at a future time stamp, thereby capturing the causality as a time-varying modal structure. We consider three examples of separated flows around a NACA0012 airfoil, namely, 1. laminar periodic wake at post-stall angles of attack, 2. strong vortex-airfoil interactions, and 3. a turbulent wake in a spanwise-periodic domain. The present approach reveals informative vortical structures associated with a time-varying lift response. For the periodic shedding cases, the informative structures vary in time corresponding to the fluctuation level from their mean values. With the second example of vortex-airfoil interactions, how the effect of vortex gust on a wing emerges in the lift response over time is identified in an interpretable manner. Furthermore, for the case of turbulent wake, the present model highlights structures near the wing and vortex cores as informative components based solely on the information metric without any prior knowledge of aerodynamics and length scales. This study provides causality-based insights into a range of unsteady aerodynamic problems.