Learning the nonlinear manifold of extreme aerodynamics

With the increased occurrence of extreme events and miniaturization of aircraft, it has become an urgent task to understand aerodynamics in highly turbulent flight environments. We propose a physics-embedded autoencoder to discover a low-dimensional compact manifold representation of extreme aerodynamics. The present method is demonstrated with the highly nonlinear dynamics of vortex gust-airfoil wake interaction around a NACA0012 airfoil over a range of configurations. The present model extracts key features of the high-dimensional airfoil wake dynamics on a physically interpretable and compact manifold, covering a massive number of wake scenarios across a huge parameter space that determines the characteristics of complex gusty flow conditions. Our data-driven approach offers a new avenue for expressing the seemingly high-dimensional fluid flow systems by identifying the low-dimensional data coordinates that can also be leveraged for data compression and flow control.