Grasping Extreme Aerodynamics on a Low-Dimensional Manifold

Modern air vehicles perform a wide range of operations, including transportation, defense, surveillance, and rescue. These aircraft can fly in calm conditions but avoid operations in gusty environments, which are seen in urban canyons, over mountainous terrains, and in ship wakes. Smaller aircraft are especially prone to such gust disturbances. With extreme weather becoming ever more frequent due to global warming, it is anticipated that aircraft, especially those that are smaller in size, encounter large-scale atmospheric disturbances and still be expected to manage stable flight. However, there exists virtually no foundation to describe the influence of extreme vortical gusts on flying bodies. To compound on this difficult problem, there is an enormous parameter space for gusty conditions wings encounter. While the interaction between the vortical gusts and wings is seemingly complex and different for each combination of gust parameters, we show in this study that the fundamental physics behind extreme aerodynamics is far simpler and low-rank than traditionally expected. It is revealed that the nonlinear vortical flow field over time and parameter space can be compressed to only three variables with a lift-augmented autoencoder while holding the essence of the original high-dimensional physics. Extreme aerodynamic flows can be optimally compressed through machine learning into a low-dimensional manifold, implying that the identification of appropriate coordinates facilitates analyses, modeling, and control of extremely unsteady gusty flows. The present findings support the stable flight of next-generation small air vehicles in atmosphere conditions traditionally considered unflyable.