Analyzing the Dynamics of Discrete Gust Encounters with Persistent Homology

When subjected to strong, discrete gusts, aerodynamic bodies are known to exhibit massive flow separation, often resulting in high levels of unsteadiness. Such flows can be challenging to characterize in a low-order fashion, due to both the nonlinearity inherent to vortex shedding, and the discrete, aperiodic nature of the disturbance. In this talk, we take a topological approach to discrete gust encounters, viewing each gust encounter as a cycle in state space. We posit that because the temporal influence of the gust is finite, these cycles should exhibit a fairly simple topology, which can be leveraged to identify appropriate low-order coordinate systems. To demonstrate this idea, we consider flowfield measurements of a discrete gust encounter. For each case, we characterize the topology of the dynamics using persistent homology, a tool that identifies "holes" in point cloud data. We then transform the dynamics to a low-order space using a nonlinear autoencoder, which we constrain such that it preserves the features identified by persistent homology. With this method, we are able to transform a family of gust encounters to a three-dimensional latent space, in which each gust encounter reduces to a simple circle, and from which the original flow can be accurately reconstructed.