Characterizing Extreme Events in Turbulent Flows through Sensitivity-Based Modal Decomposition

Extreme and rare events are common features of many chaotic dynamical systems found in nature, such as earthquakes, solar coronal mass ejections, and rapid fluctuations in turbulent flows. While the events may be rare, they can pose a threat to safe and resilient operations; therefore it is critical to model, forecast, and even mitigate these events if possible. In this work, we identify a descriptive set of low-dimensional coordinates for characterizing the energy dissipation of the chaotic Kolmogorov flow through the Covariance Balancing Reduction using Adjoint Snapshots (CoBRAS) method. We demonstrate the utility of these coordinates by using them to forecast the energy dissipation and design simple feedback controllers to prevent extreme energy dissipation events.