Statistics of Extreme Events in Fluid Flows and Waves

Abstract

Extreme events in fluid flows, waves, or structures interacting with them are critical for a wide range of areas, including reliability and design in engineering, as well as modeling risk of natural disasters. Such events are characterized by the coexistence of high intrinsic dimensionality, complex nonlinear dynamics, and stochasticity. These properties severely restrict the application of standard mathematical approaches, which have been successful in other areas. This review focuses on methods specifically formulated to deal with these properties and it is structured around two cases: (a) problems where an accurate but expensive model exists and (b) problems where a small amount of data and possibly an imperfect reduced-order model that encodes some physics about the extremes can be employed.