Abstract: Turbulence is often claimed to be "the last unsolved problem of classical mechanics," realized in the evolution of certain dynamical systems, notably those for fluid dynamics. In general these systems behave nicely in that their large time behavior is finite dimensional and possibly even smooth, but the set of all possible solutions is chaotic. This leads to incredible difficulties in predictive modeling and even understanding dynamics. For predictive modeling, one uses data assimilation (DA) to course-correct models with real-world data. In the first part of this talk I will focus on 1) how the dynamics impact the effectiveness of all DA methods and 2) how DA methods may allow us to not only predict but also understand the large time behavior of a system.

Contact: Ian Tobasco