UVic Probability and Dynamics Seminar: Elizabeth Carlson

One of the challenges of the accurate simulation of turbulent flows is that initial data is often incomplete. Data assimilation circumvents this issue by continually incorporating the observed data into the model. A new approach to data assimilation known as the Azouani-Olson-Titi algorithm (AOT) introduced a feedback control term to the 2D incompressible Navier-Stokes equations (NSE) in order to incorporate sparse measurements. In 2014, the solution to the AOT algorithm applied to the 2D NSE was proven to converge exponentially to the true solution of the 2D NSE with respect to the given initial data. In this talk, I will present our work on parameter recovery, well-posedness for the sensitivity equations, a nonlinear version of the AOT algorithm, and real-world applications in ocean models, as well as new ideas based off of these investigations.