Abstract:
For decades, numerous methods have been proposed, tested, and analyzed to predict fluid motion. Despite this extensive effort, achieving accurate long-term predictions remains elusive. This is primarily due to a range of challenges, including time discretization errors, the multiscale nature of fluid solutions, inadequate physical models for realistic settings, excessive dissipation from models or numerical schemes, poor representations of intermittency and backscatter, data inaccuracies, model complexity, legacy code limitations, and the inherently chaotic nature of fluid flows, which imposes a finite predictability horizon. This talk will focus on the last challenge: the finite predictability horizon. Among the many approaches explored, only two have shown consistent promise, ensemble simulation and data assimilation.
In the area of data assimilation, a notable disconnect exists between theory and practice. On the theoretical side, hundreds of papers rigorously analyze nudging methods, often under idealized (“spherical cow”) assumptions. On the practical side, hundreds more apply Kalman filter (KF) variants, incorporating various ad hoc modifications, also typically justified under similarly simplified assumptions.
Beginning with reviewing the underlying causes of finite predictability horizons, this talk will then discuss how the Advances in Operator 2014 Theory demonstrated that nudging, under ideal conditions, can extend predictability indefinitely. This discussion will explore why, despite this promise, nudging remains underused in practice. The presentation will then briefly introduce KF and conclude by showing how combining insights from both approaches may lead to more effective prediction methods.
This work is the result of collaborations with N. Jiang (University of Florida), A. Pakzad (University of California, Riverside) F. Siddiqua (postdoc, Georgia Tech), R. Fang (postdoc, Ohio State University), and A. Cibik. The theoretical results presented rely only on the divergence theorem and the root mean square (Euclidean) norm for basic energy estimates.
Speaker’s Bio:
Dr. Bill Layton is a professor of mathematics at the University of Pittsburgh with research in computational fluid dynamics and turbulence. He has published 200 papers, advised 45 successful Ph.D. students, had many grants, published nine books (including three on launch, exploration, and summary, one on computational fluid dynamics, and others on computational mathematics), and been cited between 9000 and 10000 times. Dr. Layton received his Ph.D. in 1980 from the University of Tennessee and is originally from a small farm (built by his grandfather) outside a village in central Georgia. Outside of fluid mechanics, he enjoys chess (Georgia Champion in 1976) and whitewater kayaking.
