Abstract: The complexities of turbulence make reduced-order models valuable for both understanding and predicting flow phenomena. Resolvent analysis of the Navier-Stokes equations identifies dominant linear energy amplification mechanisms within a flow, which have been closely connected with coherent flow structures that contribute to engineering quantities of interest such as drag and noise emission. Despite this insight, resolvent analysis has been used primarily in a qualitative manner and has been limited to academic problems of moderate size due to poor computational cost scaling with problem size.
In this seminar, I will discuss two efforts within my group to extend resolvent analysis beyond these limitations. First, we developed a novel resolvent-based flow estimation and control framework with several advantages over standard methods. When equivalent assumptions are made, the resolvent-based estimator and controller reproduce the Kalman filter and LQG controller, respectively, but at substantially lower computational cost. Unlike these methods, the resolvent-based approach can naturally accommodate forcing terms (nonlinear terms from Navier-Stokes) with colored-in-time statistics, which significantly improves the accuracy of the estimates.
Second, we developed a new computational algorithm to enable resolvent analysis of large-scale systems of practical engineering interest. Our algorithm combines concepts from randomized linear algebra with an efficient time-stepping method that exploits the direct and adjoint time-domain equations underlying the resolvent system. This combination of methods overcomes the main computational bottlenecks of previous methods and yields an algorithm that scales linearly with problem size, drastically reducing CPU and memory costs for large systems.
Bio: Aaron Towne is an Assistant Professor in the Department of Mechanical Engineering at the University of Michigan. His research develops simple, low-cost models that can be used to understand, predict, and control turbulent flows, using both physics-based and data-driven methods. Applications include aeroacoustics, aerodynamics, and wall-bounded flows, among others. Before joining the faculty at Michigan, he was a Postdoctoral Fellow in the Center for Turbulence Research at Stanford University. He received his PhD and MS degrees from the California Institute of Technology and his BS from the University of Wisconsin-Madison. He is a recipient of the 2020 Young Investigator Program Award (YIP) from the Air Force Office of Scientific Research (AFOSR) and multiple best paper awards, including the AIAA/CEAS Award for the Best Paper in Aeroacoustics.