The Bleeps, the Sweeps, and the Creeps: Convergence Rates for Dynamic Observer Patterns via Data Assimilation for the 2D Navier-Stokes Equations

Abstract

We adapt a continuous data assimilation scheme, known as the Azouani-Olson-Titi (AOT) algorithm, to the case of moving observers for the 2D incompressible Navier-Stokes equations. We propose and test computationally several movement patterns (which we refer to as "the bleeps, the sweeps and the creeps"), as well as Lagrangian motion and combinations of these patterns, in comparison with static (i.e. non-moving) observers. In several cases, order-of-magnitude improvements in terms of the time-to-convergence are observed. We end with a discussion of possible applications to real-world data collection strategies that may lead to substantial improvements in predictive capabilities. "I'm having trouble with the radar, sir. [...] I've lost the bleeps, I've lost the sweeps, and I've lost the creeps." -Michael Winslow as Radar Technician in Spaceballs [51].