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Enhanced Effication of Turbulent Flow Observations: Parameter Recovery, Sensitivity Analysis, Non-Linear Data Assimilation Algorithms, and a Real-World Implementation
Abstract
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. 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 dissertation, we test the robustness, improve, and implement the AOT algorithm, as well as generate new ideas based off of these investigations. First, we apply the AOT algorithm to the 2D NSE with an incorrect parameter and prove it still converges to the correct solution up to an error determined by the error in the parameters. This led to the development of a simple parameter recovery algorithm. The implementation of this algorithm led us to provide rigorous proofs that solutions to the corresponding sensitivity equations are in fact the Fréchet derivative of the solutions to the original equations. Next, we present a proof of the convergence of a nonlinear version of the AOT algorithm in the setting of the 2D NSE, where for a portion of time the convergence rate is proven to be double exponential. Finally, we implement the AOT algorithm in the large scale Model for Prediction Across Scales - Ocean model, a real-world climate model, and investigate the effectiveness of the AOT algorithm in recovering subgrid scale properties.
Subject Area
Mathematics
Recommended Citation
Carlson, Elizabeth Anne, "Enhanced Effication of Turbulent Flow Observations: Parameter Recovery, Sensitivity Analysis, Non-Linear Data Assimilation Algorithms, and a Real-World Implementation" (2021). ETD collection for University of Nebraska-Lincoln. AAI28490053.
https://digitalcommons.unl.edu/dissertations/AAI28490053