Towards Real-time Reconstruction of Velocity Fluctuations in Turbulent Channel Flow

We develop a streaming framework for efficient reconstruction of turbulent velocity fluctuations with the goal of enabling real-time prediction of turbulent flow features. The approach consists of training and reconstruction phases, with a minimal data requirement during reconstruction. During training, we efficiently and robustly compute the resolvent operator for channel flow via blockwise inversion. During subsequent testing, we process the incoming stream of measurements using a (temporal) sliding discrete Fourier transform to allow for continuous updates. We apply the technique to reconstruction of the flow in a minimal channel at Re_τ ≈ 186 from sparse, planar measurements and evaluate the errors incurred relative to the input data required. The combination of data-driven and equation-based approaches bolsters reconstruction efficacy beyond using either in isolation.