Physics-based multi-sensor fusion for statistically optimal reconstruction of wall-bounded turbulence

High-resolution spatiotemporal measurements of wall-bounded turbulence can be challenging to obtain in experiments. Instrumentation that can achieve the requisite temporal resolution (e.g., hot-wire anemometry) is typically confined to point measurements that restrict spatial fidelity; likewise, systems capable of obtaining spatially-resolved field measurements (e.g., PIV) usually lack the sampling rates required to achieve adequate temporal fidelity. In this study, we present a Bayesian estimation framework to fuse noisy multi-rate and multi-fidelity sensor measurements with uncertain predictions from a physics-based fluid dynamics model--derived using Rapid Distortion Theory. A “fast” Kalman filter is designed to fuse model predictions with high-rate point measurements; a “slow” Kalman filter is then used to fuse these time-resolved estimates with sub-Nyquist-rate field measurements to maintain spatial fidelity of the reconstruction. The method is demonstrated on a turbulent channel flow using direct numerical simulation data from the Johns Hopkins Turbulence Database. Optimal point-sensor placement is also investigated. Overall, the physics-based multi-sensor fusion approach yields unbiased and minimum variance spatiotemporal reconstructions of wall-bounded turbulent flows.