State estimation in turbulent channel flow using ensemble Kalman filter

We obtain the state estimation in turbulent channel flow from spatiotemporally sparse observations using the Ensemble Kalman Filter (EnKF). We use direct numerical simulations to generate the ground truth at friction Reynolds number of 180. In EnKF, an ensemble of system states are propagated in time from which error correlations are calculated. The error correlations are then used to correct the ensemble states when the observations become available.

Crucially many ensemble members may be required to correctly estimate the error correlations, posing a computational challenge. We show that EnKF can be applied locally and implemented in parallel to achieve computational efficiency. Our results demonstrate that EnKF significantly outperforms direct substitution (DS) of observations. The EnKF rapidly converges to the ground-truth in cases where the DS method fails. The findings highlight the potential of ensemble-based methods for real-time state estimation in complex flows. Thus, offering a computationally feasible adjoint-free alternative to variational techniques.