Linear estimation of coherent structures in wall-bounded turbulence at Reτ = 2000

The estimation problem for a fully-developed turbulent channel flow at Reτ = 2000 is considered. Specifically, a Kalman filter is designed using a Navier-Stokes-based linear model. The estimator uses time-resolved velocity measurements at a single wall-normal location (provided by DNS) to estimate the time-resolved velocity field at other wall-normal locations. The estimator is able to reproduce the largest scales with reasonable accuracy for a range of wavenumber pairs, measurement locations and estimation locations. Importantly, the linear model is also able to predict with reasonable accuracy the performance that will be achieved by the estimator when applied to the DNS. A more practical estimation scheme using the shear stress at the wall as measurement is also considered. The estimator is still able to estimate the largest scales with reasonable accuracy, although the estimator's performance is reduced.