State estimation in wall-bounded flow systems. Part 2. Turbulent flows

Authors: Chevalier, M.C., Hoepffner, J.P.J., Bewley, T. R., Henningson, D.S.H.
Document Type: Article
Pubstate: Published
Journal: J. Fluid Mech.
Volume: 552   167-187
Year: 2006


This work extends the estimator developed in Part 1 of this study (Hoepffner et al., J. Fluid Mech., to appear) to the problem of estimating a turbulent channel flow at Re tau=100 based on a history of noisy measurements on the wall. The key advancement enabling this work is the development and implementation of an efficient technique to extract, from direct numerical simulations, the relevant statistics of an appropriately-defined ``external forcing`` term on the Navier-Stokes equation linearized about the mean turbulent flow profile. This forcing term is designed to account for the unmodelled (nonlinear) terms during the computation of the (linear) Kalman filter feedback gains It is demonstrated that by applying the optimal feedback gains, satisfactory correlation between the actual and estimated flow is obtained in the near-wall regions. Both Kalman and extended Kalman filters are evaluated and naturally the extended filter is giving better correlations between the actual and estimated flow, however the Kalman filter gives good performance in the near-wall regions.