On combining linear stochastic estimation and proper orthogonal decomposition for flow reconstruction

International audienceWe present an estimation method combining Proper Orthogonal Decomposition (POD) and Linear Stochas-tic Estimation (LSE). The method is based on a direct mapping of the POD amplitudes from the measurement spaceto the state space. The method is tested in the turbulent boundary layer for a numerical simulation as well as forexperimental data. The goal is to recover the full velocity field on a fine grid from coarse measurements of a single(longitudinal) velocity component. A significant fraction of the turbulent kinetic energy for each component is capturedby the estimation. A scale-by-scale analysis shows that lower-order modes corresponding to large scales are recoveredaccurately. Although exact reproduction is not possible at small scales, examination of the spatial and temporal contentof the estimated field shows a good statistical agreement with the real field at all scales