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

We present an estimation method combining Proper Orthogonal Decomposition (POD) and Linear Stochastic Estimation (LSE). The method is based on a direct mapping of the POD amplitudes from the measurement space to the state space. The method is tested in the turbulent boundary layer for a numerical simulation as well as for experimental 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 captured by the estimation. A scale-by-scale analysis shows that lower order modes corresponding to large scales are recovered accurately. Although exact reproduction is not possible at small scales, examination of the spatial and temporal content of the estimated field shows a good statistical agreement with the real field at all scales.