Reconstructing the flow in the wall region from wall sensors

In this paper we examine how the flow in the wall region can be predicted from realistic (partial) measurements. The underlying motivation of this study is the improvement of control schemes for near-wall flows. We propose a method based on the proper orthogonal decomposition which provides estimated amplitudes for the coherent structures (i.e., the large scales) of the flow from wall measurements. The method is tested for the direct numerical simulation of a minimal flow unit. The large scales obtained by reconstruction from wall data are compared to those of the velocity field in the wall layer. The dominant structures—the streamwise streaks—are well recovered, the cross-stream motions less so since they are associated with higher-order structures unaccounted for in our truncation. We defined “rescaled” eigenfunctions to try to improve the representation of the cross-stream components of the flow. Aliasing effects due to realistic (large) sensor spacings were examined. We find that the spanwise spacing is the limiting factor for the estimation, so that a realistic grid will affect the reconstruction by at least 20% compared to full wall information.