What is observable from wall data in turbulent channel flow?

Estimation of the initial state turbulent channel flow from spatially and temporally resolved wall data is performed using adjoint-variational assimilation. The estimated fields satisfy Navier–Stokes equations minimize a cost function defined as difference between model predictions available observations. accuracy predicted deteriorates with distance wall, most precipitously across buffer layer beyond which only large-scale structures are reconstructed. To explain this trend, we examine domain dependence observations Hessian matrix state-estimation function, both efficiently evaluated adjoint initiated impulses at sensors. Eigenanalysis performed, eigenvalues related to capacity reconstruct represented by eigenvectors. Most eigenmodes decay layer, thus demonstrating weak sensitivity turbulence in bulk. However, when measurement time $t_m^{+} \gtrsim 20$ , some streamwise-elongated eigenfunctions remain finite outer flow, correspond motions. At much longer observation times, field becomes chaotic it amplifies exponentially, indicative extreme gradients an ill-conditioned matrix, exacerbate difficulty estimating