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We employ a resolvent-based methodology to estimate velocity and pressurefluctuations within turbulent channel flows at friction Reynolds numbers ofapproximately 180, 550 and 1000 using measurements of shear stress and pressureat the walls, taken from direct numerical simulation (DNS) databases. Martiniet al. (J. Fluid Mech., vol. 900, 2021, A2) showed that the resolvent-basedestimator is optimal when the true space-time forcing statistics are utilized,thus providing an upper bound for the accuracy of any linear estimator. We usethis framework to determine the flow structures that can be linearly estimatedfrom wall measurements, and we characterize these structures and the estimationerrors in both physical and wavenumber space. We also compare these results tothose obtained using approximate forcing models - an eddy-viscosity model andwhite-noise forcing - and demonstrate the significant benefit of using trueforcing statistics. All models lead to accurate results up to the buffer-layer,but only using the true forcing statistics allows accurate estimation oflarge-scale log-layer structures, with significant correlation between theestimates and DNS results throughout the channel. The eddy-viscosity modeldisplays an intermediate behaviour, which may be related to its ability topartially capture the forcing colour. Our results show that structures thatleave a footprint on the channel walls can be accurately estimated using thelinear resolvent-based methodology, and the presence of large-scalewall-attached structures enables accurate estimations through the logarithmiclayer.

Resolvent-based estimation of turbulent channel flow using wall measurements