State estimation in turbulent channel flow from limited observations

TL;DR

This paper demonstrates that an adjoint-variational method can accurately estimate the initial turbulent channel flow state from limited, noisy, and sparse observations, revealing thresholds for successful reconstruction and the influence of data resolution.

Contribution

It introduces a robust adjoint-variational approach for turbulent flow state estimation from limited data, establishing resolution thresholds and analyzing the coupling between flow regions.

Findings

High accuracy (over 99%) with very sparse data at 1/4096 DNS resolution.

Successful reconstruction of near-wall statistics from outer flow data.

Wall stress observations are less effective for reconstructing distant wall regions.

Abstract

Estimation of the initial state of turbulent channel flow from limited data is investigated using an adjoint-variational approach. The data are generated from a reference direct numerical simulation (DNS) which is sub-sampled at different spatiotemporal resolutions. When the velocity data are at 1/4096 the spatiotemporal resolution of DNS, the correlation coefficient between the true and adjoint-variational estimated state exceeds 99 percent. The robustness of the algorithm to observation noise is demonstrated. In addition, the impact of the spatiotemporal density of the data on estimation quality is evaluated, and a resolution threshold is established for a successful reconstruction. The critical spanwise data resolution is proportional to the Taylor microscale, which characterizes the domain of dependence of an observation location. Due to mean advection, either the streamwise or temporal data resolution must satisfy a criterion based on the streamwise Taylor microscale. A second configuration is considered where the sub-sampled data are comprised of velocities in the outer layer and wall shear stresses only. The near-wall flow statistics and coherent structures, although not sampled, are accurately reconstructed, which is possible because of the coupling between the outer flow and near-wall motions. Finally, the most challenging configuration is addressed where only the spatiotemporally resolved wall stresses are observed. The estimation remains accurate within the viscous sublayer and deteriorates significantly with distance from the wall. In wall units, this trend is nearly independent of the Reynolds number considered, and is indicative of the fundamental difficulty of reconstructing wall-detached motions from wall data.