Variational data assimilation in wall turbulence: From outer observations to wall stress and pressure

TL;DR

This paper uses adjoint-variational data assimilation to estimate near-wall turbulence in channel flow from outer measurements, achieving high accuracy when observations are close to the wall and analyzing the influence of flow scales.

Contribution

It introduces a novel adjoint-variational data assimilation method to infer near-wall turbulence and wall stresses from outer flow observations in channel turbulence.

Findings

Correlation exceeds 95% when observations are within 50 viscous units from the wall.

Estimation accuracy decreases to 40% at the wall when observations are 90 viscous units away.

The method remains robust with filtered and sub-sampled outer observations.

Abstract

Estimation of near-wall turbulence in channel flow from outer observations is investigated using adjoint-variational data assimilation. We first consider fully resolved velocity data, starting at a distance from the wall. By enforcing the estimated flow to exactly satisfy the Navier-Stokes equations, we seek a statistically stationary turbulent state that reproduces the instantaneous outer measurements. Such an estimated state provides full access to the unknown near-wall turbulence, including the wall shear stresses and pressure. When the first observation is within fifty viscous units from the wall, the correlation coefficient between the true and estimated state exceeds 95%. As the observations are further separated from the wall, at ninety viscous units, the accuracy of the assimilated wall stresses decreases to 40% at the wall. This trend is nearly independent of the Reynolds number. The Fourier spectrum of the estimation error is qualitatively consistent with the coherence spectrum between the outer and the inner state variables: observed long wavelength structures in the outer flow have deeper coherence into the unobserved near-wall region, and therefore the error is lowest at large scales. Nevertheless, the adjoint-variational approach provides a more rigorous quantification of the capacity to accurately predict the instantaneous near-wall turbulence from outer measurements. Lastly, we demonstrate the robustness of the estimation accuracy using filtered and sub-sampled outer observations.