Reconstructing wall shear stress from thermal wall imprints

Abstract

We reconstruct the wall shear stress of plane Couette flow from thermal wall imprints generated by direct numerical simulation at Reτ=263 using an imposed surface temperature flux and fixed temperature at the bottom and top boundary, respectively. We explore the strong correlation between wall shear stress and wall temperature by analysing their joint probability density function and cross variance spectrum, before developing a spectral model based on linear regression. We then use observed symmetries in the estimator parameters to reduce the degrees of freedom of the model. The reconstructed wall shear stress reproduces streamwise streaky structures well. The relative error in the ℓ2-norm of 0.25 is primarily associated with the absence of local maxima in the reconstructed wall shear stress.