Reconstructing wall shear stress from thermal wall imprints

We reconstruct the wall shear stress of plane Couette flow from thermal wall imprints generated by direct numerical simulation at Re-tau = 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 l(2)-norm of 0.25 is primarily associated with the absence of local maxima in the reconstructed wall shear stress.

Automated summary

In this study, we reconstruct the wall shear stress of plane Couette flow using thermal wall imprints generated by direct numerical simulation. We explore the relationship between wall shear stress and wall temperature, and develop a spectral model based on linear regression to reconstruct the wall shear stress. The reconstructed wall shear stress successfully reproduces the streamwise streaky structures.