From coarse wall measurements to turbulent velocity fields through deep learning

This work evaluates the applicability of super-resolution generative adversarial networks (SRGANs) as a methodology for the reconstruction of turbulent-flow quantities from coarse wall measurements. The method is applied both for the resolution enhancement of wall fields and the estimation of wall-parallel velocity fields from coarse wall measurements of shear stress and pressure. The analysis has been carried out with a database of a turbulent open-channel flow with a friction Reynolds number $Reτ=180$ generated through direct numerical simulation. Coarse wall measurements have been generated with three different downsampling factors $fd=[4, 8, 16]$ from the high-resolution fields, and wall-parallel velocity fields have been reconstructed at four inner-scaled wall-normal distances $y+=[15, 30, 50, 100]$⁠. We first show that SRGAN can be used to enhance the resolution of coarse wall measurements. If compared with the direct reconstruction from the sole coarse wall measurements, SRGAN provides better instantaneous reconstructions, in terms of both mean-squared error and spectral-fractional error. Even though lower resolutions in the input wall data make it more challenging to achieve highly accurate predictions, the proposed SRGAN-based network yields very good reconstruction results. Furthermore, it is shown that even for the most challenging cases, the SRGAN is capable of capturing the large-scale structures that populate the flow. The proposed novel methodology has a great potential for closed-loop control applications relying on non-intrusive sensing.