Assimilating Rough Features: A Data-Driven Framework to Infer Rough Wall Properties from Sparse Experimental Data

Abstract

Surface roughness influences turbulent boundary layers (TBLs) primarily through the roughness function \(\Delta U^+\) and the equivalent sand-grain roughness height \(k_s\). Direct determination of \(k_s\) typically requires detailed velocity and wall-shear stress measurements, which are often impractical. As an alternative, this study presents a data assimilation framework that modifies a smooth-wall Reynolds-Averaged Navier–Stokes (RANS) baseline to match sparse rough-wall particle image velocimetry (PIV) data in the fully rough regime. Through this approach, secondary variables such as the friction velocity, \(u_\tau\), and \(k_s\) can be inferred from the assimilated flow fields. The assimilated TBL reproduces experimental velocity profiles within 1% and predicts friction velocity within 1–6% of the experimental measurements. Furthermore, the \(k_s\) values inferred from the assimilation also match the experimental data up to 1%. These results demonstrate the potential of data assimilation as a cost-effective alternative to high-fidelity methods and support the generalisation of the framework to model streamwise-varying roughness by treating \(k_s\) as a function of fetch length.