Assimilating rough features: A data-driven framework to infer rough wall properties from sparse experimental data

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.