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

TL;DR

The paper tackles the challenge of characterizing rough-wall turbulent boundary layers when direct measurements of the roughness height $k_s$ are impractical. It introduces a variational data-assimilation approach that perturbs a smooth-wall RANS baseline to fit sparse rough-wall PIV data, embedding a design variable $\eta$ within a revised wall function to capture roughness effects and recover secondary quantities like the friction velocity $u_τ$ and $k_s$. Across multiple datasets, the assimilations reproduce mean velocity fields within tight tolerances and recover $u_τ$ and $k_s$ with errors typically within a few percent, while maintaining physical consistency and enabling 2D computations to suffice. The method also demonstrates predictive capability by extrapolating to higher Reynolds numbers with $C_f$ matches within ~5% and shows potential for modeling fetch-length dependent roughness in heterogeneous surfaces. Overall, the framework offers a cost-effective, data-driven route to infer rough-wall properties from limited measurements and to extend RANS-based predictions to practical, complex flows.

Abstract

Surface roughness influences turbulent boundary layers (TBLs) primarily through the roughness function $ΔU^+$ 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, \(u_τ\), 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.

Figures (9)

• Figure 1: Definition of roughness function, $\Delta U^+$, as (a) the difference between smooth and rough mean velocity log-profiles in viscous units, and (b) as a function of roughness Reynolds number, $k_s^+$
• Figure 2: Equivalent sand-grain roughness height definition. Figure adapted from Formichetti2025
• Figure 3: DAFoam set-up with bottom smooth wall, top zero-gradient wall, tripped 2cm high TBL at inlet, pressure outlet and front and back symmetry patches. The 2D domain only has 1 cell in the z-direction, while the 3D domain has $n$-cells and solves for the z-component as well
• Figure 4: Objective function convergence for sensitivity tests, the colour map used is explained in Table \ref{['tab2']}
• Figure 5: (a) Mean streamwise velocity contour plot with top panel: experimental data used in the assimilation from Gul2021 - case P24 18ms$^{-1}$ - and bottom panel: assimilated field. (b) Streamwise averaged mean velocity profiles from all sensitivity tests listed in Table \ref{['tab2']}