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Accepted · first revision · record

Title: Predicting rough-wall drag from surface topography alone
Plain: Rough surfaces such as fouled ship hulls or corroded pipes raise turbulent friction, and engineers summarize the effect by one number, an equivalent sand-grain roughness height. Nobody can yet compute that number from a measured map of a surface without testing the surface in a flow.
Precise: In fully rough wall turbulence the mean-velocity shift is $\Delta U+ = (1/\kappa)\ln k_s+ + \mathrm{const}$, which defines the equivalent sand-grain height $k_s$. Determine whether $k_s/k$ ($k$ a roughness height) is a function of a finite set of topographic statistics (rms height, effective slope, skewness, correlation lengths) for generic random surfaces, give that function, and predict the transitionally rough curve $\Delta U+(k_s+)$. Answer: a relation with error well below 10 percent on surfaces not used for calibration.
Settled by: Blind predictions of $k_s$ for new random surfaces confirmed by roughness-resolved DNS or experiments in the fully rough regime.
Kind: well-posed
Answer type: identification
References: (empty)
Literature status: open
Status note: Prediction uncertainty for full-scale drag is at least 10 percent (Chung, Hutchins, Schultz, Flack, Annual Review of Fluid Mechanics 2021).
Posed since: (empty)