A DNS-calibrated two-layer framework for rough-wall turbulent channel and pipe flows

A DNS-calibrated framework is developed for reconstructing mean velocity profiles in turbulent flow over rough walls using a two-layer reference-plane approach. The model divides the near-wall domain into a roughness-dominated lower region, represented by a parabolic velocity profile, and an upper region resolved using the standard RANS equations starting from a reference plane located a distance 𝑘 𝑠 above the adopted wall-normal origin. To parameterize the lower region, three velocity profile coefficients, 𝑎 1 , 𝑎 2 , and 𝑎 3 , are extracted from DNS data and correlated with the roughness function and roughness geometric metrics, including effective slope and root-mean-square roughness height. A new scaling variable, 𝛾 , is introduced to quantify the contribution of the lower region to the total volume flow rate. The framework is assessed against additional DNS cases of turbulent channel and pipe flows with three-dimensional roughness, demonstrating its ability to reconstruct mean velocity profiles under conditions where the required roughness information is prescribed. The formulation maintains roughness-geometry sensitivity without requiring additional fitting for the assessment cases and offers a path forward for embedding geometric effects into RANS wall treatments through physically meaningful parameters. The framework requires the hydrodynamic roughness information, 𝑘 𝑠 and Δ ⁢ 𝑈 + , to be prescribed or obtained from an independent roughness-function or drag relation; it is therefore not intended as a standalone predictor of rough-wall drag.