Modeling turbulent flow over rough surfaces remains a fundamental challenge in Reynolds-Averaged Navier–Stokes (RANS) simulations. Traditional approaches rely on equivalent sand grain roughness, \(k_s^ + \) , to represent roughness effects, but this hydrodynamic scaling often fails to capture the influence of complex surface geometries, particularly in the transitionally rough regime. This study presents a novel extension of the \({v^2} - f - k - \omega \) turbulence model for rough-wall duct flows. The test case adopted is turbulent channel flow with \(R{e_\tau } = 1000\) to \(2000\) and \(0 \le k_s^ + \le {\rm{ 100}}\) . The study investigates, for the first time within a RANS \({v^2} - f - k - \omega \) framework, the use of a roughness-sensitive boundary condition (BC) for the wall-normal Reynolds stress \(\langle {v^2}\rangle \) . The primary objective is to examine whether roughness effects on \(\langle {v^2}\rangle _w^ + \) can be represented using equivalent sand-grain roughness scaling. The calibration based on Nikuradse data indicates that \(k_s^ + \) alone is insufficient to characterize the near-wall behavior of \({v^2}_w^ + \) , and that the near-wall behavior of \(\langle {v^2}\rangle _w^ + \) also depends on the global flow state through \(R{e_\tau }\) within the fully developed channel-flow configuration considered here. When coupled with standard treatments for \(k\) and \(\omega \) based on \(k_s^ + \) the BC is shown to improve predictions of the roughness function and friction factor across both transitional and fully rough regimes. Next, the model is further extended by introducing a scaling framework that relates \({v^2}\) at the wall to the geometric roughness metrics: effective slope, skewness, and root mean square height of roughness based on the analysis of experimental results from the literature. This metric-based formulation introduces roughness geometry directly into the wall-normal Reynolds stress BC, while retaining conventional \(k_s^ + \) -based wall treatments for the remaining turbulence variables, and demonstrates agreement with DNS data for the roughness function and to a lesser degree friction factor, especially in the transitionally rough regime where geometry exerts a strong influence. The results highlight both the strengths and limitations of current RANS approaches: while global quantities such as roughness function and friction factor can be reproduced, the near-wall physics is approximated through an elevated eddy viscosity rather than explicit resolution of the pressure drag.
