New Submission An Improved Two-Parameter Model for Turbulent Rough-Wall Flows: Addressing the Limitations of Colebrook and Gioia–Chakraborty

Despite decades of research, a complete and predictive description of turbulent flow over rough walls remains elusive, particularly when different roughness mechanisms coexist. Traditional models, such as the Colebrook–White equation and the Gioia–Chakraborty spectral formulation, rely on single-parameter approaches that cannot fully capture the complexity of blended roughness types. In this work, a new two-parameter model is developed to distinguish between the contributions of sand grain-type and industrial-type roughness elements. Building on recent advances in near-wall turbulence scaling, the proposed formulation combines vortex-driven resistance and form drag effects within a physically consistent framework. The model corrects key assumptions in previous theories, notably improving on the additive treatment of dissipative and roughness scales adopted by Gioia and Chakraborty. Comparison with classical experimental datasets, including Nikuradse and Colebrook–White measurements, demonstrates that the two-parameter approach accurately predicts the friction factor across moderate and high Reynolds number regimes, including the smooth regime, and fully rough conditions. The results highlight the limitations of single-parameter models and provide a more complete description of turbulent rough-wall flows, offering improved predictive capabilities for both fundamental studies and engineering applications.