IMPROVED UNDERSTANDING AND MODELING OF TURBULENT FLOWS AT HIGH REYNOLDS NUMBERS

Abstract

Turbulent flow modeling at high Reynolds numbers remains a fundamental challenge in fluid dynamics due to the multiscale nature of turbulence and the dominance of nonlinear transport mechanisms. This study presents a mathematically consistent and physically transparent formulation for high Reynolds number turbulence based on the Reynolds-averaged Navier–Stokes (RANS) equations coupled with the standard – closure. Unlike conventional approaches that emphasize empirical tuning or numerical implementation alone, the governing equations are systematically derived from first principles and analyzed in the asymptotic high Reynolds number limit. The formulation explicitly highlights the confinement of viscous effects to near-wall regions and the dominance of turbulent transport in the bulk flow, thereby clarifying the physical assumptions underlying eddy-viscosity models. A fully reproducible numerical framework is developed, incorporating pressure–velocity coupling, turbulence transport equations, convergence criteria, and explicit numerical datasets. Numerical results demonstrate that the model accurately captures essential features of high Reynolds number wall-bounded turbulence, including logarithmic mean velocity profiles, near-wall peaks in turbulent kinetic energy and Reynolds shear stress, and the predominance of eddy viscosity over molecular viscosity. Validation against established theoretical and empirical trends confirms the reliability of the proposed formulation. The study provides a unified framework bridging mathematical modeling, physical interpretation, and numerical implementation, offering a solid foundation for advanced turbulence modeling and future hybrid and data-driven extensions.