The Reynolds-averaged Navier–Stokes (RANS) equations are time-averaged equations of motion specifically designed to model turbulent flows. The core idea, pioneered by Osborne Reynolds, is Reynolds decomposition, which separates an instantaneous flow variable into its mean and fluctuating parts. When applied to the standard Navier–Stokes equations, this process generates a new term called the Reynolds stress, which mathematically represents the momentum transfer caused by turbulent eddies. Since this nonlinear term prevents direct solving, engineers rely on various turbulence models to approximate it and "close" the equations. As a result, RANS equations offer a practical way to obtain approximate time-averaged solutions for complex fluid dynamics, making them a cornerstone of computational fluid dynamics.