The Reynolds-averaged Navier–Stokes (RANS) equations are the time-averaged form of the Navier–Stokes equations obtained by decomposing each instantaneous flow variable into a mean (time-averaged) component and a fluctuating turbulent component, then averaging the equations over time or ensemble ^[1]. Substituting the decomposed velocity and pressure into the instantaneous Navier–Stokes equations and averaging introduces an additional unknown term—the Reynolds stress tensor, representing the momentum transport by turbulent fluctuations—so that the RANS system is no longer closed and requires a turbulence model to relate the Reynolds stresses to the mean flow field ^[1]. The closure problem is resolved by eddy-viscosity models, which express the Reynolds stresses through an eddy (turbulent) viscosity obtained from algebraic, one-equation, or two-equation transport models, or by Reynolds-stress transport models that solve transport equations for the individual stress components ^[2]. RANS equations predict only the statistically averaged mean flow rather than resolved turbulent motions, and are distinguished from direct numerical simulation, which resolves all scales, and from large-eddy simulation, which resolves large eddies while modeling only small scales ^[3].