Reynolds-averaged Navier-Stokes (RANS) equations

The Reynolds-averaged Navier-Stokes (RANS) equations are a set of mathematical formulas used to describe how fluids like air or water flow. They break down complex, turbulent movements into average flows and smaller fluctuations, making it easier to predict and analyze the overall flow behavior. Engineers use RANS equations to design efficient aircraft, cars, and pipelines by understanding how fluids behave in realistic, turbulent conditions without needing to simulate every tiny swirl. Essentially, RANS provides a practical way to model and analyze real-world fluid flow where turbulence is present.