Reynolds-averaged Navier–Stokes equations

Summary

The Reynolds-averaged Navier–Stokes equations, or RANS equations, are the equations of motion for the mean flow of a turbulent fluid. They are obtained by applying the Reynolds decomposition to the Navier–Stokes equations and averaging. They look like the Navier–Stokes equations for the mean velocity, with an extra term, the divergence of the Reynolds stress. Closing them with a turbulence model is the most common way to compute turbulent flows in engineering.