# Zero-Equation Eddy Viscosity Models

## Mixing-Length Model

The Prandtl mixing-length model for Reynolds-averaged Navier-Stokes (RANS) is based on the assumption that turbulent eddies can be expressed in terms of a product of a velocity scale and a length scale. It has the advantages of fast computation and relatively accurate prediction for simple two-dimensional flows.

However, there exists a limitation in predicting turbulent flows where the turbulent length scale varies (for example, separation or circulation). Currently, the applications of mixing-length models are hardly adopted in commercial CFD codes, but are usually employed to describe near wall behaviors such as wall boundary treatments for more complex turbulence models.

### Kinematic Eddy Viscosity

The kinematic eddy viscosity for the mixing-length model is computed using the following relationship (1) ${\nu }_{t}={l}_{m}^{2}|\frac{\partial \overline{u}}{\partial y}|$

where ${l}_{m}$ is the mixing-length and $\frac{\partial \overline{u}}{\partial y}$ is the mean velocity gradient.