Analytical eddy viscosity models were developed for channel flow applications   (see Absi, 2019, Fluid Dyn 54: 137. https://doi.org/10.1134/S0015462819010014)  Later, Ludwig Prandtl introduced the additional concept of the mixing length, along with the idea of a boundary layer. For wall-bounded turbulent flows, the eddy viscosity must vary with distance from the wall, hence the addition of the concept of a 'mixing length'. In the simplest wall-bounded flow model, the eddy viscosity is given by the equation:  This simple model is the basis for the "law of the wall", which is a surprisingly accurate model for wall-bounded, attached (not separated) flow fields with small pressure gradients. More general have evolved over time, with most modern turbulence models given by field equations similar to the Navier–Stokes equations. Joseph Smagorinsky was the first who proposed a formula for the eddy viscosity in Large Eddy Simulation models, based on the local derivatives of the velocity field and the local grid size:  In the context of Large Eddy Simulation, turbulence modeling refers to the need to parameterize the subgrid scale stress in terms of features of the filtered velocity field. This field is called subgrid-scale modeling. The Boussinesq hypothesis is employed in the Spalart–Allmaras (S–A), "k"–ε ("k"–epsilon), and "k"–ω ("k"–omega) models and offers a relatively low cost computation for the turbulence viscosity formula_8. The S–A model uses only one additional equation to model turbulence viscosity transport, while the "k"–ε and "k"–ω models use two. The following is a brief overview of commonly employed models in modern engineering applications. The Spalart–Allmaras model is a one-equation model that solves a modelled transport equation for the kinematic eddy turbulent viscosity. The Spalart–Allmaras model was designed specifically for aerospace applications involving wall-bounded flows and has been shown to give good results for boundary layers subjected to adverse pressure gradients. It is also gaining popularity in turbomachinery applications. K-epsilon (k-ε) turbulence model is the most common model used in computational fluid dynamics (CFD) to simulate mean flow characteristics for turbulent flow conditions.