Mathematical and numerical analysis of a turbulent viscosity model

The turbulent viscosity assumption is the simplest turbulent closure of the Navier-Stokes equations. Of the possible models, some are of physical interest. In the case of the plane duct, a model based on the length scale, Uf, of the flow seems appropriate. Moreover, the introduction of such a model in the Navier-Stokes equations leads to a novel nonlinear parabolic equation, whose mathematical study is the subject of this paper.