On a Rotational Smagorinsky Model for Turbulent Fluids: An Overview of Recent Results in the Steady and Unsteady Cases

In this chapter, we summarize and collect several results on a nonlinear rotational model used to simulate large scales in turbulent flows. The model we consider is a generalization of the classical Smagorinsky model and is particularly interesting to properly simulate the vorticity near solid boundaries. We report about existence of weak solution explaining how the use of classical techniques may work or fail showing also perspectives for future studies of more general classes of solutions.