SCS Colloquium: Simulation of turbulent flow

Turbulence readily arises in numerous flows in nature and technology. The large number of degrees of freedom of turbulence poses serious challenges to experimental and numerical approaches aimed at understanding and controlling such flows. While the Navier-Stokes equations are commonly accepted to precisely describe fluid flow, including turbulence, alternative coarsened descriptions need to be developed. These coarsened descriptions aim at capturing the primary features of a flow, at considerably reduced computational effort. Such coarsening introduces a `closure problem' that requires additional phenomenological modeling. Attention will be given to methods for reducing the computational complexity. Their development in the context of turbulent mixing will be sketched and the total errors incurred in this approach will be quantified.