Statistics and scaling laws of turbulent scalar mixing at high Reynolds numbers

The turbulent motion of fluids and scalars is a highly complex problem. It is still one of the unsolved problems of classical physics, cf. Nelkin (1992) and Shraiman and Siggia (2000), and the description remains challenging. The understanding of turbulent flows and turbulent mixing is of great interests for many applications. Prominent examples are the turbulent combustion of chemical reactants and the dynamics of the atmosphere or the oceans. In those cases the evolution of the scalar affects the turbulent flow itself. Here, we focus on the case where the scalar is both conserved and passive and does not affect the flow field.