Fluid Mixing and Dynamical Systems

We consider problems of mixing in fluid flows and show how the methods of dynamical systems may be used in the analysis of these problems. In particular, we consider the problem of passive scalar mixing in incompressible fluid flows and decompose the problem into three stages as follows. The first problem is to express the desired quantities (reactant consumption rate .... ) in terms of statistics or functionals of the flow field u(x, t). The second is to compute the flow field (or a sufficiently accurate characterization of it) and, the third, determine the desired statistical properties.