ABSTRACT
Complexity arises in fluid systems because the shape of a blob of fluid is indeterminate. Nothing prevents an initially simple fluid blob from deforming into the weirdest shape imaginable. It is the absence of any kind of blob-shape constraint that allows complexity to enter fluid science. The appropriate definition of complexity is being figured out by the participants of the School. The chapter describes a few areas in which complexity arises and has to be dealt with. These lectures will be roughly divided as follows: physical and mathematical description of fluids and flows, flow transport and ergodic theory, magnetic dynamos and related problems, flow instabilities and turbulence. A typical hydrostatics problem usually involves determining the shape of a fluid body for which all forces balance. Fluid equations have even been used to model the dynamics of large atomic nuclei or to investigate unusual modes of radioactive decay.
