Turbulence

A good example of a phenomena which seems simple but which gets very complex - water flowing through a pipe.
At low speeds the flow is smooth and predictable but at higher speeds turbulence makes things complicated. According to this report:
"A team of researchers from Austria, Germany and the U.K. has succeeded in building a model that shows the process that occurs when a liquid moves from a smooth state to one of turbulence inside of a pipe."
This is a good item to use to introduce in a general way the modelling of physical processes.