Here's one I wrote about modelling vortex motions using Ultra Fractal.  Turns out the a great many complex motions can be captured relatively simply.

Kerry

http://www.fractalus.com/kerry/articles/vortical_flow1.pdf

This is a very good example.

I have only once refused to do a job for an employer, and it related to fluid flow. The Hagen-Poiseuille equations are not adequate to describe fluid flow properly. There are too many simplifying assumptions.

Later, at the University of Liverpool, I attended a supercomputer exhibition. Rolls-Royce had employed a company to use a transputer supercomputer to analyse the airflow around their carbon-fibre turbine blades. Each transputer dealt with only a tiny square area, using the input-output principle. The airflow into the next blade must match the output from the last, and by symmetry this is the airflow out of that next blade.

The input and output were compared, and the error found. To avoid the model oscillating, this error-feedback was "diluted". This led to a slow convergence on the results.

The entire array of transputers ran for months.

Anything that simplifies such computations is a great service to industry.

By the way, there was no chaos theory, no transputers and no PCs in the sixties. I was right to refuse. I would still be working on it by hand today.

Charles

I have read the article and found it interesting. The application to turbulence is better described by charles brief reply. Maybe a 16 square grid could be investigated to give some initial experience of modelling fluid turbulence in a stirred cup of tea? Mine black with no sugar and one  little drop of milk.