# Chaos

Back in the mid 90’s, when I was on a winter army exercise, I was lent a copy of James Gleick’s Chaos. We were in the middle of Alberta and it was cold – so cold we had moved our accommodations out of tents and into a heated H-hut (H-huts were built as temporary army barracks during WWII that were still in use). Our exercise was shut down until the temperature increased, so I had plenty of time to read.

I have always read about math and science. On one command post exercise, the brigade commander caught me reading during a lull in the action. In jest, he made a big deal of it. I suspect he thought I was reading a trashy romance novel, but instead I was reading a book on math. Shocked to discover the topic of my reading material, he told me that if math was what I was reading about then I was welcome to read on any of his exercises.

The book Chaos was the first time I had heard of chaos theory. I loved it. The fact that seemingly simple processes could generate such complexity was fascinating. Now I saw dripping faucets and swinging pendulums as gateways to observing chaos. To me, the most fascinating chaotic idea was turbulence. Water is complex! Move it just a bit and all sorts of phenomenon spring up including eddies and whorls.

Chaotic turbulent motions are found within the surface of stars, in combustion, in the ocean – even in water flowing from a faucet. Leonardo da Vinci included turbulence in his extensive studies, and he probably wasn’t the first to study it. In all the centuries turbulence has been studied, we still haven’t come up with a precise definition of what turbulence is. We know turbulence is what takes over when smooth fluid motion breaks into a complex network of eddy-like structures at all scales. Da Vinci’s sketches of tiny eddies within small eddies within larger eddies and so on demonstrates the different size scales through which turbulent flow breaks up.

In Chaos, James Gleick describes turbulence this way: ‘It is a mess of disorder at all scales, small eddies within large ones. It is unstable. It is highly dissipative, meaning that turbulence drains energy and creates drag. It is motion turned random.’

Okay, a picture of waves breaking on a beach isn’t exactly a picture of turbulence, but it is the best I have.