Chapter 5: Strange Attractors

This chapter presented numerous concepts that I found interesting. It is very detailed and long, so I will split the topics into two sections.   

The first topic presented dealt with turbulence, and the way it presents interest that is usually one-sided. Many people are in favour of its disappearance, while few others give supporting evidence for its importance. In some cases turbulence is desirable- for example, inside a jet engine, where efficient burning depends on rapid mixing. However, in most cases turbulence leads to

disaster. For example, turbulent airflow above an airplane’s wings destroys its lift. So, what really is turbulence? It is a mess of disorder that drains energy and creates drag. The process by which flow changes to turbulence is quite interesting. When something shakes a fluid, the fluid starts to move vigorously, as energy drains out of it.  As the liquid shakes, energy is added at low frequency, or large wavelengths, and the large wavelengths decompose into small ones. This is when eddies form, as they dissipate the fluid’s energy. An eddy is the swirling of a fluid and the reverse current created. Knowing all this, there is the question of what happens just when turbulence begins. The theory to understanding this question came from Lev D. Landau, a Russian scientist. His theory on fluid dynamics explained how when more energy comes into a system, new frequencies begin one at a time, such as how a violin responds to harder bowing by vibrating with a second, dissonant tone, and goes on until the sound gets louder. In Landau’s view, wild motion, such as oscillation, simply accumulate one on top of the other, creating rhythms with overlapping speeds.

The rest of this chapter goes on to explain a different idea- phase space and the strange attractor. The strange attractor is a complex attractorwith chaotic motion, which lives in phase space. Phase space 

is a space in which all possible states of a system are represented. It gives way to obtaining essential information from a system of moving parts and making a road map to all its possibilities, and predicting future behaviour. One point in phase space contains all the information about the state of a dynamic system at any instant. In phase space, when looking at a pendulum, with friction as a factor, a central point, where velocity is zero, “attracts” the orbits, as friction takes away some of the energy from the system. This is an example of an attractor, which exhibits predictable behaviour. A strange attractor in phase space is a very interesting concept. The situation is presented when a bounded chaotic system has a long-term pattern that is not a simple periodic orbit. If this situation is plotted on a graph over an extended period, patterns that were not obvious in the short term will be apparent as the system attempts to reach equilibrium. A strange attractor represents a path where a system changes from system to system without settling down. Like snow flakes, they come in great variety and no two are alike.