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By Sellwood, Astrophysical discs.

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X 48 Similarly, phase space represents the state of an object in a multi-dimensional plane. The motion of the simple pendulum could be shown on a graph where the x-axis is the angle of displacement from the vertical and the y-axis is the angular velocity. On this phase space diagram, the simple pendulum shows as a circle. Phase space turns dull statistical data into a telling picture, abstracting all the essential information from the moving parts and providing us with an easy to grasp overview of the system's behaviour over time.

How can so much be going on in such a tiny space? Why infinite logic to understand what a point in time is going to do? Ruelle suspected that the visible patterns in turbulent flow - that come and go at random - must be related to some laws that had not yet been discovered. One thing that was known about turbulence was that a broad spectrum of cycles was present at once. But how could this be represented? Could it arise from simple equations? The attractor would have to be stable and represent the final state of the dynamic system.

The column of water seems as if motionless - but, of course, the tap is running. If you open the tap a little more - carefully - you may be able to arrange regular pulsations of the water column. This is periodic motion. I I When the tap is open a little further, the pulsations become irregular. Finally, when the tap is wide open, you have a total mess - very irregular flow. This is turbu- lence. 57 How Does Turbulence Happen? Turbulence is a mess of disorder at all scales. It is unstable and highly dissipative, meaning that it drains energy and creates drag.

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An EC summer school by Sellwood, Astrophysical discs.

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