User:Pankajgarg india/The lorenzian waterwheel
The lorenzian waterwheel is a thought experiment. Imagine a waterwheel, with an array of equally-spaced buckets around a rim that is able to rotate and damped around its axis. The buckets are mounted on swivels.The buckets are mounted in such a way that buckets always open upwards and each bucket has a small hole in the bottom, so that the water can trickle out. The entire waterwheel system is than mounted under a water source. The rotation of waterwheel shows a blend of properties of rotating cylinders of fluid in the process of convection. The former i.e The waterwheel is driven by water and the latter i.e rotating cylinders of fluid in convection by heat, but both dissipate energy.The long term behaviors of the systems depend on the intensity of the driving energy.
Begin pouring water from the water source. At low speeds, the water will trickle into the top bucket, and immediately trickle out through the hole in the bottom. Nothing happens. Increase the flow a bit, however, and the waterwheel will begin to revolve as the buckets fill up faster than they can empty. The heavier buckets containing more water let water out as they descend, and when the water is gone, the now-light buckets ascend on the other side, ultimately, to be refilled. The system is in a steady state; the wheel will, like a waterwheel mounted on a stream and hooked to grindstone, continue to spin at a fairly constant rate. But even this simple system, sans boxes or heated gases, exhibits chaotic motion. Increase the flow of water, and strange things will happen. The waterwheel will revolve in one direction as before, and then suddenly jerk about and revolve in the other direction. The conditions of the buckets filling and emptying will no longer be so synchronous as to facilitate just simple rotation; chaos has taken over. The explanation for the irregular movement of the gas lies at the molecular level. While the box sides may seem smooth and thus the flow of the should always be regular, at molecular levels the sides of the box are quite irregular due to the motion of atoms and molecules. After all, in any solid not at absolute zero, total entropy is positive and there must be some irregularity in the molecular structure of the sides of the box. Molecular interactions are tiny, however.the theory underlying,How can such tiny things like slightly misplaced molecules affect the flow of the gas in such a great way cause seemingly random motion is small deviations can lead to large deviations lies at the heart of chaos theory. The explanation is simple, and subtle explanation commonly known as "sensitive dependence on initial conditions" i.e the object would follow a very different path with slightest change of initial condition.
lorenzian waterwheel is a simple experiment exemplifying chaos theory, the science dealing with non-linearity.
- chaos making of a new science by james gleik