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Title: Deterministic chaos in Malkus' waterwheel
Author: Alonso, David Becerra
Awarding Body: University of the West of Scotland
Current Institution: University of the West of Scotland
Date of Award: 2010
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In 1972, W.V.R. Malkus invented and constructed the waterwheel that bears his name, along with a publication on toroidal convection that presents the same dynamics. The waterwheel's dynamics closely resembles those of the well-known Lorenz system, and therefore can be viewed as its mechanical analogy. The physical waterwheel is simple in its conception, yet not completely intuitive in its performance. A constant flow of water pours in at the top bucket of a simple circular symmetrical waterwheel. Low amounts of incoming water make the wheel roll permanently in the same direction. As we quasi-stationarily increase the incoming flow, the waterwheel enters a chaotic regime where it reverses in an apparently unpredictable way. A further increase in the incoming flow makes the waterwheel return to a periodic state, this time oscillating back and forth at fixed intervals. Since it was first proposed, a few experimental and real-world applications have been related to the waterwheel dynamics. Among these we find the dynamics for Electro-rotation, Haline Oceanic Flow, and Rayleigh-Benard Convection. This thesis aims to study the waterwheel where most publications to this date have focused on its simplified analogies. We want to provide a measure of how much more complex and rich it can be, and accompany these approaches with a wide range of experiments. Finally, we present numerical evidence on the degree of similarity between the waterwheel and its Lorenzian derivations.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available