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The Malkus–Lorenz water wheel revisited
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| American Journal of Physics |
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The Malkus–Lorenz water wheel is analyzed in a more direct way. Two new dimensionless parameters associated with properties of the water wheel are used in place of the traditional Lorenz parameters, which relate only to Lorenz's fluid model. The primary result is a performance map in the new dimensionless parameter space, which shows where the major behavior types occur and associated bifurcations. A slice across this map is examined by a bifurcation plot that shows details of the transitions between various types of behavior. An example of a 12-cup water wheel model is provided, and its behavior is compared over a wide range of parameters on the performance map to that of the Malkus-Lorenz water wheel. It is shown how the map with its water wheel parameters can be simply converted to the map with Lorenz's fluid dynamics parameters.
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Malkus–Lorenz water wheel, bifurcation, chaos, computational fluid dynamics
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