Lorenz's Water Wheel

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

In Lorenz's water wheel, equally spaced buckets hang in a circular array. Water pours into the top bucket and leaks out of each bucket at a fixed rate. The wheel behaves chaotically for certain choices of parameters, showing unpredictable changes in the direction of rotation. This behavior of this system is analogous to that of a Lorenz attractor.

Contributed by: Enrique Zeleny (August 2012)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The equations of motion are:

where:

is the radius of the wheel is the leakage rate is the flow rate into the top bucket is the rotational damping rate is the moment of inertia of the wheel is gravitational acceleration

The system is modeled as a ring; by assumption, the amount of water in a section (represented by a bucket) of the ring is proportional to , where is the angle of the bucket moving with angular velocity for initial conditions , , and .

Reference

[1] T. Tél and M. Gruiz, Chaotic Dynamics, An Introduction Based on Classical Mechanics, New York: Cambridge University Press, 2006.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send