Experiments with a Malkus-Lorenz water wheel: Chaos and Synchronization

TL;DR

This paper presents an experimental water wheel that exhibits chaotic and periodic behaviors consistent with the Lorenz model, and demonstrates high-quality chaos synchronization between the physical wheel and the Lorenz equations.

Contribution

It provides an experimental implementation of the Malkus-Lorenz water wheel and validates the Lorenz model's accuracy in describing its dynamics, including chaos synchronization.

Findings

Chaotic and periodic behaviors observed as parameters change

High-quality chaos synchronization achieved between water wheel and Lorenz model

Lorenz equations accurately describe the water wheel dynamics

Abstract

We describe a simple experimental implementation of the Malkus-Lorenz water wheel. We demonstrate that both chaotic and periodic behavior is found as wheel parameters are changed in agreement with predictions from the Lorenz model. We furthermore show that when the measured angular velocity of our water wheel is used as an input signal to a computer model implementing the Lorenz equations, high quality chaos synchronization of the model and the water wheel is achieved. This indicates that the Lorenz equations provide a good description of the water wheel dynamics.