On the butterfly effect

TL;DR

This paper investigates the butterfly effect in complex 2D ideal fluid flows, demonstrating through numerical simulations that it can be robust, reproducible, and present in more complicated systems than previously shown.

Contribution

It extends the understanding of the butterfly effect by showing its presence in more complex 2D ideal fluid flows through numerical simulations.

Findings

The butterfly effect is demonstrated in complex 2D ideal fluid flows.

The effect is shown to be robust and reproducible.

Previous simpler models did not exhibit the effect.

Abstract

The term "butterfly effect" means an extreme sensitivity of a dynamical system to small perturbations: "The beating of a butterfly wing in South America can result in the considerable change of positions and force of a tropical cyclon in Atlantic 2 weeks later". Numerical simulations of R.Robert show the absence of the butterfly effect in some simple flows of 2-d ideal incompressible fluid which is a model of the atmosphere. In this work a more complicated flow is considered. Numerical simulation demonstrates the butterfly effect in the strongest form. The effect is robust, and the experiment is 100% reproducible.