Route to Chaos in the Fluidic Pinball

TL;DR

This paper investigates how the fluidic pinball system transitions to chaos as the Reynolds number increases, revealing a route characterized by quasi-periodicity and symmetry-breaking bifurcations.

Contribution

It identifies the specific route to chaos in the fluidic pinball, including the sequence of bifurcations and symmetry-breaking phenomena, without using actuation.

Findings

Route to chaos is of the Newhouse-Ruelle-Takens type.

Secondary pitchfork bifurcation breaks flow symmetry.

Flow transitions to quasi-periodicity before chaos.

Abstract

The fluidic pinball has been recently proposed as an attractive and effective flow configuration for exploring machine learning fluid flow control. In this contribution, we focus on the route to chaos in this system without actuation, as the Reynolds number is smoothly increased. It was found to be of the Newhouse-Ruelle-Takens kind, with a secondary pitchfork bifurcation that breaks the symmetry of the mean flow field on the route to quasi-periodicity.