Feigenbaum universality in subcritical Taylor-Couette flow

TL;DR

This paper demonstrates Feigenbaum universality in subcritical Taylor-Couette flow, accurately computing bifurcations and predicting the transition to chaos using a novel method based on early bifurcations.

Contribution

It is the first to show Feigenbaum universality in a fluid flow and introduces a method to predict bifurcation diagrams up to chaos from initial bifurcations.

Findings

Feigenbaum constants are reproduced with high accuracy in fluid flow.

A new method predicts bifurcation diagrams up to chaos from early bifurcations.

Predictions remain valid beyond the accumulation point, even in chaotic regimes.

Abstract

Feigenbaum universality is shown to occur in subcritical shear flows. Our testing ground is the counter-rotation regime of the Taylor-Couette flow, where numerical calculations are performed within a small periodic domain. The accurate computation of up to the seventh period doubling bifurcation, assisted by a purposely defined Poincar\'e section, has enabled us to reproduce the two Feigenbaum universal constants with unprecedented accuracy in a fluid flow problem. We have further devised a method to predict the bifurcation diagram up to the accumulation point of the cascade based on the detailed inspection of just the first few period doubling bifurcations. Remarkably, the method is applicable beyond the accumulation point, with predictions remaining valid, in a statistical sense, for the chaotic dynamics that follows.