# A critical point for bifurcation cascades and featureless turbulence

## TL;DR

This paper investigates how bifurcation cascades and turbulence coexist in fluid flows, revealing the nature of transitions and attractors through analysis of toroidal pipe flow at different curvatures.

## Contribution

It demonstrates that bifurcation cascades and turbulence can share phase space, identifying the supercritical transition as Ruelle--Takens type and analyzing competing attractors.

## Key findings

- Supercritical transition is of Ruelle--Takens type.
- Bifurcation cascades and turbulence can coexist in phase space.
- Transition mechanisms depend on pipe curvature.

## Abstract

In this Letter we show that a bifurcation cascade and fully sustained turbulence can share the phase space of a fluid flow system, resulting in the presence of competing stable attractors. We analyse the toroidal pipe flow, which undergoes subcritical transition to turbulence at low pipe curvatures and supercritical transition at high curvatures, as was previously documented. We provide decisive evidence that the nature of the supercritical transition is of Ruelle--Takens type and that, in a narrow range of intermediate curvatures, its dynamics competes with that of sustained turbulence emerging through subcritical transition mechanisms.