# Critical Point for Bifurcation Cascades and Featureless Turbulence.

@article{Canton2020CriticalPF, title={Critical Point for Bifurcation Cascades and Featureless Turbulence.}, author={Jacopo Canton and Enrico Rinaldi and Ramis {\"O}rl{\"u} and Philipp Schlatter}, journal={Physical review letters}, year={2020}, volume={124 1}, pages={ 014501 } }

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 analyze the toroidal pipe flow, which undergoes subcritical transition to turbulence at low pipe curvatures (pipe-to-torus diameter ratio) and supercritical transition at high curvatures, as was previously documented. We unveil an additional step in the bifurcation cascade and provide evidence that, in a…

## 9 Citations

### Routes to turbulence in Taylor-Couette flow

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- 2022

1Universität Bremen, Center of Applied Space Technology and Microgravity (ZARM), 28359 Bremen, Germany. 2Department of Physics, Willamette University,Salem, OR 97214, USA. 3Department of Physics,…

### A model for the collapse of the edge when two transitions routes compete

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- 2020

The transition to turbulence in many shear flows proceeds along two competing routes, one linked with finite-amplitude disturbances and the other one originating from a linear instability, as in e.g.…

### Edge tracking in spatially developing boundary layer flows

- PhysicsJournal of Fluid Mechanics
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Recent progress in understanding subcritical transition to turbulence is based on the concept of the edge, the manifold separating the basins of attraction of the laminar and the turbulent state.…

### Edge manifold as a Lagrangian coherent structure in a high-dimensional state space

- Physics
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Dissipative dynamical systems characterised by two basins of attraction are found in many physical systems, notably in hydrodynamics where laminar and turbulent regimes can coexist. The state space…

### ON THE ONSET OF TRANSITION IN 90◦-BEND PIPE FLOW

- Physics, Engineering
- 2019

The present work deals with the global stability analysis of the flow in a 90◦-bend pipe with curvature δ = R/Rc = 0.3, being R the radius of the cross-section of the pipe and Rc the radius of…

### Pressure-driven flows in helical pipes: bounds on flow rate and friction factor

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- 2020

Abstract In this paper, we use the well-known background method to obtain a rigorous lower bound on the volume flow rate through a helical pipe driven by a pressure differential in the limit of large…

### Flow in a weakly curved square duct: Assessment and extension of Dean's model

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The laminar flow in a weakly bent pipe exhibits very rich dynamical properties. The flow is stationary, periodic or chaotic depending on one control parameter. A very practical simplification…

### Modeling the collapse of the edge when two transition routes compete.

- MathematicsPhysical review. E
- 2020

This investigation is devoted to the evolution of the edge manifold when linear stability is added in such subcritical systems, a situation poorly studied despite its prevalence in realistic fluid flows.

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