Related papers: Geometry of transient chaos in streamwise-localize…
Lower-branch traveling waves and equilibria computed in pipe flow and other shear flows appear intermediate between turbulent and laminar motions. We take a step towards connecting these lower-branch solutions to transition by deriving a…
For Hagen-Poiseuille flow the mechanism of laminar-to-turbulent transition originated from the deceleration of disturbed streams on the pipe wall is analyzed. An expression for the critical Reynolds number and the disturbance in the form of…
According to a recent theory \cite{Li14}, when the Reynolds number is large, fully developed turbulence is caused by short term unpredictability (rough dependence upon initial data); when the Reynolds number is moderate, often transient…
In shear flows at transitional Reynolds numbers, localized patches of turbulence, known as puffs, coexist with the laminar flow. Recently, Avila et al., Phys. Rev. Let. 110, 224502 (2013) discovered two spatially localized relative periodic…
Tunnelling from a chaotic potential well is explained in terms of a set of complex periodic orbits which contain information about the real dynamics inside the well as well as the complex dynamics under the confining barrier. These orbits…
In linearly stable shear flows at moderate Re, turbulence spontaneously decays despite the existence of a codimension-one manifold, termed the edge of chaos, which separates decaying perturbations from those triggering turbulence. We…
We study numerically a succession of transitions in pipe Poiseuille flow that leads from simple travelling waves to waves with chaotic time-dependence. The waves at the origin of the bifurcation cascade possess a shift-reflect symmetry and…
Fluid flows between rotating concentric cylinders exhibit two distinct routes to turbulence. In flows dominated by inner-cylinder rotation, a sequence of linear instabilities leads to temporally chaotic dynamics as the rotation speed is…
Transition from laminar to turbulent flow drastically changes the mixing, transport, and drag properties of fluids, yet when and how turbulence emerges is elusive even for simple flow within pipes and rectangular channels. Unlike the onset…
In the past two decades, our understanding of the transition to turbulence in shear flows with linearly stable laminar solutions has greatly improved. Regarding the susceptibility of the laminar flow, two concepts have been particularly…
A family of three-dimensional travelling waves for flow through a pipe of circular cross section is identified. The travelling waves are dominated by pairs of downstream vortices and streaks. They originate in saddle-node bifurcations at…
We report the results of three-dimensional direct numerical simulations for incompressible viscous fluid in a circular pipe flow with a sudden expansion. At the inlet, a parabolic velocity profile is applied together with a finite amplitude…
The recent discovery of unstable travelling waves (TWs) in pipe flow has been hailed as a significant breakthrough with the hope that they populate the turbulent attractor. We confirm the existence of coherent states with internal fast and…
We analyse the dynamics within the stability boundary between laminar and turbulent square duct flow with the aid of an edge-tracking algorithm. As for the circular pipe, the edge state turns out to be a chaotic attractor within the edge if…
In shear flows like pipe flow and plane Couette flow there is an extended range of parameters where linearly stable laminar flow coexists with a transient turbulent dynamics. When increasing the amplitude of a perturbation on top of the…
In wall-bounded flows, the laminar regime remain linearly stable up to large values of the Reynolds number while competing with nonlinear turbulent solutions issued from finite amplitude perturbations. The transition to turbulence of plane…
The transition of the flow in a duct of square cross-section is studied. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers; this flow is thus a good candidate to investigate the 'bypass' path…
An iterface structure between turbulence and laminar flow is investigated in two-dimensional channel flow. This spatially localized structure not only sustains itself, but also converts laminar state into turbulence actively. In other…
Despite recent progress, laminar-turbulent coexistence in transitional planar wall-bounded shear flows is still not well understood. Contrasting with the processes by which chaotic flow inside turbulent patches is sustained at the local…
Turbulent spots surrounded by laminar flow are a landmark of transitional shear flows, but the dependence of their kinematic properties on spatial structure is poorly understood. We here investigate this dependence in pipe flow for Reynolds…