Journal ArticleDOI
Discontinuous transition to spatiotemporal intermittency in plane Couette flow
TLDR
In this article, the plane Couette flow undergoes a globally subcritical transition to turbulence, and the lifetime histograms of patches quenched in the range R[Ru,Rc] display a well-defined exponentially decreasing tail.Abstract:
The plane Couette flow undergoes a globally sub-critical transition to turbulence. Turbulent spots generated by localized finite-amplitude perturbations evolve differently depending on the Reynolds number R. Below Ru 312 they decay rapidly; above Rc 323 a fraction of spots turns to sustained turbulent patches and an average turbulent fraction can be defined, that slowly increases with R. Lifetime histograms of patches quenched in the range R[Ru,Rc] display a well-defined exponentially decreasing tail. This behavior is reminiscent of the discontinuous transition to spatiotemporal chaos via spatiotemporal intermittency observed in certain two-dimensional lattices of coupled map.read more
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Journal ArticleDOI
The onset of turbulence in pipe flow
Kerstin Avila,David Moxey,Alberto de Lozar,Marc Avila,Dwight Barkley,Dwight Barkley,Björn Hof +6 more
TL;DR: It is shown that in pipes, turbulence that is transient at low Reynolds numbers becomes sustained at a distinct critical point and is intrinsic to the nature of fluid turbulence.
Journal ArticleDOI
Turbulence transition in pipe flow
TL;DR: Pipe flow is a prominent example among the shear flows that undergo transition to turbulence without mediation by a linear instability of the laminar profile as discussed by the authors, which can consistently be explained on the assumption that the turbulent state corresponds to a chaotic saddle in state space.
Journal ArticleDOI
Homotopy of exact coherent structures in plane shear flows
TL;DR: In this paper, three-dimensional steady states and traveling wave solutions of the Navier-Stokes equations are computed in plane Couette and Poiseuille flows with both free slip and no-slip boundary conditions.
Journal ArticleDOI
Exact coherent structures in channel flow
TL;DR: In this paper, exact coherent states in Poiseuille flow are calculated by homotopy from free-slip to no-slink boundary conditions, where the coherent states consist of wavy low-speed streaks flanked by staggered streamwise vortices.
Journal ArticleDOI
Visualizing the geometry of state space in plane Couette flow
TL;DR: In this paper, a dynamical, 10^5-dimensional state-space representation of plane Couette flow at Re = 400 in a small, periodic cell is presented and a new method of visualizing invariant manifolds embedded in such high dimensions.