Streamwise-localized solutions at the onset of turbulence in pipe flow

Abstract

Although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. A recent proposition is that in analogy to low dimensional chaotic systems, turbulence is organized around unstable solutions of the governing equations which provide the building blocks of the disordered dynamics. We report the discovery of periodic solutions which just like intermittent turbulence are spatially localized and show that turbulence arises from one such solution branch.

4 pages, 4 figures

References in corpus (5)

• Turbulence transition and the edge of chaos in pipe flow
• Periodic orbits near onset of chaos in plane Couette flow
• Revealing the state space of turbulent pipe flow by symmetry reduction
• Relative periodic orbits in transitional pipe flow
• From travelling waves to mild chaos: a supercritical bifurcation cascade in pipe flow

Cited by in corpus (63)

• The rise of fully turbulent flow
• Relative periodic orbits form the backbone of turbulent pipe flow
• Ecological collapse and the emergence of traveling waves at the onset of shear turbulence
• The Openpipeflow Navier--Stokes Solver
• Spatially localized solutions of shear flows
• Exact coherent states and connections to turbulent dynamics in minimal channel flow
• Linear instability of viscoelastic pipe flow
• The genesis of streamwise-localized solutions from globally periodic travelling waves in pipe flow
• Koopman mode expansions between simple invariant solutions
• Streamwise and doubly-localised periodic orbits in plane Poiseuille flow
• Reduction of SO(2) symmetry for spatially extended dynamical systems
• A doubly-localized equilibrium solution of plane Couette flow
• Crisis bifurcations in plane Poiseuille flow
• On the nature of laminar-turbulence intermittency in shear flows
• Capturing Turbulent Dynamics and Statistics in Experiments with Unstable Periodic Orbits
• Symmetry reduction in high dimensions, illustrated in a turbulent pipe
• Transition to turbulence in shear flows
• Increasing lifetimes and the growing saddles of shear flow turbulence
• Transition to magnetorotational turbulence in Taylor--Couette flow with imposed azimuthal magnetic field
• Periodically bursting edge states in plane Poiseuille flow
• Small scale exact coherent structures at large Reynolds numbers in plane Couette flow
• Sudden relaminarisation and lifetimes in forced isotropic turbulence
• Suppression of turbulence and travelling waves in a vertical heated pipe
• Heteroclinic path to spatially localized chaos in pipe flow
• Unstable manifolds of relative periodic orbits in the symmetry-reduced state space of the Kuramoto-Sivashinsky system
• Long wavelength instability of coherent structures in plane Couette flow
• Surfing the edge: using feedback control to find nonlinear solutions
• Dynamics of laminar and transitional flows over slip surfaces: effects on the laminar-turbulent separatrix
• Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow
• Studying edge geometry in transiently turbulent shear flows
• Heteroclinic and Homoclinic Connections in a Kolmogorov-Like Flow
• Self-sustainment of coherent structures in counter-rotating Taylor-Couette flow
• The edge as a Lagrangian Coherent Structure in a high-dimensional state space
• Homoclinic snaking in plane Couette flow: bending, skewing, and finite-size effects
• Vertically localised equilibrium solutions in large-eddy simulations of homogeneous shear flow
• A nonlinear approach to transition in subcritical plasmas with sheared flow
• Geometry of transient chaos in streamwise-localized pipe flow turbulence
• Direct path from turbulence to time-periodic solutions
• Linear feedback control of invariant solutions in channel flow
• Upper edge of chaos and the energetics of transition in pipe flow
• Intermittent direction reversals of moving spatially-localized turbulence observed in two-dimensional Kolmogorov flow
• Self-similar invariant solution in the near-wall region of a turbulent boundary layer at asymptotically high Reynolds numbers
• Deterministic and stochastic aspects of the transition to turbulence
• Streamwise decay of localized states in channel flow
• Harbingers and latecomers - The order of appearance of exact coherent structures in plane Poiseuille flow
• Localization in a spanwise-extended model of plane Couette flow
• Analysis and modeling of localized invariant solutions in pipe flow
• Transition in the asymptotic suction boundary layer over a heated plate
• New equilibrium solution branches of plane Couette flow discovered using a project-then-search method
• Chaotic self-sustaining structure embeded in turbulent-laminar interface
• The origin of localized snakes-and-ladders solutions of plane Couette flow
• A spotlike edge state in plane Poiseuille flow
• Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow
• Damping filter method for obtaining spatially localized solutions
• Edge state modulation by mean viscosity gradients
• Aging and memory of transitional turbulence
• Modified snaking in plane Couette flow with wall-normal suction
• The universality class of the transition to turbulence
• A Characteristic Dynamic Mode Decomposition
• The role of periodic orbits and bubbles of chaos during the transition to turbulence
• A set-oriented path following method for the approximation of parameter dependent attractors
• Dynamics-based machine learning of transitions in Couette flow
• Bifurcation structure of unstable periodic orbits in plane Couette flow with the Smagorinsky model