Highly symmetric travelling waves in pipe flow

The recent theoretical discovery of finite-amplitude travelling waves (TWs) in pipe flow has reignited interest in the transitional phenomena that Osborne Reynolds studied 125 years ago. Despite all being unstable, these waves are providing fresh insight into the flow dynamics. We describe two new classes of TWs, which, while possessing more restrictive symmetries than previously found TWs of Faisst & Eckhardt (2003 Phys. Rev. Lett. 91, 224502) and Wedin & Kerswell (2004 J. Fluid Mech. 508, 333–371), seem to be more fundamental to the hierarchy of exact solutions. They exhibit much higher wall shear stresses and appear at notably lower Reynolds numbers. The first M-class comprises the various discrete rotationally symmetric analogues of the mirror-symmetric wave found in Pringle & Kerswell (2007 Phys. Rev. Lett. 99, 074502), and have a distinctive double-layered structure of fast and slow streaks across the pipe radius. The second N-class has the more familiar separation of fast streaks to the exterior and slow streaks to the interior and looks like the precursor to the class of non-mirror-symmetric waves already known.

• Publication year

  2008

• Venue

  Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

• Publication date

  2008-04-30

• Fields of study

  Medicine, Physics, Engineering

• Identifiers
  DOI 10.1098/rsta.2008.0236arXiv 0804.4854PMID 19000971
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Relative periodic orbits in transitional pipe flow

  2008influential reference
• The Dynamics of Transition to Turbulence in Plane Couette Flow

  2007cited by this paper
• Turbulence transition and the edge of chaos in pipe flow.

  2007cited by this paper
• Transition in pipe flow: the saddle structure on the boundary of turbulence

  2007influential reference
• Asymmetric, helical, and mirror-symmetric traveling waves in pipe flow.

  2007influential reference
• Finite-amplitude thresholds for transition in pipe flow

  2007cited by this paper
• Recurrence of Travelling Waves in Transitional Pipe Flow

  2007influential reference
• Coherent structures in localized and global pipe turbulence.

  2007influential reference
• Pipe flow dynamics on the critical threshold.

  2007cited by this paper
• Statistical analysis of coherent structures in transitional pipe flow.

  2006influential reference
• Recurrent motions within plane Couette turbulence

  2006cited by this paper
• Edge of chaos in a parallel shear flow.

  2006cited by this paper
• Turbulence regeneration in pipe flow at moderate Reynolds numbers.

  2005cited by this paper
• Experimental Observation of Nonlinear Traveling Waves in Turbulent Pipe Flow

  2004cited by this paper
• Linearized pipe flow to Reynolds number 10 7

  2003influential reference
• Traveling waves in pipe flow.

  2003influential reference
• Homotopy of exact coherent structures in plane shear flows

  2003cited by this paper
• Exact coherent structures in pipe flow: travelling wave solutions

  2003cited by this paper
• The Dynamics of Bursting Process in Wall Turbulence

  2001cited by this paper
• Exact coherent structures in channel flow

  2001cited by this paper
• New results in rotating Hagen–Poiseuille flow

  2000cited by this paper
• Low-dimensional dynamics embedded in a plane Poiseuille flow turbulence : Traveling-wave solution is a saddle point ?

  1999cited by this paper
• THREE-DIMENSIONAL COHERENT STATES IN PLANE SHEAR FLOWS

  1998cited by this paper
• On a self-sustaining process in shear flows

  1997influential reference
• Regeneration mechanisms of near-wall turbulence structures

  1995cited by this paper
• On the generation of helical waves in circular pipe flow

  1990cited by this paper
• Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity

  1990cited by this paper
• Amplitude-dependent neutral modes in the Hagen-Poiseuille flow through a circular pipe

  1982cited by this paper
• On transition in a pipe. Part 2. The equilibrium puff

  1975cited by this paper
• On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug

  1973cited by this paper
• III. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels

  year unknowncited by this paper
• Ueber die Bewegung des Wassers in engen cylindrischen Röhren

  year unknowncited by this paper

• Ten lectures on turbulence: 1. turbulent structures

  2026cites this paper
• On the correlation between particle dynamics and erosion pattern in pipe bends: Insights via numerical simulation

  2026cites this paper
• Chaotic and time-periodic edge states in square duct flow

  2025cites this paper
• Convection in a Rapidly Rotating Spherical Shell: Newton’s Method Using Implicit Coriolis Integration

  2025cites this paper
• Mathematically established chaos and forecast of statistics with recurrent patterns in Taylor–Couette flow

  2024cites this paper
• Dynamics of a data-driven low-dimensional model of turbulent minimal pipe flow

  2024cites this paper
• Stabilising nonlinear travelling waves in pipe flow using time-delayed feedback

  2024cites this paper
• Periodic bursting cycles on the edge to square duct turbulence

  2024cites this paper
• Nonlinear evolution of vortical disturbances entrained in the entrance region of a circular pipe

  2024cites this paper
• Three-dimensional coherent structures in a curved pipe flow

  2024influential citation
• Transition to Turbulence in Pipe Flow

  2022cites this paper
• Insights and prospects for ion mobility-mass spectrometry in clinical chemistry

  2022cites this paper
• Computational Challenges of Nonlinear Systems

  2020cites this paper
• Bump Attractors and Waves in Networks of Leaky Integrate-and-Fire Neurons

  2020cites this paper
• Suppression of turbulence and travelling waves in a vertical heated pipe

  2020influential citation
• Nonlinear exact coherent structures in pipe flow and their instabilities

  2019cites this paper
• Bifurcations and instabilities in sliding Couette

  2019cites this paper
• Flow Separation at Inlet Causing Transition and Intermittency in Circular Pipe Flow

  2019cites this paper
• Saddle-node bifurcations of traveling waves in the asymptotic suction boundary layer flow

  2019cites this paper
• Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics

  2018influential citation
• Exact Coherent Structures in power-law fluids in pipe geometry

  2018cites this paper
• Complexity of the laminar-turbulent boundary in pipe flow

  2018cites this paper
• Surfing the edge: using feedback control to find nonlinear solutions

  2017cites this paper
• Small scale exact coherent structures at large Reynolds numbers in plane Couette flow

  2017cites this paper
• Surfing the edge: finding nonlinear solutions using feedback control

  2017cites this paper
• About the numerical robustness of biomedical benchmark cases: Interlaboratory FDA's idealized medical device

  2017cites this paper
• The Openpipeflow Navier-Stokes solver

  2017cites this paper
• Nonlinear waves with a threefold rotational symmetry in pipe flow: influence of a strongly shear-thinning rheology

  2017cites this paper
• On the instability of vortex–wave interaction states

  2016cites this paper
• Edge states and transition to turbulence in boundary layers

  2016cites this paper
• Permeability models affecting nonlinear stability in the asymptotic suction boundary layer: the Forchheimer versus the Darcy model

  2016cites this paper
• Travelling wave states in pipe flow

  2016cites this paper
• Travelling wave states in pipe flow

  2015influential citation
• Exact coherent states and connections to turbulent dynamics in minimal channel flow

  2015cites this paper
• The role of periodic orbits and bubbles of chaos during the transition to turbulence

  2015influential citation
• Transition sous-critique à la turbulence : étude de la croissance de poches turbulentes dans l’écoulement de Couette plan

  2015cites this paper
• Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence.

  2015cites this paper
• Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow

  2015cites this paper
• Exact coherent structures in spatiotemporal chaos: From qualitative description to quantitative predictions

  2015cites this paper
• Relative periodic orbits form the backbone of turbulent pipe flow

  2015cites this paper
• Unstable flow structures in the Blasius boundary layer

  2014cites this paper
• Transition to turbulence in the asymptotic suction boundary layer

  2014cites this paper
• Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

  2013cites this paper
• Genesis of streamwise-localized solutions from globally periodic traveling waves in pipe flow.

  2013cites this paper
• Fold-pitchfork bifurcation for maps with Z(2) symmetry in pipe flow.

  2013cites this paper
• On coherent structure in wall turbulence

  2013cites this paper
• Long-wavelength instability of coherent structures in plane Couette flow.

  2013cites this paper
• Finite amplitude solutions in sliding Couette flow

  2013cites this paper
• Spanwise-localized solutions of planar shear flows

  2013cites this paper
• Drag reduction and the dynamics of turbulence in simple and complex fluidsa)

  2013cites this paper
• A note on the mirror-symmetric coherent structure in plane Couette flow

  2013cites this paper
• Open Archive Toulouse Archive Ouverte (OATAO)

  2013cites this paper
• Revealing the state space of turbulent pipe flow by symmetry reduction

  2012cites this paper
• Edge state in pipe flow experiments.

  2012cites this paper
• Travelling Wave Solutions in Square Duct Flow

  2012cites this paper
• Cartography of high-dimensional flows: a visual guide to sections and slices.

  2012cites this paper
• A purely nonlinear route to transition approaching the edge of chaos in a boundary layer

  2012influential citation
• Asymmetric travelling waves in a square duct

  2012cites this paper
• Dynamics on the laminar-turbulent boundary and the origin of the maximum drag reduction asymptote.

  2011cites this paper
• NONLINEAR TRAVELLING WAVE SOLUTIONS IN SQUARE DUCT FLOW

  2011influential citation
• Bifurcations and instabilities in sliding Couette flow

  2011cites this paper
• Minimal seeds for shear flow turbulence: using nonlinear transient growth to touch the edge of chaos

  2011cites this paper
• Lecture 8 : Edge Tracking – Walking the Tightrope Rich Kerswell

  2011cites this paper
• Experimental Studies of Transition to Turbulence in a Pipe

  2011cites this paper
• From travelling waves to mild chaos: a supercritical bifurcation cascade in pipe flow

  2011cites this paper
• Spatio-temporal dynamics in pipe flow

  2011cites this paper
• États limites et bouffées turbulentes en conduite cylindrique

  2010cites this paper
• Petrov-Galerkin computation of nonlinear waves in pipe flow of shear-thinning fluids: First theoretical evidences for a delayed transition

  2010cites this paper
• A new nonlinear vortex state in square-duct flow

  2010influential citation
• Slug genesis in cylindrical pipe flow

  2010influential citation
• Takens–Bogdanov bifurcation of travelling-wave solutions in pipe flow

  2010cites this paper
• Transition to turbulence for flows without linear criticality

  2010cites this paper
• Optimally amplified large-scale streaks and drag reduction in turbulent pipe flow.

  2010cites this paper
• Coherent structures in fully-developed pipe turbulence

  2009cites this paper
• Localized edge states in plane Couette flow

  2009cites this paper
• Nonlinear coherent structures in a square duct

  2009cites this paper
• Introduction. Turbulence transition in pipe flow: 125th anniversary of the publication of Reynolds' paper

  2009cites this paper
• Spatiotemporal perspective on the decay of turbulence in wall-bounded flows.

  2009cites this paper
• Three-dimensional traveling waves in a square duct.

  2009cites this paper
• Turbulent dynamics of pipe flow captured in a reduced model: puff relaminarization and localized ‘edge’ states

  2007cites this paper
• Transition in pipe flow: the saddle structure on the boundary of turbulence

  2007influential citation