Dynamical systems and the transition to turbulence in linearly stable shear flows

No abstract is available for this paper.

• Publication year

  2008

• Venue

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

• Publication date

  2008-04-13

• Fields of study

  Medicine, Physics

• Identifiers
  DOI 10.1098/rsta.2007.2132PMID 17984033
• 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.

• Periodic motion representing isotropic turbulence

  2018cited by this paper
• Turbulence transition and the edge of chaos in pipe flow.

  2007influential reference
• Turbulence transition in pipe flow

  2007cited by this paper
• Asymmetric, helical, and mirror-symmetric traveling waves in pipe flow.

  2007cited by this paper
• Decay of turbulence in pipe flow.

  2006cited by this paper
• Statistical analysis of coherent structures in transitional pipe flow.

  2006cited by this paper
• RECENT OBSERVATIONS OF THE TRANSITION TO TURBULENCE IN A PIPE

  2006cited by this paper
• Finite lifetime of turbulence in shear flows

  2006influential reference
• Edge of chaos in pipe flow.

  2006cited by this paper
• Critical behavior in the relaminarization of localized turbulence in pipe flow.

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

  2006cited by this paper
• IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions

  2005cited by this paper
• INVITED ARTICLE: Recent progress in understanding the transition to turbulence in a pipe

  2005cited by this paper
• Dynamical Systems and the Transition to Turbulence

  2005cited by this paper
• Turbulence regeneration in pipe flow at moderate Reynolds numbers.

  2005cited by this paper
• Fractal lifetimes in the transition to turbulence.

  2004cited by this paper
• Experimental Observation of Nonlinear Traveling Waves in Turbulent Pipe Flow

  2004cited by this paper
• A low-dimensional model for turbulent shear flows

  2004cited by this paper
• Streak breakdown instability in pipe Poiseuille flow

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

  2003influential reference
• Linearized pipe flow to Reynolds number 10 7

  2003cited by this paper
• Sensitive dependence on initial conditions in transition to turbulence in pipe flow

  2003cited by this paper
• Traveling waves in pipe flow.

  2003cited by this paper
• A periodic-like solution in channel flow

  2003cited by this paper
• Homotopy of exact coherent structures in plane shear flows

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

  2001cited by this paper
• Periodic motion embedded in plane Couette turbulence: regeneration cycle and burst

  2001cited by this paper
• Persistent turbulence in annealed plane Couette flow

  2000cited by this paper
• Transition from the Couette-Taylor system to the plane Couette system.

  2000cited by this paper
• The onset of shear flow turbulence

  2000cited by this paper
• Transition to turbulence in a shear flow.

  1999cited by this paper
• Low-dimensional dynamics embedded in a plane Poiseuille flow turbulence : Traveling-wave solution is a saddle point ?

  1999cited by this paper
• Discontinuous transition to spatiotemporal intermittency in plane Couette flow

  1998influential reference
• Experimental evidence of streamwise vortices as finite amplitude solutions in transitional plane Couette flow

  1998influential reference
• Statistical analysis of the transition to turbulence in plane Couette flow

  1998influential reference
• Three-dimensional traveling-wave solutions in plane Couette flow

  1997cited by this paper
• Fractal Stability Border in Plane Couette Flow

  1997cited by this paper
• Tertiary and quaternary solutions for plane Couette flow

  1997influential reference
• Nonlinear solutions of modified plane Couette flow in the presence of a transverse magnetic field

  1996cited by this paper
• On the instability of pipe Poiseuille flow

  1996cited by this paper
• Transition to Turbulence in Pipe Flow

  1995cited by this paper
• Transition to turbulence in constant-mass-flux pipe flow

  1995cited by this paper
• Optimal energy density growth in Hagen–Poiseuille flow

  1994cited by this paper
• Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment

  1994cited by this paper
• Periodic orbit analysis of the Lorenz attractor

  1994cited by this paper
• Bénard cells and Taylor vortices

  1993cited by this paper
• Experiments on transition in plane Couette flow

  1992cited by this paper
• Subcritical transition to turbulence in plane Couette flow.

  1992influential reference
• Three-dimensional convection in a horizontal fluid layer subjected to a constant shear

  1992cited by this paper
• Periodic orbit expansions for classical smooth flows

  1991cited by this paper
• Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity

  1990cited by this paper
• Turbulence without strange attractor

  1989cited by this paper
• Irregular scattering

  1988influential reference
• Integrable and chaotic motions of four vortices II. Collision dynamics of vortex pairs

  1988cited by this paper
• Onset of Turbulence in a Pipe

  1988cited by this paper
• Point vortex dynamics: recent results and open problems

  1987cited by this paper
• Repellers, semi-attractors, and long-lived chaotic transients

  1985cited by this paper
• Escape from strange repellers.

  1984cited by this paper
• NONLINEAR OSCILLATIONS, DYNAMICAL SYSTEMS, AND BIFURCATIONS OF VECTOR FIELDS (Applied Mathematical Sciences, 42)

  1984cited by this paper
• Stochastic aspect of two-particle scattering

  1983cited by this paper
• Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

  1983cited by this paper
• The Stability of Plane Couette Flow.

  1976cited by this paper
• Stability of plane Couette flow

  1969cited by this paper
• Hydrodynamic and Hydromagnetic Stability

  1961cited by this paper

• Steady-state bifurcation and regularity of nonlinear Burgers equation with mean value constraint

  2025cites this paper
• Search for unstable relative periodic orbits in channel flow using symmetry-reduced dynamic mode decomposition

  2025cites this paper
• On the oscillatory dynamics of a Saffman–Taylor finger with a bubble at its tip

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

  2025cites this paper
• Route to turbulence in magnetohydrodynamic square duct flow

  2025cites this paper
• A comprehensive experimental and numerical study of Taylor–Couette flow on superhydrophobic surfaces

  2025cites this paper
• Chaotic edge regimes in magnetohydrodynamic channel flow: An alternative path towards the tipping point

  2024cites this paper
• Sustainable drag reduction in Taylor-Couette flow using riblet superhydrophobic surfaces

  2024cites this paper
• A simple and rigorous method of modal and nonmodal linear stability analysis of Hagen-Poiseuille laminar flow in pipe

  2024cites this paper
• A Cascade Model for the Discontinuous Absorbing Phase Transition Between Turbulent and Laminar Flows

  2024cites this paper
• Periodic dynamics in viscous fingering

  2024cites this paper
• Finding the point of no return: dynamical systems theory applied to the moving contact-line instability

  2023cites this paper
• Homoclinic bifurcation and switching of edge state in plane Couette flow.

  2023cites this paper
• HOMOCLINIC BIFURCATION, EDGE STATES, AND BOUNDARY CRISIS IN PLANE COUETTE FLOW

  2022cites this paper
• High dimensional tori and chaotic and intermittent transients in magnetohydrodynamic Couette flows

  2022cites this paper
• The unpredictable nature of bubble evolution

  2022cites this paper
• Orr mechanism in transition of parallel shear flow

  2021cites this paper
• Symmetry-reduced dynamic mode decomposition of near-wall turbulence

  2021cites this paper
• Collapse of transitional wall turbulence captured using a rare events algorithm

  2021cites this paper
• Exact coherent structures and shadowing in turbulent Taylor–Couette flow

  2021cites this paper
• Stability and bifurcation of dynamic contact lines in two dimensions

  2021cites this paper
• Dynamics of laminar and transitional flows over slip surfaces: effects on the laminar–turbulent separatrix

  2020cites this paper
• The life and fate of a bubble in a geometrically perturbed Hele-Shaw channel

  2020cites this paper
• Basis for finding exact coherent states.

  2020cites this paper
• The influence of invariant solutions on the transient behaviour of an air bubble in a Hele-Shaw channel

  2019cites this paper
• A Model of a Tidally Synchronized Solar Dynamo

  2019cites this paper
• Self-sustained elastoinertial Tollmien–Schlichting waves

  2019cites this paper
• The onset of transient turbulence in minimal plane Couette flow

  2019cites this paper
• An experimental investigation into spatiotemporal intermittencies in turbulent channel flow close to transition

  2019cites this paper
• Resonance-driven ion transport and selectivity in prokaryotic ion channels.

  2019cites this paper
• Heteroclinic and homoclinic connections in a Kolmogorov-like flow.

  2019cites this paper
• A Model of a Tidally Synchronized Solar Dynamo

  2018cites this paper
• Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics

  2018cites this paper
• High-speed shear-driven dynamos. Part 2. Numerical analysis

  2018cites this paper
• Small scale exact coherent structures at large Reynolds numbers in plane Couette flow

  2017cites this paper
• New equilibrium solution branches of plane Couette flow discovered using a project-then-search method

  2017cites this paper
• Exact coherent states with hairpin-like vortex structure in channel flow

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

  2017cites this paper
• Using nonlinear optimization to understand coherent structures in turbulence and transition

  2017cites this paper
• Laminar-Turbulent Patterning in Transitional Flows

  2017cites this paper
• The engine behind (wall) turbulence: perspectives on scale interactions

  2017cites this paper
• State space analysis of minimal channel flow

  2017cites this paper
• Turbulent Taylor–Couette flow with stationary inner cylinder

  2016cites this paper
• Exact coherent states for grooved Couette flows

  2016cites this paper
• Generalised nonlinear stability of stratified shear flows: adjoint-based optimisation, Koopman modes, and reduced models

  2016cites this paper
• Self-organisation processes in (magneto)hydrodynamic turbulence

  2016cites this paper
• Topological stability criteria for networking dynamical systems with Hermitian Jacobian

  2016cites this paper
• Surface-roughness restricts families of exact coherent structures in wall-bounded flows

  2016cites this paper
• Transition to turbulence in wall-bounded flows: Where do we stand?

  2016cites this paper
• Transition in the asymptotic suction boundary layer over a heated plate

  2016cites this paper
• Sudden Relaminarization and Lifetimes in Forced Isotropic Turbulence.

  2015cites this paper
• Towards a model of large scale dynamics in transitional wall-bounded flows

  2015cites this paper
• HOMOCLINIC ORBITS IN TRANSITIONAL PLANE COUETTE FLOW

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

  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
• Recurrent flow analysis in spatiotemporally chaotic 2-dimensional Kolmogorov flow

  2014cites this paper
• Groebner Basis Methods for Stationary Solutions of a Low-Dimensional Model for a Shear Flow

  2014cites this paper
• Reduced description of exact coherent states in parallel shear flows.

  2014cites this paper
• Verfolgung transitionaler Strömungstrukturen bei kleinen Reynoldszahlen in einer 3200D Rohrmessstrecke Tracking transitional flow structures at low Reynolds number in a 3200D pipe flow facility

  2014cites this paper
• On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular

  2014cites this paper
• Streamwise and doubly-localised periodic orbits in plane Poiseuille flow

  2014cites this paper
• Splitting of a turbulent puff in pipe flow

  2014cites this paper
• Groebner Basis Methods for Stationary Solutions of a Low-Dimensional Model for a Shear Flow

  2014cites this paper
• Periodically bursting edge states in plane Poiseuille flow

  2013cites this paper
• Progress in Transition Modeling and Control

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

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

  2013cites this paper
• HOMOCLINIC ORBITS AND THEIR RELEVANCE TO THE ONSET OF TRANSIENT TURBULENCE IN WALL FLOW

  2013cites this paper
• Local Reynolds number and thresholds of transition in shear flows

  2013cites this paper
• An Application of Robust Parameter Estimation in Environmental Physics

  2013cites this paper
• Local Reynolds number and thresholds of transition in shear flows

  2013cites this paper
• Exact Coherent State with Travelling Hairpin Vortex in Plane Couette Flow

  2012cites this paper
• Numerical Bifurcation Methods and their Application to Fluid Dynamics: Analysis beyond Simulation

  2012cites this paper
• Ten Chapters in Turbulence: Dynamics of Wall-Bounded Turbulence

  2012cites this paper
• Subcritical transition to turbulence: What we can learn from the physics of glasses.

  2012cites this paper
• Turbulence transition in shear flows: chaos in high-dimensional spaces

  2012cites this paper
• Edge states for the turbulence transition in the asymptotic suction boundary layer

  2012cites this paper
• On the growth of laminar–turbulent patterns in plane Couette flow

  2012cites this paper
• 6 Dynamics of Wall-Bounded Turbulence

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

  2011cites this paper
• From temporal to spatiotemporal dynamics in transitional plane Couette flow.

  2011influential citation
• On the decay of turbulence in plane Couette flow

  2011cites this paper
• Transient turbulence in Taylor Couette flow

  2011influential citation
• Pattern Fluctuations in Transitional Plane Couette Flow

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

  2011cites this paper
• The Significance of Simple Invariant Solutions in Turbulent Flows

  2011influential citation
• Universal threshold of the transition to localized turbulence in shear flows

  2011cites this paper
• Coherent structures in transitional plane Couette flow

  2011cites this paper
• On the decay of turbulence in plane Couette flow

  2011cites this paper
• Turbulent shear flow in a rapidly rotating spherical annulus

  2010cites this paper
• On modelling transitional turbulent flows using under-resolved direct numerical simulations: the case of plane Couette flow

  2010influential citation
• A Robust Control Approach to Understanding Nonlinear Mechanisms in Shear Flow Turbulence

  2010cites this paper
• On Matrix-Free Computation of 2D Unstable Manifolds

  2010cites this paper
• Takens–Bogdanov bifurcation of travelling-wave solutions in pipe flow

  2010cites this paper
• Homoclinic tangle on the edge of shear turbulence.

  2010cites this paper
• Angular redistribution of nonlinear perturbations: a universal feature of nonuniform flows.

  2010cites this paper
• Introduction. Turbulence transition in pipe flow: 125th anniversary of the publication of Reynolds' paper

  2009cites this paper
• Particle Tracking Velocimetry in Transitional Plane Couette Flow

  2009cites this paper
• About the oscillatory possibilities of the dynamical systems

  2009influential citation
• Geometry of state space in plane Couette flow

  2009cites this paper