Asymmetric, helical and mirror-symmetric travelling waves in pipe flow
arXiv:physics/0703210 · doi:10.1103/PhysRevLett.99.074502
Abstract
New families of three-dimensional nonlinear travelling waves are discovered in pipe flow. In contrast to known waves (Faisst & Eckhardt Phys. Rev. Lett. 91, 224502 (2003), Wedin & Kerswell, J. Fluid Mech. 508, 333 (2004)), they possess no rotational symmetry and exist at much lower Reynolds numbers. Particularly striking is an `asymmetric mode' which has one slow streak sandwiched between two fast streaks located preferentially to one side of the pipe. This family originates in a pitchfork bifurcation from a mirror-symmetric travelling wave which can be traced down to a Reynolds number of 773. Helical and non-helical rotating waves are also found emphasizing the richness of phase space even at these very low Reynolds numbers. The delay in Reynolds number from when the laminar state ceases to be a global attractor to turbulent transition is then even larger than previously thought.
4 pages, 7 figures (2 at low resolution)
References in corpus (7)
- Travelling waves in pipe flow
- Scaling of the turbulence transition threshold in a pipe
- Low-dimensional dynamics embedded in a plane Poiseuille flow turbulence : Traveling-wave solution is a saddle point ?
- Lower branch coherent states in shear flows: transition and control
- Transition to turbulence in particulate pipe flow
- Recurrence of Travelling Waves in Transitional Pipe Flow
- Statistical analysis of coherent structures in transitional pipe flow
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- Transition in pipe flow: the saddle structure on the boundary of turbulence
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- Minimal seeds for shear flow turbulence: using nonlinear transient growth to touch the edge of chaos
- Recurrence of Travelling Waves in Transitional Pipe Flow
- On the transient nature of localized pipe flow turbulence
- Relative periodic orbits form the backbone of turbulent pipe flow
- Revealing the state space of turbulent pipe flow by symmetry reduction
- Relative periodic orbits in transitional pipe flow
- Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow
- Highly-symmetric travelling waves in pipe flow
- The critical layer in pipe flow at high Reynolds number
- An optimal path to transition in a duct
- On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular
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- Dimensionality Reduction and Reduced Order Modeling for Traveling Wave Physics
- Extended localized structures and the onset of turbulence in channel flow
- From travelling waves to mild chaos: a supercritical bifurcation cascade in pipe flow
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- Takens-Bogdanov bifurcation of travelling wave solutions in pipe flow
- Stable Manifolds and the Transition to Turbulence in Pipe Flow
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- Suppression of turbulence and travelling waves in a vertical heated pipe
- Heteroclinic path to spatially localized chaos in pipe flow
- Long wavelength instability of coherent structures in plane Couette flow
- Complexity of the laminar-turbulent boundary in pipe flow
- Heteroclinic and Homoclinic Connections in a Kolmogorov-Like Flow
- An adaptive preconditioner for steady incompressible flows
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- Transition in the asymptotic suction boundary layer over a heated plate
- Dynamics of a Data-Driven Low-Dimensional Model of Turbulent Minimal Pipe Flow
- Exact and Asymptotic Conditions on Traveling Wave Solutions of the Navier-Stokes Equations
- Three-dimensional coherent structures in a curved pipe flow
- A traveling wave bifurcation analysis of turbulent pipe flow
- The chimera revisited: Wall- and magnetically-bounded turbulent flows
- The role of periodic orbits and bubbles of chaos during the transition to turbulence