| 1. |
- Duguet, Yohann, et al.
(author)
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Relative periodic orbits in transitional pipe flow
- 2008
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In: Physics of fluids. - : AIP Publishing. - 1070-6631 .- 1089-7666. ; 20:11, s. 114102-
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Journal article (peer-reviewed)abstract
- A dynamical system description of the transition process in shear flows with no linear instability starts with knowledge of exact coherent solutions, among them traveling waves (TWs) and relative periodic orbits (RPOs). We describe a numerical method to find such solutions in pipe flow and apply it in the vicinity of a Hopf bifurcation from a TW which looks to be especially relevant for transition. The dominant structural feature of the RPO solution is the presence of weakly modulated streaks. This RPO, like the TW from which it bifurcates, sits on the laminar-turbulent boundary separating initial conditions which lead to turbulence from those which immediately relaminarize.
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| 2. |
- Pringle, Chris C. T., et al.
(author)
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Highly symmetric travelling waves in pipe flow
- 2009
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In: Philosophical Transactions. Series A. - : The Royal Society. - 1364-503X .- 1471-2962. ; 367:1888, s. 457-472
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Journal article (peer-reviewed)abstract
- 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.
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