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Highly-symmetric travelling waves in pipe flow

Chris Pringle*, Yohann Duguet* † & Rich Kerswell* *University of Bristol † Linné Flow Centre, KTH Mechanics. Highly-symmetric travelling waves in pipe flow. Pipe Flow. Linearly stable for all Reynolds numbers Sustained turbulence possible after Re ≈ 1700-2000

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Highly-symmetric travelling waves in pipe flow

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  1. Chris Pringle*, Yohann Duguet*† & Rich Kerswell* *University of Bristol †Linné Flow Centre, KTH Mechanics Highly-symmetric travelling waves in pipe flow

  2. Pipe Flow • Linearly stable for all Reynolds numbers • Sustained turbulence possible after Re ≈ 1700-2000 Re based upon mean velocity and pipe diameter Poiseuille 1840 Hagen 1839

  3. Travelling Waves Asymmetric (S1) S2 S3 Mirror Symmetric Faisst & Eckhardt (2003), Wedin & Kerswell (2004), Pringle & Kerswell (2007)

  4. Travelling Waves in Phase space S2 S3 Faisst & Eckhardt (2003), Wedin & Kerswell (2004), Pringle & Kerswell (2007)

  5. Travelling Waves within the Edge • Strikingly different cross-sections • Alternative axial evolution • Additional mirror symmetry A3 C3 S2 Duguet, Willis & Kerswell (2008)

  6. Symmetries • All of the TWs originally discovered only possess shift-&-reflect symmetry

  7. M-class Travelling Waves M2 M3 M4 • Double layer of streaks • Rolls bisect layers • Relatively quiescent center

  8. N-class Travelling Waves N2 N3 N4 • Stronger, more active rolls • Larger streaks

  9. M1 and N1 • M1 is known from Pringle & Kerswell (2007) • N1 is entirely new

  10. Travelling Waves in Phase space

  11. Travelling Waves in Phase space

  12. S3 and N3

  13. Stability of N2

  14. Stability of N2

  15. Summary • Two new classes of TW have been explored • They occur earlier than previously seen TWs • They exhibit much higher friction factors – they are ‘more nonlinear’ • Appear to be more fundamental – the original TWs bifurcate off them

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