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 S2 S3 Asymmetric (S1) 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 A3C3S2 Duguet, Willis & Kerswell (2008)

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

7. M-class Travelling Waves Double layer of streaks Rolls bisect layers Relatively quiescent center M2M3M4

8. N-class Travelling Waves Stronger, more active rolls Larger streaks N2N3N4

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

10. Travelling Waves in Phase space

12. S3 and N3

13. 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