Chris Pringle, Yohann Duguet

1
Highly-symmetric travelling waves in pipe flow

• Chris Pringle, Yohann Duguet Rich Kerswell
• University of Bristol
• Linné Flow Centre, KTH Mechanics

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
A3
C3
S2

• Strikingly different cross-sections
• Alternative axial evolution
• Additional mirror symmetry

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