Highly-symmetric travelling waves in pipe flow
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Transcript of 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 Re based upon mean velocity and pipe diameter
Poiseuille 1840Hagen 1839
Travelling Waves
S2
S3
Asymmetric(S1)
Mirror Symmetric
Faisst & Eckhardt (2003), Wedin & Kerswell (2004), Pringle & Kerswell (2007)
Travelling Waves in Phase spaceS2
S3Faisst & Eckhardt (2003), Wedin & Kerswell (2004), Pringle & Kerswell (2007)
Travelling Waves within the Edge
• Strikingly different cross-sections• Alternative axial evolution• Additional mirror symmetry
A3 C3 S2
Duguet, Willis & Kerswell (2008)
Symmetries
• All of the TWs originally discovered only possess shift-&-reflect symmetry
M-class Travelling Waves
• Double layer of streaks• Rolls bisect layers• Relatively quiescent center
M2 M3 M4
N-class Travelling Waves
•Stronger, more active rolls•Larger streaks
N2 N3 N4
• M1 is known from Pringle & Kerswell (2007)
• N1 is entirely new
M1 and N1
Travelling Waves in Phase space
Travelling Waves in Phase space
S3 and N3
Stability of N2
Stability of N2
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