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Travelling waves in elliptic pipe flow

Published online by Cambridge University Press:  22 July 2021

Ozge Ozcakir Open the ORCID record for Ozge Ozcakir [Opens in a new window]  and
Philip Hall Open the ORCID record for Philip Hall [Opens in a new window]
Ozge Ozcakir*
Affiliation:
School of Mathematical Sciences, Monash University, Clayton, VIC 3800, Australia
Philip Hall
Affiliation:
School of Mathematical Sciences, Monash University, Clayton, VIC 3800, Australia
*
†Email address for correspondence: [email protected]
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Abstract

Families of exact coherent states in elliptical pipe flow obtained from the travelling-wave solutions in circular pipe flow by a continuation approach are found. Results are given in a regime of the aspect ratio $A$ in which the laminar flow is linearly stable. The results suggest the possibility of two distinct classes of solutions of elliptical travelling waves at higher values of $A$: (i) rotationally symmetric centre-mode states that collapse towards the pipe centre and (ii) rotationally asymmetric vortex–wave interaction states with additional mirror symmetry exhibiting organization of the waves around a critical layer. These are the first calculations of three-dimensional travelling waves in elliptical pipes. Investigation of these states has the potential to provide fresh insight into the relationship between exact coherent structures in Poiseuille flow in pipes and channels.

JFM classification

Instability: Nonlinear instability Instability: Transition to turbulence
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 923 , 25 September 2021 , R3
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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