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Exact coherent structures in pipe flow in the presence of wall transpiration

Published online by Cambridge University Press:  19 April 2022

O. Ozcakir Open the ORCID record for O. Ozcakir [Opens in a new window] ,
P. Hall Open the ORCID record for P. Hall [Opens in a new window]  and
H.M. Blackburn Open the ORCID record for H.M. Blackburn [Opens in a new window]
O. Ozcakir*
Affiliation:
School of Mathematical Sciences, Monash University, Clayton, VIC 3800, Australia Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC 3800, Australia
P. Hall
Affiliation:
School of Mathematical Sciences, Monash University, Clayton, VIC 3800, Australia
H.M. Blackburn
Affiliation:
Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC 3800, Australia
*
†Email address for correspondence: [email protected]
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Abstract

The linear instability of the flow in a pipe subjected to a wavelike transpiration velocity at the walls is considered. The fully nonlinear problem is formulated at high Reynolds numbers and small transpiration velocities. Solutions of the nonlinear system describing the bifurcation of disturbances caused by the transpiration are calculated and a complex bifurcation structure is uncovered with several nonlinear states possible at some transpiration amplitudes. The symmetries and structure of the nonlinear solutions are discussed.

JFM classification

Instability: Transition to turbulence Turbulent Flows: Pipe flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 940 , 10 June 2022 , A41
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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