Exact coherent structures in pipe flow: travelling wave solutions

H Wedin, RR Kerswell

Research output: Contribution to journalArticle (Academic Journal)peer-review

316 Citations (Scopus)


Three-dimensional travelling wave solutions are found for pressure-driven fluid flow through a circular pipe. They consist of three well-defined flow features - streamwise rolls and streaks which dominate and streamwise-dependent wavy structures. The travelling waves can be classified by the m-fold rotational symmetry they possess about the pipe axis with m = 1, 2, 3, 4, 5 and 6 solutions identified. All are born out of saddle-node bifurcations with the lowest corresponding to m = 3 and traceable down to a Reynolds number (based on the mean velocity) of 1251. The new solutions are found using a constructive continuation procedure based upon key physical mechanisms thought generic to wall-bounded shear flows. It is believed that the appearance of these new alternative solutions to the governing equations as the Reynolds number is increased is a necessary precursor to the turbulent transition observed in experiments.
Translated title of the contributionExact coherent structures in pipe flow: travelling wave solutions
Original languageEnglish
Pages (from-to)333 - 371
Number of pages39
JournalJournal of Fluid Mechanics
Publication statusPublished - Jun 2004

Bibliographical note

Publisher: Cambridge University Press
Other identifier: IDS Number: 832RG


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