Asymmetric, helical, and mirror-symmetric traveling waves in pipe flow

Chris C T Pringle, Rich R. Kerswell

Research output: Contribution to journalArticlepeer-review

91 Citations (Scopus)


New families of three-dimensional nonlinear traveling waves are discovered in pipe flow. In contrast with known waves, they possess no discrete rotational symmetry and exist at a significantly lower Reynolds numbers (Re). First to appear is a mirror-symmetric traveling wave which is born in a saddle node bifurcation at Re=773. As Re increases, "asymmetric" modes arise through a symmetry-breaking bifurcation. These look to be a minimal coherent unit consisting of one slow streak sandwiched between two fast streaks located preferentially to one side of the pipe. Helical and nonhelical rotating waves are also found, emphasizing the richness of phase space even at these very low Reynolds numbers.

Original languageEnglish
Article number074502
JournalPhysical Review Letters
Issue number7
Publication statusPublished - 16 Aug 2007

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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