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Exact coherent structures in pipe flow: travelling wave solutions

  • H. WEDIN (a1) and R. R. KERSWELL (a1)

Abstract

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.

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Author to whom correspondence should be addressed: R.R.Kerswell@bris.ac.uk
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Exact coherent structures in pipe flow: travelling wave solutions

  • H. WEDIN (a1) and R. R. KERSWELL (a1)

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