Coherent structures in localized and global pipe turbulence.
The recent discovery of unstable traveling waves (TWs) in pipe flow has been hailed as a significant breakthrough with the hope that they populate the turbulent attractor. We confirm the existence of coherent states with internal fast and slow streaks commensurate in both structure and energy with known TWs using numerical simulations in a long pipe. These only occur, however, within less energetic regions of (localized) "puff" turbulence at low Reynolds numbers (Re=2000-2400), and not at all in (homogeneous) "slug" turbulence at Re=2800. This strongly suggests that all currently known TWs sit in an intermediate region of phase space between the laminar and turbulent states rather than being embedded within the turbulent attractor itself. New coherent fast streak states with strongly decelerated cores appear to populate the turbulent attractor instead.
Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom. A.Willis@bris.ac.uk
Ashley P
AP
Willis
Rich R
RR
Kerswell