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Chapter: Turbulence?

( blog, chapter Turbulence?) — Predrag Cvitanovic 2009-03-08

(the latest posts within a section at the top, blog-style)

A literature blog

Plumbers unite! A manifesto

A plane Couette blog

A pipe blog

A Taylor-Couette blog

A baroclinic blog


Mark here when summary completed.


Here all references to external literature (avoid them in the text proper, it is meant to be self-contained).


a streak is a region of streamwise velocity deviation from the mean streamwise velocity

rolls, vortices are defined in terms of spanwise normal section in-plane velocity (streammwise vorticity)


F.H. Busse\cite[BC96a]: Many fluid flows exhibit sequences of bifurcations in which new dynamical mechanisms are introduced. Symmetries may be broken at each bifurcation.

  • primary state exhibits full symmetries of the system (example: laminar solution)
  • secondary states take - for planar flows - form of 2d rolls
  • tertiary states are full 3d structures (examples: equilibria of plane Couette)
  • quaternary states a time-periodic 3d invariant solutions (examples: traveling waves?)

In plane Couette experiments a transition to turbulent from laminar occurs at Re of order of Re=1600/4, with 3d structures realized\cite{DD95} as early as Re=640/4



Mark here when correctly ordered. OK to have references not cited, as long as they are relevant to this chapter.

title = {Bifurcation Sequences in Fluid Flows and Coherent Structures in
      the Turbulent State},
author = {Busse, F. H. and Clever, R. M.},
year = {1996},
booktitle = {Advances in Turbulence VI},
editor = {Gavrilakis, S. and Machiels, L. and Monkewitz, P. A.},
series = {Proceedings of the Sixth European Turbulence Conference},
pages = {309-312}
@Article{ DD95,
  author = "O. Dauchot and F. Daviaud",
  title = "Finite-amplitude perturbation and spots growth mechanism in plane {C}ouette flow",
  journal = "Phys. Fluids",
  volume = "7",
  year = "1995",
  pages = "335--343"
AUTHOR = {van Veen, L. and Kawahara, G.},
TITLE = {The significance of simple invariant solutions
       in turbulent flows},
YEAR = {2012},
JOURNAL = {Ann. Rev. Fluid Mech.},
VOLUME = {44},
PAGES = {203–25}
AUTHOR = {van Veen, L. and Kawahara, G.},
TITLE = {Homoclinic tangle at the edge of shear turbulence},
YEAR = {2011},
JOURNAL = {Phys. Rev. Lett.},
VOLUME = {107},
PAGES = {114501}
chaosbook/pdes.txt · Last modified: 2012/04/13 08:20 by predrag