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<- [[:chaosbook]]

====== Chapter: Turbulence? ======

(ChaosBook.org blog, chapter [[http://chaosbook.org/paper.shtml#PDEs|Turbulence?]])  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-08//

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

{{gtspring2009:pc.jpg}} 

===== Plumbers unite! A manifesto =====

[[researchProgram|click here]]

===== A plane Couette blog =====

[[pCf|click here]]

===== Rėsumė =====

 Mark here when summary completed.

===== Commentary =====

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

==== Bifurcations - nomenclature ====

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''


===== Exercises =====

===== References =====

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


  @InProceedings{BC96a,
  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"
  }

~~DISCUSSION~~
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