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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}} ===== Blog ===== **2009-11-25 Humbledt Plumber to Benny Lautrup:** methinks, "Pipes and planes" glides down your tongue like poetry "Plates and pipes" (chapter title in Lautrup's book) is strictly engineering - no physicists thinks of a "plate"; infinite in all directions is called a "plane". **2009-07-27 Balu /BALASUBRAMANYA Nadiga/** Your comments/suggestions on [[http://ChaosBook.org/library/NaLu01.pdf|Global Bifurcation of Shilnikov Type in a Double-Gyre Ocean Model]] by Nadiga and Luce, a paper on homoclinic chaos on the way to turbulence in the simpler setting of the barotropic vorticity eqn. in the context of ocean flows would be very much appreciated. ===== Plumbers unite! A manifesto ===== [[researchProgram|click here]] ===== A plane Couette blog ===== [[pCf|click here]] ===== A pipe blog ===== [[pipes|click here]] ===== A Taylor-Couette blog ===== [[Taylor-Couette|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). ==== Nomenclature ==== 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) **bifurcations**: 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~~
