chaosbook:pdes

(ChaosBook.org blog, chapter Turbulence?) — *Predrag Cvitanovic 2009-03-08*

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

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)

**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`

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" }

@Article{KaUhVe12, 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} }

@Article{VeKa11, 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