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gtspring2009:research_projects:siminos:blog

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Siminos research blog, spring 2009

:?: Is $L_y$ fixed to 2 everywhere in channelflow?

Moved this question to the channelflow programming Q&A page. John Gibson 2009-02-10 10:16 EST

LB unstable manifold movies. W03 box: α=1.14, γ=2.5. Re=400

u_o=u_LB+ 0.001 \mathbf{u}_1, where \mathbf{u}_1 the unstable eigenvector. Integrated for t=0 to 500.

u_o= u_LB- 0.001 \mathbf{u}_1. Integrated for t=0 to 500.

:-( I cannot get dokuwiki flashplayer plugin to work so I have uploaded avi files on flickr and embedded here. Can you leave your broken dokuwiki plugin code in the blog so that I can diagnose it? John Gibson 2009-02-10 10:18 EST Well, this was before you've posted instructions on uploading movies, now I know what was wrong. I like the quality of the movies in flickr so I will not remove them. I'll try flashplayer plugin next time. No time to get rid of gray background and crop, sorry. — Evangelos Siminos 2009-02-16 13:34

:-( I also got corrupted avi files from matlab, so I had to modify makemovie.m to generate png frames and then used dvd-slideshow to generate the movie (in vob format) and WinFF to convert to avi. Bummer. The matlab movie-making system is not as robust as I'd like. I saw plenty of inexplicable glitches while developing the scripts and then I would tweak until they disappeared. I would really like to hook up to a more robust and open-source visualization system, prefereably with a Python interface. Would be a great project for someone…. John Gibson 2009-02-10 10:18 EST

:-| I wait for instruction on phase-space projections in the tutorial as I can't understand those videos. Is the only available documentation the one through the –help option? Thanks for the reminder. I will write documentation on this a.s.a.p. John Gibson 2009-02-10 10:18 EST

:?: It looks like the dynamics approaches the laminar state but very slowly. Why?

:!: Laminar state's least contracting eigenvalue is very small (hopefully it is listed in a paper with Halcrow, and we have the discussion in one of the old Gibson's blogs, hard to fish out which one), hence once a trajectory gets close to death, it dies sloooowly. It's worth your time to go through John's derivation, as it is the only set of stability eigenvalues that can be computed anlytically. Contraction rate is slow presumably because laminar state is the least dissipation state, so small smooth perturbations dissipate away very slowly. — Predrag Cvitanovic 2009-02-10 04:07

:-) After discussing with John we concluded it could as well be an artifact of matlab rescaling the vectors' magnitudes in the movies. The state comes very close to laminar as one can see by looking at the L2 norm. — Evangelos Siminos 2009-02-16 13:34

Two continuous symmetry reduction papers of interest: Rowley and Marsden 2000: rowley_and_marsden_-_2000_-_reconstruction_equations_and_the_karhunen-loeve_ex.pdf Rowley et.al. 2003: no3404.pdf. The procedure looks like a trick Arnol'd suggests in “Ordinary differential equations” book. It works “locally” but how are the pieces glued together?

gtspring2009/research_projects/siminos/blog.1235272155.txt.gz · Last modified: 2009/02/21 19:09 by siminos