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====== Siminos research blog, spring 2009 ====== :?: Is <latex>$L_y$</latex> fixed to 2 everywhere in channelflow? ===== LB unstable manifold movies. W03 box: α=1.14, γ=2.5. Re=400 ===== <latex>u_o=u_LB+ 0.001 \mathbf{u}_1</latex>, where <latex>\mathbf{u}_1</latex> the unstable eigenvector. Integrated for t=0 to 500. <html> <object type="application/x-shockwave-flash" width="640" height="480" data="http://www.flickr.com/apps/video/stewart.swf?v=67090" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000"> <param name="flashvars" value="intl_lang=en-us&photo_secret=71f2508ddd&photo_id=3249057643"></param> <param name="movie" value="http://www.flickr.com/apps/video/stewart.swf?v=67090"></param> <param name="bgcolor" value="#000000"></param> <param name="allowFullScreen" value="true"></param><embed type="application/x-shockwave-flash" src="http://www.flickr.com/apps/video/stewart.swf?v=67090" bgcolor="#000000" allowfullscreen="true" flashvars="intl_lang=en-us&photo_secret=71f2508ddd&photo_id=3249057643" height="480" width="640"></embed></object> </html> <latex>u_o= u_LB- 0.001 \mathbf{u}_1</latex>. Integrated for t=0 to 500. <html> <object type="application/x-shockwave-flash" width="640" height="480" data="http://www.flickr.com/apps/video/stewart.swf?v=67090" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000"> <param name="flashvars" value="intl_lang=en-us&photo_secret=47633fec8a&photo_id=3249057653"></param> <param name="movie" value="http://www.flickr.com/apps/video/stewart.swf?v=67090"></param> <param name="bgcolor" value="#000000"></param> <param name="allowFullScreen" value="true"></param><embed type="application/x-shockwave-flash" src="http://www.flickr.com/apps/video/stewart.swf?v=67090" bgcolor="#000000" allowfullscreen="true" flashvars="intl_lang=en-us&photo_secret=47633fec8a&photo_id=3249057653" height="480" width="640"></embed></object> </html> :-( I cannot get dokuwiki flashplayer plugin to work so I have uploaded avi files on flickr and embedded here. :-( 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. :-| 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? :?: 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@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-10 04:07//
