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request to John: Can you pencil in the group orbit of the Nagata upper branch on the same kind of plot as full states space portrait? The last time you plotted this was 2006-01-02 (the figure inserted here), and that was before we knew how to project onto solutions in the states space, so I suspect the wiggles in the far end of the torus are due to the projection on Fourier modes. The reason I need the group orbit traced out is to illustrate that several slices might be needed to reduce the symmetry. A slice is a (d-2) hyperplane in this plot, and it intersects the group orbit torus in at least two points - the closest and the furthest to the template. However, as turbulent solutions involve of order of at least 100 Fourier/Chebyshev modes of comparable magnitude, the torus embedded into the state space should be quite wiggly, and have a number of local extrema (intersections with the slice hyperplane). Ashly has done it for a pipe lower-branch equilibrium, but that one is too nice a torus to illustrate the general problem… Gratful if you could do it - involves only translating the UB in spanwise/streamwise increments and plotting the issuing mesh. — Predrag Cvitanovic 2011/08/05 12:35
Woods Hole GFD snippets: Listening to Tom Mullin: the flow in expanding pipes experiments are very interesting. Bifurcation analysis is worth dog turds - messy stuff happens much earlier. This problem is seriously begging for symmetry reduction. — Predrag Cvitanovic 2011/08/10 08:06
Woods Hole GFD snippets: Listening to Dan Hennignson: watching their movies of the boundary layer is very fascinating - if you find them on their homepage, please put a link here. Used 5000 processors for 6 months; amounts to 40 cm of Boing 747. Wu & Moin recent work claims that the initial forest of hairpin vortices survives. Not correct. They do not look at as high Reynolds numbers. They do not get the averages right. Henningson results are much better, and the transition region does not persist. For plane Couette, 800 1/2 heights domain, showed a movie that shows that initial noisy conditions go into stripes. That justifies using smaller cells.
Study this: They use Lagrange multipliers method to get to the adjoint Navier-Stokes evolution (this might be the way to deal with Domenico's noise evolution for hyperbolic fixed points, as well). Dan finds it remarkable that it works in optimized perturbation settings. This was discussed in detail in the talk “Questioning the question: The role of nonlinear optimal perturbations in the transition to turbulence of plane Couette flow” by Colm-cille Caulfield. (Colm-cille is an Irish name). Concerning finite amplitude perturbations for plane Couette transition from laminar to optimal (Monokrousos et al (2011)): For dissipation norm, with the same energy disturbance, localized disturbances are optimal (but not too localized - would be interesting to understand the scale). Numerical observations support this - the point where transition happens are localized. He showed a few movies where localized → vortex pair → streak, grow due lift-up effect → and pretty turbulent looking edge state. It is the Orr mechanism of generating a 2D packet (the strongest transient growth mechanism in 2D, a version of Kelvin circulation theorem), but it is essential that disturbance is 3D, or Orr mechanism would make the perturbation die away. — Predrag Cvitanovic 2011/08/04 07:12
If you want to fall asleep, biology video journal is the way to go. Still, it is intriguing way to publish, might be useful for complicated state-space narratives. — Predrag Cvitanovic 2011-02-01 20:23
Plumbers have been publicity grabbing recently: you might want to read Guenter Ahlers: Turbulent convection and NYT 09/28/09 Finding Order in the Apparent Chaos of Currents for your own edification. I have hear two very good talks by Guenter Ahlers recently, if I find them somewhere I'll link them here. Especially cute is their Santa Barbara work on turbulence within a cyllinder; the turbulent flow drifts, dragged by Earth's Corriolis force.
PC 2009-07-30: On spatially localized solutions: go hetero, or go unstable periodic?
a more detailed report from Trieste Turbulence 2009. Read in particular the new text in Halcrow svn blog. If someone would like to do something new of interest to the turbulence community, Yakhot suggest computing several scaling exponents from our exact solutions. — Predrag Cvitanovic 2009-07-29 03:17
Dustin, John Hyatt, would either of you be interested in seeing which of our EQB solutions could be continued to [2pi,2, pi] or [4pi, 2, 2pi]? It would be nice if most of them carried over and we could abandon our strange [2pi/1.14, 2, 2pi/2.5] box. Also, I would like to replace the binary .ff files in the database with H5 datafiles. UPDATE For the record I have already continued EQ1, EQ2, EQ4, EQ7, EQ9, and EQ10 to Lx,Lz = 2pi,pi. John Gibson 2009-07-29
Moved channelflow subversion server from zero.physics.gatech.edu to http://svn.channelflow.org/channelflow. Allows easier and more universal access (no need to tunnel through ssh.physics.gatech.edu, online browsing via WebSVN). For study group participants, I recommend downloading channelflow via SVN rather than using the tarballs. It's much better for distributing quick fixes. See Installation. John Gibson 2009-07-20 22:30 EST
There is a new paper by Nigel Goldenfeld's group that predicts super-exponential scaling of the lifetimes of transitional states with increasing Reynolds number. As far as I'm aware, it is the first theoretical prediction for a scaling law. You can find it arXiv.org/abs/0906.3572 — D. Borrero 2009-07-08 13:35
for Daniel: how to compress data files.
Posted a list of field properties of the W03 solutions in my blog. I think the table should not only be added to, but also put in a more resourceful location. I am up for suggestions. — Dustin Spieker 2009-07-06 15:00
See the PACE howto. Thanks for the tip on the continuesoln bug. I'm back from Minnesota but will not be on skype until I get a new sound card. Will try to do that this afternoon. John Gibson 2009-06-29 10:09 EST
to John: Can you put up an example script that you would qsub to the PACE cluster? —Dustin Spieker 2009-06-17 12:00
I'll be off in Minnesota for two weeks, June 13th-27th (schedule, phone numbers). Just wanted to alert you all. Internets access will be spotty but I will check in when I can.
Notes on Itano and Generalis paper. Nothing earthshaking - there are a few unanswered questions among the comments marked red. Their visualization is very pretty. It is interesting how hard (or impossible) is to recognize the same equilibrium from different visualizations.
The P47.18 orbit and others in the W03/GHC cell are now posted on the database. Continuation of solutions via repeated changegrid and findorbit should work fine. When you get the hang of that, try out the continuation utility. Its advantages are speed (it can take larger steps in parameter space), automation, and ability to continue around a corner from a lower to and upper branch (or vice versa). / John Gibson 2009-06-05 12:22 EST
to John: Could you post a data file for the 47.18 periodic orbit for me? Also, I have generated about 90 flow fields that I think are continuations of the Upper Branch Solution. I say “I think” because instead of using the continue solution utility, I used changegrid then I used findorbit to find a solution. Do these calculations have merit or do I need to use continuesoln? — Dustin Spieker 2009-06-02 09:24
Hi, Dustin. Sorry for the wait. I was at a conference, then had a long weekend, and now computer trouble (am reinstalling SUSE-11.1 on my home desktop as we speak). It sounds to me like findorbit is looking for equilibrium solutions rather than periodic orbits. The current version requires you to specify -orb or -eqb, which adds/removes the integration time T to/from the search space. If the version you're running doesn't require -orb or -eqb, it defaults to one or the other. Run findorbit -h to see which. I bet it defaults to eqb, in which case T=47 is a long time and close enough to the period of the unstable oscillation around EQ2 that it might be stuck in a local minimum. John Gibson 2009-05-27 11:33 EST
For John G: John, I had a quick question about the convergence of the findorbit program and you haven't been on Skype recently to talk about it. Recently I was seeing if the 47.18 Periodic orbit could be found from flow fields represented on the poincare sections I was producing. Close to the solution along the unstable manifold, findorbit only found the Upper Branch Equilibrium, even though I specified that the solution it should be looking for was periodic. But that is of secondary concern right now. I moved a little farther away from the equilibrium solution, and ran findorbit with the same input, namely:
findorbit -T 47.18 uPo4.ff
The run went through all 20 Newton hook steps and converged to a r(u,t) of about 0.0006. Because this was working well (at least I think), I saved all the data I had generated into a directory and continued the calculation using ubest.ff. Now the r(u,t) value, after another 18 Newton Hook Steps has only decreased to about 0.0003. Do you think that this calculation is still worth pursuing. I could send you the log files if you think your perusal would shed some light on the situation. — Dustin Spieker 2009-05-20 10:13
Everybody: I have been really sick with something I caught at the end of finals I'm better now and will be going back to work on 8-fold symmetry equilibria as per my orders from John G unless someone tells me otherwise. I need to get a PACE account, which I think involves someone emailing the OIT guy? John Hyatt 2009-05-10 14:42
Disappointing Poincare section results. I will explain these plots tomorrow in the study group. Corrections and suggestions are welcome. John Gibson 2009-04-13 14:58 EST
I'd like to talk to someone about me doing some actual research - more in the nite fishin' blog. John Hyatt 2009-04-09 13:41
Continuation of HKW orbits in Re. Ran 1,500th PACE job this weekend, since March 2008. If only that were publications…. John Gibson 2009-04-06 12:27 EST
Comments on color_scaling and another argument to not plot eigenvectors superimposed on the laminar flow. John Gibson 2009-04-03 14:22 EST
John H: The problems with your blog were caused by a missing ] to close off a link in my recent post –sorry. I found the error by looking in the dokuwiki source near the last word before the strange cut-off. John Gibson 2009-04-03 10am EST
Having problems updating my blog…every time I try to edit or restore an old edit it goes back to what it is now, where some of John G's most recent post and all of my response to it have vanished. I will try again tomorrow. John Hyatt 2009-04-03 3:00
1. why not to **add** laminar to plots of eigenfunctions. 2. In case you haven't noticed, there is a “Recent changes” button at the top right of the each page. It's a good way to find recent edits. 3. responses in hyatt nite fishin blog. 4. Boo-hoo, why doesn't any ever call? John Gibson 2009-04-01
Have I labeled UB eigenvectors correctly? (Re e_11,Im e_11) is the least contracting stable eigenvalue pair? Also, a vote against subtracting laminar from eigenvectors. — Predrag Cvitanovic 2009-03-31
New recurrence plots showing some interesting behavior between periodic and turbulent flow at 2dturbulence EDIT: added corresponding movies of the runs and velocity fields Jon Paprocki 2009-03-26 1:04 PM
Note on how to note on resize PNGs. John Gibson 2009-03-25 13:54 EST
Re howto:format page: I would like to get the APS Nonlinear Gallery to require flash and flash only (at least half of the formats used this year needed downloading things like VLC media player in order to be seen).
Study group participants: Don't be shy about calling me. johnfgibson on skype, 617-441-3609 begin_of_the_skype_highlighting 617-441-3609 end_of_the_skype_highlighting begin_of_the_skype_highlighting 617-441-3609 end_of_the_skype_highlighting begin_of_the_skype_highlighting 617-441-3609 end_of_the_skype_highlighting begin_of_the_skype_highlighting 617-441-3609 end_of_the_skype_highlighting begin_of_the_skype_highlighting 617-441-3609 end_of_the_skype_highlighting begin_of_the_skype_highlighting 617-441-3609 end_of_the_skype_highlighting begin_of_the_skype_highlighting 617-441-3609 end_of_the_skype_highlighting begin_of_the_skype_highlighting 617-441-3609 end_of_the_skype_highlighting on phone. I have a brand-new, clear-as-a-bell headset for skype. John Gibson 2009-03-25 10:53 EST
Same here - if I'm on skype, call - I can help with dynamical systems kinds of questions. — Predrag Cvitanovic 2009-03-25 07:58
New Poincare sections. It's hard to interpret 2D slices of 10^5 dimensions. Comments appreciated. John Gibson 2009-03-24 14:56 EST
New channelflow tarball on download page. Should help in compilation of poincare section code. John Gibson 2009-24-09 12:16 EST
Wrote How to compute a Poincare section. Not for the faint of heart. Also, more on factoring out the 4th-order translation symmetry. John Gibson 2009-03-20 12:29 EST
On quotienting the discrete translation pCf isotropy subgroup — John F. Gibson 2009-03-19
A Poincare section of the Nagata upper branch unstable manifold. Just a first stab. — John F. Gibson 2009-03-17
There are some nice movies in this year's APS gallery of nonlinear dynamics. In particular, JohnE and JohnG, check out Unstable Kolmogorov flow in granular matter - different physics, but strikingly like our plane Couette. — Predrag Cvitanovic 2009-03-15 10:43
Completed continuation of P19.02 orbit in Reynolds number. The plumbers are clamoring for this. Automation is unavoidable. John F. Gibson 2009-03-11 EST 15:42
Please sign up for my office hours tomorrow if you would like to talk one-on-one about your project. Proposal for tomorrow's meeting in the schedule and comments on Dustin's shell scripting howto. John Gibson 2009-03-09 12:27 EST
Pick your project by Tuesday, March 3 2009.
made all clickable movies in ChaosBook.org/tutorials flash. IExplorer woes: pop-ups come misformated, with all toolbars showing. If you have suggestions, please blog them. Are flash pop-ups working for browsers you use? — Predrag Cvitanovic 2009-02-27 03:11
Posted new channelflow-1.3.4.tgz tarball with continuation and Poincare section utilities. John Gibson 2009-02-26 12:09 EST
added links to videos, JF Gibson and P Cvitanovic Newton Institute 2008 presentations — Predrag Cvitanovic 2009-02-22 16:07
Wrote quadratic continuation utility in which the cell size can vary. Continuation parameter is arbitrary. Enabled continuation equilibria into previously uncharted territory. John Gibson 2009-02-13 13:42 EST
A new periodic orbit P47.18 in the W03 cell that clings closely to the unstable manifold of the Nagata upper branch equilibrium. Predrag, you were right: there's a non-wandering set near the Nagata UB. Need to factor out the discrete symmetry and produce plots that show this orbit's relation to the UB unstable manifold more vividly.
Wrote documentation for construction of low-d basis and projection of trajectories in tutorial
Dual-view movies of new periodic orbits. John Gibson 2009-02-08 22:19 P.S. Anyone care to join me with a micro-thumbnail headshot? Would require fewer brain cells than the smiley → person map.
Some new periodic orbits in the narrow cell. John Gibson 2009-02-05 13:55
More on Roman's question on how Krylov subspace methods can find an answer to a singular Ax=b problem, when x = A-1 b is dominated by the huge eigenvalues of A-1. Krylov subspace methods work somewhat like SVD in finding a least-squares approximation to x. With SVD you project the original problem onto a subspace with no singular directions, and the solution to the projected problem is the least-squares solution to the original. I.e. you find the zero singular values and simply throw them away. The Krylov subspace methods are similar, in that they detect and learn to ignore singular directions because perturbations in those directions don't help reduce the least-squares residual |Ax-b|2. John Gibson 2009-02-05 13:55
Dustin posted two videos of simulations he was eventually able to hack his way through. Links can be found on his blog. He is starting to get really excited about all of this. — Dustin Spieker 2009-02-03 16:25 That turns my into a ! John Gibson 2009-02-05 8:43
G. Tanner commented on noisy paper by Domenico and Predrag
For 2009-01-27 Tuesday's meeting we will have a “channelflow installfest”. For next week we'll have an assignment involving a calculation with channelflow. For more information, see the schedule. — John F. Gibson, 2009-01-26 09:00