gtspring2009

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gtspring2009 [2011/08/05 12:52] predrag request to John: an upper branch group orbit, projected? |
gtspring2009 [2011/08/10 08:11] predrag John, please confirm that you get notices about channelflow updates |
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{{gtspring2009:pc.jpg }} request to John: Can you pencil in the group orbit of the Nagata upper branch on the same kind of plot as [[http://chaosbook.org/tutorials/Images/a1.14_g2.png|full states space portrait]]? The last time you plotted this {{:chaosbook:pipes:tangenta.png?200 |}} 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 | {{gtspring2009:pc.jpg }} request to John: Can you pencil in the group orbit of the Nagata upper branch on the same kind of plot as [[http://chaosbook.org/tutorials/Images/a1.14_g2.png|full states space portrait]]? The last time you plotted this {{:chaosbook:pipes:tangenta.png?200 |}} 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@physics.gatech.edu|Predrag Cvitanovic]] 2011/08/05 12:35// | the UB in spanwise/streamwise increments and plotting the issuing mesh. --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2011/08/05 12:35// | ||

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+ | {{gtspring2009:pc.jpg }} Woods Hole GFD snippets: Listening to [[http://www.mcnd.manchester.ac.uk/mullin.html|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@physics.gatech.edu|Predrag Cvitanovic]] 2011/08/10 08:06// | ||

{{gtspring2009:pc.jpg }} Woods Hole GFD snippets: Listening to [[http://www.mech.kth.se/~henning/|Dan Hennignson]]: watching their [[http://www.youtube.com/watch?v=4KeaAhVoPIw|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 [[http://www.youtube.com/watch?v=GW2LRo2ZigQ|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. | {{gtspring2009:pc.jpg }} Woods Hole GFD snippets: Listening to [[http://www.mech.kth.se/~henning/|Dan Hennignson]]: watching their [[http://www.youtube.com/watch?v=4KeaAhVoPIw|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 [[http://www.youtube.com/watch?v=GW2LRo2ZigQ|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. |

gtspring2009.txt ยท Last modified: 2011/08/10 08:11 by predrag