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gtspring2009 [2011/02/01 20:26]
predrag a video journal link
gtspring2009 [2011/08/10 08:11] (current)
predrag John, please confirm that you get notices about channelflow updates
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 <span style="​color:​red;​font-size:​80%;​text-align:​right;">​please check this page a few times a week, there will be no emails: , click on [Recent changes], select changed page, then [Old revision], compare versions</​span>​ <span style="​color:​red;​font-size:​80%;​text-align:​right;">​please check this page a few times a week, there will be no emails: , click on [Recent changes], select changed page, then [Old revision], compare versions</​span>​
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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
 +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//
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 +{{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. ​
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 +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 [[http://​www.damtp.cam.ac.uk/​people/​c.p.caulfield/​|Colm-cille Caulfield]]. ([[http://​en.wikipedia.org/​wiki/​Columba|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@physics.gatech.edu|Predrag Cvitanovic]] 2011/08/04 07:12//
  
 {{gtspring2009:​pc.jpg }} If you want to fall asleep, [[http://​www.jove.com/​details.php?​id=2152|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@physics.gatech.edu|Predrag Cvitanovic]] 2011-02-01 20:23// {{gtspring2009:​pc.jpg }} If you want to fall asleep, [[http://​www.jove.com/​details.php?​id=2152|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@physics.gatech.edu|Predrag Cvitanovic]] 2011-02-01 20:23//
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