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gtspring2009:research_projects:gibson:blog [2009/01/06 08:51]
gibson
gtspring2009:research_projects:gibson:blog [2010/02/02 07:55] (current)
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 ====== State space of HKW cell ====== ====== State space of HKW cell ======
-===== Basis sets for HKW cell  ​=====+===== Basis sets =====
  
-2008-12-30 through ​1009-01-06+2008-12-30 through ​2009-01-06
  
 I have been dissatisfied for quite a while with the projection basis sets I've used for plotting periodic orbits in the HKW cell. We don't have good equilibria there, so we can't easily do the translational-basis set we used for the narrow cell in the JFM08 paper. I have previously used a POD basis from the data of a single periodic orbit (P87p89). The plots were good, in that they showed turbulent trajectories lying in the same regions of state space as the periodic orbits, and forming similar pretty-well-defined shapes in whatever projection we looked at. But Predrag never liked this since it involved POD and averages, and to me, it was rhetorically weak to use a basis based on periodic orbits to argue that the periodic orbits live where turbulence is.  I have been dissatisfied for quite a while with the projection basis sets I've used for plotting periodic orbits in the HKW cell. We don't have good equilibria there, so we can't easily do the translational-basis set we used for the narrow cell in the JFM08 paper. I have previously used a POD basis from the data of a single periodic orbit (P87p89). The plots were good, in that they showed turbulent trajectories lying in the same regions of state space as the periodic orbits, and forming similar pretty-well-defined shapes in whatever projection we looked at. But Predrag never liked this since it involved POD and averages, and to me, it was rhetorically weak to use a basis based on periodic orbits to argue that the periodic orbits live where turbulence is. 
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 I know this probably sounds like an arbitrary concoction, but it does establish something new and important, I think: that those periodic orbits and the turbulent flow really are strongly associated with the complex instability of frozen streak+roll structures. ​ I know this probably sounds like an arbitrary concoction, but it does establish something new and important, I think: that those periodic orbits and the turbulent flow really are strongly associated with the complex instability of frozen streak+roll structures. ​
 +
 +===== State space portraits ​ =====
 +
 +2009-01-07
 +
 +{{pod_e0e1.png?​250}}{{p87pod_e0e1.png?​250}}{{ssp_e0e2.png?​250}}{{p87meantrans_e0e1.png?​250}}
 +
 +{{pod_e1e2.png?​250}}{{p87pod_e1e2.png?​250}}{{ssp_e1e2.png?​250}}
 +
 +{{pod_e1e3.png?​250}}{{p87pod_e1e5.png?​250}}{{ssp_e2e3.png?​250}}
 +
 +{{pod_e1e4.png?​250}}{{p87pod_e1e3.png?​250}}
 +
 +
 +====== Playground ======
 +
 +This area is for testing embedded movies in blogs, particularly the namespace issues.
 +
 +
gtspring2009/research_projects/gibson/blog.1231260681.txt.gz ยท Last modified: 2009/01/06 08:51 by gibson