gtspring2009:research_projects:gibson:blog
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gtspring2009:research_projects:gibson:blog [2009/01/07 11:41] 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 from above basis sets ===== | + | ===== State space portraits ===== |
| 2009-01-07 | 2009-01-07 | ||
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| {{pod_e1e2.png?250}}{{p87pod_e1e2.png?250}}{{ssp_e1e2.png?250}} | {{pod_e1e2.png?250}}{{p87pod_e1e2.png?250}}{{ssp_e1e2.png?250}} | ||
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| + | {{pod_e1e3.png?250}}{{p87pod_e1e5.png?250}}{{ssp_e2e3.png?250}} | ||
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| + | {{pod_e1e4.png?250}}{{p87pod_e1e3.png?250}} | ||
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| + | ====== Playground ====== | ||
| + | |||
| + | This area is for testing embedded movies in blogs, particularly the namespace issues. | ||
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gtspring2009/research_projects/gibson/blog.1231357268.txt.gz · Last modified: 2009/01/07 11:41 by gibson
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