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gtspring2009:first_try

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Here are the first twelve (12) eigenvectors of the UB equilibrium: — Dustin Spieker 2009-03-25

e_1
Re e_2 Im e_2
Re e_4 Im e_4
Re e_6 Im e_6
e_8

[2 marginal eigenvalues - do they have nontrivial eigenvectors?]

Re e_11 Im e_11
e_13
Re e_14

Thanks. They are the full space eigenvalues, not restricted to S-invariant subspace, right? I have labeled them correctly? (Re e_11,Im e_11) is the least contracting stable eigenvalue pair? 400 x 300 pixels is good, but in the next version, can you crop them tightly, remove the white acreage around them? Compare with JohnG's blog (he has about 20 of them, so there might be a better version - I'm not strong enough to find it). — Predrag Cvitanovic 2009-03-27 12:23

A couple suggestions: It might make be better to plot these fields with the laminar flow removed. They're eigenfunctions of EQ2, so if they're superimposed on anything, it should be that. But best on their own, I think. Also, the scale of these fields is arbitrary. You can play around with the scale parameter of the matlab plotbox function to get less saturation of red and blue.

I vote for not subtracting the laminar flow. Adding a constant to u(x,t) does not change the matrix of state-space velocity gradients A, or its eigenvalues, eigenvectors. Do play with the scale parameter. I'm curious: what do the the eigenvectors of the two marginal eigenvalues look like? They should point along the two continuous translations, streamwise and spanwise. Perhaps obvious…

I found a better zoom to make the plots better in 400×300. I'll look into the scaling now. — Dustin Spieker 2009-03-29 09:21

gtspring2009/first_try.1238345085.txt.gz · Last modified: 2009/03/29 09:44 by dspieker