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:-) Here are the first twelve (12) eigenvectors of the UB equilibrium: --- //[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-03-25//

**e**_1 {{:gtspring2009:ubef1.png|Eigenfunction 1}}\\
Re **e**_2 {{:gtspring2009:ubef2.png|Eigenfunction 2}} Im **e**_2 {{:gtspring2009:ubef3good.png|Eigenfunction 3}}\\
Re **e**_4 {{:gtspring2009:ubef4.png|Eigenfunction 4}} Im **e**_4 {{:gtspring2009:ubef5.png|Eigenfunction 5}}\\
Re **e**_6 {{:gtspring2009:ubef6.png|Eigenfunction 6}} Im **e**_6 {{:gtspring2009:ubef7.png|Eigenfunction 7}}\\
**e**_8 {{:gtspring2009:ubef8.png|Eigenfunction 8}}

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

Re **e**_11 {{:gtspring2009:ubef9.png|Eigenfunction 9}} Im **e**_11 {{:gtspring2009:ubef10.png|Eigenfunction 10}}\\
**e**_13 {{:gtspring2009:ubef11.png|Eigenfunction 11}}\\
Re **e**_14 {{:gtspring2009:ubef12.png|Eigenfunction 12}}

{{gtspring2009:pc.jpg}} Thanks. They are the [[gtspring2009:gibson:w03#eq2_eigenvalues_full_space|full space eigenvalues]], not restricted to [[gtspring2009:gibson:w03#eq2_eigenvalues_s-invariant_subspace|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 [[gtspring2009:howto:format#preferences|crop them tightly]], remove the white acreage around them? 
Compare with {{:gtspring2009:061206ubeigen.pdf|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@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-27 12:23//

{{gtspring2009:gibson.png?24}} 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.

{{gtspring2009:pc.jpg}} 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 400x300.  I'll look into the scaling now. --- //[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-03-29 09:21//
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