gtspring2009:spieker_blog:ub_eigenvectors:first_try
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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}} | ||
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| + | [2 marginal eigenvalues - do they have nontrivial eigenvectors?] | ||
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| + | 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}} | ||
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| + | {{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// | ||
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| + | {{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. | ||
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| + | {{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... | ||
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| + | :-) 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// | ||
gtspring2009/spieker_blog/ub_eigenvectors/first_try.txt ยท Last modified: 2010/02/02 07:55 (external edit)
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