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gtspring2009:spieker_blog:ub_eigenvectors:first_try

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 — gtspring2009:spieker_blog:ub_eigenvectors:first_try [2010/02/02 07:55] (current) 2009/03/29 09:48 dspieker created 2009/03/29 09:48 dspieker created Line 1: Line 1: + :-) 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//