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All of the fields with and without the laminar field added.

Laminar subtracted on the left, laminar omitted on the right:

{{:gtspring2009:spieker_blog:ub_eigenvectors:laminar:ef1_lam.png|Ef1 Laminar}}
{{:gtspring2009:spieker_blog:ub_eigenvectors:laminar:ef1_nolam.png|Ef1 Non-laminar}}

{{:gtspring2009:spieker_blog:ub_eigenvectors:laminar:ef2_lam.png|Ef2 Laminar}}
{{:gtspring2009:spieker_blog:ub_eigenvectors:laminar:ef2_nolam.png|Ef2 Non-laminar}}

{{:gtspring2009:spieker_blog:ub_eigenvectors:laminar:ef3_lam.png|Ef3 Laminar}}
{{:gtspring2009:spieker_blog:ub_eigenvectors:laminar:ef3_nolam.png|Ef3 Non-laminar}}

{{:gtspring2009:spieker_blog:ub_eigenvectors:laminar:ef4_lam.png|Ef4 Laminar}}
{{:gtspring2009:spieker_blog:ub_eigenvectors:laminar:ef4_nolam.png|Ef4 Non-laminar}}

{{:gtspring2009:spieker_blog:ub_eigenvectors:laminar:ef5_lam.png|Ef5 Laminar}}
{{:gtspring2009:spieker_blog:ub_eigenvectors:laminar:ef5_nolam.png|Ef5 Non-laminar}}

{{:gtspring2009:spieker_blog:ub_eigenvectors:laminar:ef6_lam.png|Ef6 Laminar}}
{{:gtspring2009:spieker_blog:ub_eigenvectors:laminar:ef6_nolam.png|Ef6 Non-laminar}}

I could go either way on whether or not to include the laminar solution on top of the eigenvalue.  

{{gtspring2009:pc.jpg}} Dustin or JohnG, can you explain why one would subtract laminar from eigenvectors? Adding a constant to //**u**(x,t)// does not change the matrix of state-space velocity gradients //A//, or its eigenvalues, eigenvectors, or am I missing something? --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-31 07:10//

{{gtspring2009:pc.jpg}} Dustin, in [[gtspring2009:spieker_blog:ub_eigenvectors:first_try|your first try]] I went through the exercise of guessing which of your eigenvectors correspond to which eigenvalues. Did you recheck my labeling? It's important one gets this correctly to get the right behavior and right symmetries in close passages to equilibria, and in particular for their heteroclinic connections.  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-31 07:10//


{{gtspring2009:pc.jpg}} Should you scale colors to bring some structure in the leading eigenvector **e**_1? In principle the most important one in the full state space?  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-31 07:40//

{{gtspring2009:pc.jpg}} 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...   --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-03-31 07:10//
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