# channelflow.org

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gtspring2009:spieker_blog:ub_eigenvectors:color_scaling

## Color Scaling

Various schemes that try to minimize saturation of color in the flowfield. This parameter might have to be changed for each individual eigenvector.

I used a velocity field that had a lot of dark patches or saturation points (Im e_11 or eigenflow 10) as the field to do the comparison. All of these have laminar flow added in.

I feel that on velocity fields with dark red and blue spots like this, a scaling factor of about .4 is optimal. A scale of ~0.4 smooths streamwise features without completely blurring out the spanwise features.

Sorry, I forgot to rescale these before I posted them.

In this case the scaling of the field and the color scale is closely related to the question of whether or not to add the laminar flow to the field. By adding the laminar flow in and scaling the eigenvector, you are plotting (laminar + scale * eigenvector), a linear combination of two unrelated fluid states. The shapes in the plot will be quite dependent on the relative strength of the two different fields in the sum. On the other hand, if you leave the laminar flow out and just plot (scale * eigenvector), the shapes will be constant but the color scale will be more or less intense. If you are interested in understanding the eigenvector, the latter is preferable: you see the shape of the eigenvector, not the eigenvector mixed with an unrelated fluid state.

You might also be interested in plotting (equilibrium + scale * eigenvector), or (laminar + equilibrium + scale * eigenvector). These are linear combinations of fluid states with physical meaning: both show a perturbation along the unstable manifold of an equilibrium, with and without the laminar flow.

But, as I wrote elsewhere, (laminar + scale * eigenvector) doesn't make much sense. It's a perturbation of one equilibrium (laminar) along another equilibrium's eigenfunction.

P.S. I rescaled the figs with dokuwiki image commands: {{fig.png?200}} rescales fig.png to 200 pixels width.

John Gibson 2009-04-03