# Scaling/non-dimensional navier-stokes

VooDoo
Hey guys,

Just trying to non-dimensionalise the navier stokes equation. We were taught how to do it when you scale x,y,z with one reference length L...just wondering how to do it if I scale x,y,z with a,b,c respectively.

Edit - this is what I already know http://www.mme.tcd.ie/~craigm/Cnotes/4b6/nodes/week1.php#SECTION00080000000000000000 [Broken] they use one reference length L to scale as well

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Why would you want to non-dimensionalize with 3 different reference lengths? In fact, I don't even think that you 'can' do this. When you non-dimensionalize, you only get a 1/Re because there is a 1/L in every term.

Maybe I am misunderstanding your problem, perhaps you can elaborate a little more on what you mean by scaling with a,b, and c?

John Creighto
Why would you want to non-dimensionalize with 3 different reference lengths? In fact, I don't even think that you 'can' do this. When you non-dimensionalize, you only get a 1/Re because there is a 1/L in every term.

Maybe I am misunderstanding your problem, perhaps you can elaborate a little more on what you mean by scaling with a,b, and c?

Yes, you can. It is done in climate science.

http://arxiv.org/ftp/physics/papers/0407/0407002.pdf
http://www.mne.psu.edu/cimbala/me33web_Fall_2005/Lectures/Nondimensionalization_of_NS_equation.pdf [Broken]

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Phrak
Yes, you can. It is done in climate science.
I don't believe this would be coordinate invarant, would it?

John Creighto
I don't believe this would be coordinate invarant, would it?

I'm sorry, I'm not sure what that means. The transformations do seem to get rid of the units though.