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About integration along a direction--Taylor--Görtler vortex

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Old   April 3, 2014, 10:24
Default About integration along a direction--Taylor--Görtler vortex
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Huang Xianbei
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I'm working on the Taylor--Görtler vortex in channel flow. First, the whole field average is defined as, where ui is the instantaneous velocity, Lx is the x direction length, streamwise, Lz is the spanwise length. T is the time, thus this is the temporal and spacial integration of the instantaneous velocity.

And the steamwise integration as flows

the upper one minus the latter one, the TG fluctuation can be obtained

So the problem is how to do the spacial integration?
As I have got the U and UMean, the temporal integration is already done, so the only thing needed is 1/Lx*Lz(integration(UMean)x,z),am I right?
and also the ui(with '~' )
can anyone help?
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