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

Hi,all:
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.
http://www.cfd-online.com/Forums/mem...ldaverage.jpeg
And the steamwise integration as flows
http://www.cfd-online.com/Forums/mem...seaverage.jpeg
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?