[Shrey]

Please help me how to calculate two point velocity correlation in matlab . I have 16440 points with u and v velocity . these are for 350 time frames . I calculated
fluctation velocity component for all the point . But facing some problem in implementing correlation formula in matlab . Also I need to calculate integral length scale from the above correlation . Please help me . If someone has code can you please post it or explain me .

[LuckyTran]

The formula is nothing special and you shouldn't have any issues. If you have u(nx,ny,ntime) and v(nx,ny,ntime) then you just do something like

for i=1:ntime
temp(i) = (u(:,:,i).*v(:,:,i))
end
Ruv = sum(temp,3)

This example is zero-shift example. Then you just repeatedly shift one of the matrices. Don't forget zero-padding. Finally you normalize it to get either the cross-covariance or cross-correlation depending on your needs.

But this brute force method is really slow and it is much faster to use the built-in matlab xcorr or conv which uses the fft ifft approach. I would still recommend to use the time-domain formula since 350 images is not many, you probably have tons of memory left, and its straightforward and will give you less headaches.

There's several ways to get the integral length scale. One is to just integrate the auto-correlation.

Both these are good exercises and I encourage you to discover the method to getting them on your own. You can ask specific questions but I would not give up and just ask for someone to give you the code (at least I won't). I think space & time-resolved techniques like PIV/LES/DNS are great tools but the user needs to be worthy of them.