# Integral length of turbulence

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1. Aug 22, 2016

### ATY

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Hey guys, I need your help. It is about the integral length of turbulence flow.
So we got data from some wind measurement, recorded at 60000Hz.
My tutor already told me that we should get something like 0.18 m as result.
We got the formula L = 1/<u^2(x)>*sum(autocorrelation(Data))
I tried to use
Code (Text):
L=sum(xcorr(Data)/max(xcorr(Data)));
L=L*(1/freq)*meanu/mean(Data.^2);
(I used (1/freq)*mean) to give "L" a unit)

I get the correct result of around 0.18 m, but the autocorrelation function is a triangle

So this does not seem to be correct. I tried it also with some other formula which I found around the Internet.

Code (Text):
x = [ Data];
X_psd = abs(X).^2;
r_xx = ifft(X_psd);
r_xxx=r_xx(:,1)
I still get the same result for the integral length, but this time the function is different.

So...I am not sure about this one. Maybe it is correct, just the way the function is shown is weird.

I also tried the regular autcorr thing it matlab, which gave me wrong results (or I have simply no clue how to use it correctly) for the length but a good image
Code (Text):
sum((autocorr(Data,length(Data)-1))/freq*meanu)

I hope that somebody can give me an advice or a hint where the problem is.

2. Aug 27, 2016