Rules of Reynolds Averaging

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According to the rules of Reynold's Averaging, Which can be found here under 11.1,
. Is there anyway to show this and the other rules in Matlab either numerically or symbolically?
I tried to create an array, u:
u = [1,3,6,8,24];
uprime = diff(u)
which output a vector of differences (not sure if this is what I wanted).
Then I tried to take an average of uprime using the following code below:
According to the rule, I should have gotten 0, but I got an average of the numbers in the vector which was nonzero. Am I misinterpreting the rule or is the diff function not actually taking a derivative?

Accepted Answer

Alan Stevens
Alan Stevens on 2 Oct 2020
uprime doesn't mean du/dt here. It means u - umean.
u = [1,3,6,8,24];
umean = mean(u);
uprime = u-umean;
ans =

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