Rules of Reynolds Averaging

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:

mean(uprime)   

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?

Answer 1

[Alan Stevens]

uprime doesn't mean du/dt here. It means u - umean.

u = [1,3,6,8,24];
umean = mean(u);
uprime = u-umean;
mean(uprime)

ans =

  -3.5527e-16