Typo in the TKE evaluation

[Stefano Marcocci]

Hi William,

I would like to thank you for the new features in the 3.10 realease of PIVlab.

Speaking of which, while I was reading the codes you have modified I've found a typo in the evaluation of the TKE, in particular in the v_prime calculation (line 197 of the function 'temporal_operation_Callback.m', as shown by the attached figure). It should be 'v_prime = vmittelselected - repmat(v_mean, [1, 1, nt]);' instead of 'umittelselected' since in that line you are evaluating the fluctuations on the vertical component of the velocity.

Best regards,

Stefano Marcocci

[thielickeoptolution]

Oh thanks, that seems to make sense!

[Stefano Marcocci]

You're welcome!

In any case, I would have found a better way to implement the evaluation of each component of the turbulent kinetic energy. As a matter of fact, since the TKE of each component of the velocity depends only by its variance, it would be sufficient to evaluate both component of TKE as follows:

-----------------------------------------------------------

TKE_u=0.5*var(umittelselected,0,3,'omitnan');

TKE_v=0.5*var(vmittelselected,0,3,'omitnan');

-----------------------------------------------------------

I've put 0 as weight in the variance function (i.e. normalization by N-1 with N number of observation) since you are evaluating the standard deviation in the same way. In my opinion, this strategy is better for two reasons.

The first is that this fixes a problem related to the fact that, in the way you have implemented the TKE calculation, you are normalizing by N the variance, as you can see if you run the lines below as test:

-----------------------------------------------------------

A=1:10;

A_prime=A-mean(A);

A_prime_squared_mean=mean(A_prime.^2);

var1=var(A,0); %normalized by N-1

var2=var(A,1); %normalized by N

check=[A_prime_squared_mean==var1 A_prime_squared_mean==var2];

-----------------------------------------------------------

You will see that check=[0 1], meaning that in the way you are evaluating the TKE, you are normalizing by N the variance, but this is in contrast with what you did for the evaluation of the standard deviation some lines below (lines 219-220 in the 'temporal_operation_Callback.m' function), where you have normalized by N-1 (weight 0 in the std function).

The second advantage of following my suggested method is that you avoid a creation of two (unnecessary) 3D matrix like u_prime and v_prime, saving RAM memory (this may be crucial if you are analyzing thousands of images) and computational cost.

Therefore, I would suggest to change lines 189-205 in the 'temporal_operation_Callback.m' function with the lines I have proposed. Please do not hesitate to contact me should you have questions or doubts.

Best regards,

Stefano

[thielickeoptolution]

Dear Stefano, thanks, sounds logical and I have changed the code accordingly:

https://github.com/Shrediquette/PIVlab/commit/00eee9562df3e150eb6dd385bd7c4af45fb66c6b