Thanks a lot for this. It clarified some thoughts I had on the matter. Your entire series on Turbulence has been great so far, going to check out part 8 now. Thanks Prof. Schluter.
Hi, Prof. Schluter! I want to know how we can compute the autocorrelation numerically. For example, I have a time series of the streamwise velocity at a fixed point in a channel flow and it is represented by U(t_i). Of course, the flow has reached statistical stationary.
Hello Dr Schluter, I would like you to kindly clarify the term in the denominator of the auto-correlation (u^2). As I understand, it should be the average of the square of the velocity, which means that the power term should be inside the average and not outside.
My intuition is it is a measure of how "correlated" the signal of current time and s time latter. If s = 0, then rho(s) = 1, it means signal is perfectly correlated to itself, it does make sense because what happens at current time fully determines itself (or 0 time latter). If s > 0, what happens at current time might "somehow" correlated to what happens at s time latter, but it might not be that "perfect". I think it might be proved to be less than 1 by math, but it is just my intuition.
I think the normalization factor for the auto-correlation function should be instead of ^2 ... the latter obviously does not yield a normalized 1 at the start since rho(0) = / ^2 =/= 1 ^ it does not necessarily give 1, if not always different than 1. Similarly, for the cross-correlation with the addition of the x-component, as so: ...
Thanks a lot for this. It clarified some thoughts I had on the matter. Your entire series on Turbulence has been great so far, going to check out part 8 now. Thanks Prof. Schluter.
in the denominator, the square should be inside. else, really helpful! thank you.
excellent video
Thank you so much. I really enjoyed it!
Hi, Prof. Schluter! I want to know how we can compute the autocorrelation numerically. For example, I have a time series of the streamwise velocity at a fixed point in a channel flow and it is represented by U(t_i). Of course, the flow has reached statistical stationary.
Dissipation time scale?
Hi professor, this is a really helpful video, thanks a lot for it
Hello Dr Schluter, I would like you to kindly clarify the term in the denominator of the auto-correlation (u^2). As I understand, it should be the average of the square of the velocity, which means that the power term should be inside the average and not outside.
Hi thanks for this great explanation, very very helpful.
QUESTION. Why rho(s) is always less than one? See diagram at 7:50. Thanks.
My intuition is it is a measure of how "correlated" the signal of current time and s time latter. If s = 0, then rho(s) = 1, it means signal is perfectly correlated to itself, it does make sense because what happens at current time fully determines itself (or 0 time latter). If s > 0, what happens at current time might "somehow" correlated to what happens at s time latter, but it might not be that "perfect". I think it might be proved to be less than 1 by math, but it is just my intuition.
becuz it is normalized, taking rho(0) the maximum value and equal to 1
I think the normalization factor for the auto-correlation function should be instead of ^2 ... the latter obviously does not yield a normalized 1 at the start since
rho(0) = / ^2 =/= 1
^ it does not necessarily give 1, if not always different than 1.
Similarly, for the cross-correlation with the addition of the x-component, as so: ...
Indeed, the square should be inside the average brackets. I think this is also stated in Pope's/Lumley's book.
True. I was wondering the same.