I have a question about turbulent energy spectra. I am now doing some analysis on PIV results. I do not know how to get this energy spectra out of 2-D PIV Data.
I have let's say 1000 instantaneous velocity fluctuation (u',v') maps. The sampling frequency was not so high to resolve in time. So I decided to find spatial spectra. Here I have power of 2 numbers of points (8,16,32,etc) in one horizontal line in my PIV domain. I have 1000 u' and v' samples for each point. location of these points (x,y) is known. I have to do FFT on these u' and v' values. but the thing is I do not have the frequency or wave number here. How can I relate the locations of these points to wavenumber? can anyone help me with that?
First, do you assume the 1000 values over a spatial lenght L that is the period of the flow problem along the direction? Otherwise, the Fourier transform requires special care for the non-periopdic case.
Then, the wavenumber is directly related to the spatial resolution kq=q*2*pi/L. The highest wavelenght is L and the frequency is (q=1) k = 2*pi/L while the smallest wavelengt (Nyquist) is 2*h (h the step sampling) corresponding to kmax=qmax*2*pi/L.
You can consider that L=N*h, N being the number of your sample nodes.
Thank you Fillippo for the answer. the problem is I have 1000 realizations in time. not along this line. alonh this line I could have maximum 150 points due to my spatial resolution. I saw some works that they could generate power spectrum by just using 16 or 32 points. The question is how and what are these special care you are talking in fft ?
You can consider my previous comment concerning the time lime, too. Just consider L to be substituted by the period T. Then h is the time spacing dt.
However, with 150 nodes in space (are they equally spatied?) you can perform a spectral analysis also in space.
Using 16, 32, 64...nodes is just due to the fact that the FFT works with power of 2.
You can avoid spectra by using velocity differences (aka velocity increments), and by using spatial variance as a function of scale (see paper by Vogelzang et al). The Vogelzang et al paper also shows how these three measures are related. We have found that the spatial variance (as a function of scale) is the best method and the most easily understood. This is demonstrated in a paper that is currently under review (pending reviewer to OK after corrections to minor comments).
https://1drv.ms/f/s!AuGfYRYXOVk9iQ0krM5CPgY8sOFe
Human Amiri Hi Human, i'm currently working on a similar situation and i was wondering if the advices and recomendations that Filipo mention worked for you?
Hello Juan. Its been a long time but as far as I remember it was useful.
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