Energy spectra
 

I am working on large eddy simulation and doing simulation in
turbulent channel flow. I read your paper "Self-Sustained Process at
Large Scales in Turbulent Channel Flow" published in PRL. I want to
compute streamwise power spectrum.

I recorded instantaneous u of x-z plane for 4000 time step. Then in a
matlab code-- 1. first I calculated mean from that 4000 time step
value and calculate u fluctuation (u' ).

2. Then I selected
u' Vs x data for a particular z location

3. Then calculate
fft(u') and power=sqrt(fft(u').conjugate(u'))

4. Then plot power
vs Kx. for a particular time step. It was not showing smooth curve.
so, i did fft for all 4000 time step

and did the
time average power. Then Power(time averaged)Vs Kx.



(a)Is my procedure correct?
(b)As, I read in the text book that, power spectra is the fft of
correlation of u' ,but here we did directly fft of u'. so is my
process is correct.

Please, give me suggestion. If you please, give me the code to
calculate the power spectrum, it will be a great help to me.