Energy spectra
 

Hi, everyone

I have simulated turbulent channel flow with Re_tau=180. The mean velocity and stresses profiles agree with those in Kim, Moin and Moser's paper (JFM 1987, vol 177, pp 133-166). Now, I have problem to plot the one-dimensional spectra.

Taking the spectrum E_uu (k_x) for example. I calculated it with the following steps:
1. Output the 2D velocity field at y+ = 5, and then obtained uu(x,z).
2. With a given z, such as z=0, I performed FFT for uu(x,0) and obtained uu(k_x) at z=0.
3. Averaged uu(k_x) over all z.

The obtained spectrum was much different from the one in reference. However, I think the sharp of the profile is right.

I know there should be something wrong in my steps. And, the E_uu and k_x still need to be normalized by some reference variables, but I don't know how to choose them.

Any help from you would be appreciated. Thanks.


Yong

Hi Yong,

the procedure you described is correct, for a given distance from the wall (say y*) you take your Nz (taken in the transverse coordinate direction) velocity vectors (say x velocity component along the x coordinate), FFT and average them (each coefficient is the average over the Nz ones).

It seems to me that the problem is in the proper "normalization".

I suggest you to check your spectral routine toward some test sin functions

Hi Sbaffini,

Thanks for your reply. Yes, the key point is to find out the way to normalize k_x and E_uu.

I think there should be some ones who have simulated the same flow in this forum, as Kim's paper is seen as a benchmark for turbulent flow. I searched and read corresponding threads, but didn't find out the way.

Ok, this morning i was too lazy to check my routine. Now i did it, you can find it attached. It works for MATLAB and, given the velocity field along a direction, it provides you with the correct abscissa and the coefficients to be averaged.

Just to be sure, this is the database we are talking about:

http://turbulence.ices.utexas.edu/da...n180.xspec.178

Hi,

Thanks very much. Yes, I am using the data from the same website as the reference. I am comparing the spectra at y+=5.

I am using Qtiplot to perform FFT and don't have Matlab now. I will have a try. What are the characteristic parameters used for normalization?

According to my memory there are no parameters used for normalization. However, the code you are using to perform the FFT may use some kind of windowing (like the Pwelch mentioned in the file). While this can be useful or even required for several reasons, this does not apply in this case because would invalidate the comparison (and you already average your coefficients in time and transverse directions, so it is not needed).

Hi Sbaffini,

Thanks very much. Finally, I didn't compare my sepctra with those from Kim's paper. I just calculated the Komlogorov length scale eta, and plotted E_uu via k*eta.

Hi Yong,
I understand this is a very old post. But this is the only one I could find here which is relevant to what I am doing.

Are there any references for this procedure to calculate 1D spectrum?

Have you ever tried check your spectral routine toward some test sin function?