[agustinvo]

If I understood well:

For a spatial spectrum, I need, at a given time, at different positions, the different velocity components.

0. I get the correlation Rij in space, with a dX

1. Then, I get the FFT in the desiderated direction
2. I obtain the power of the FFT, it is the Fourier coefficients times their conjugate, it is Ek1_uu on each cell
3. I perform an average in the homogeneous direction of Ek1_uu

Then you get the different wavelength number, and you have your spectra, isn't it?

For, for a time spectrum, at a given position, I have the different velocity components.

0. I get the correlation Rij in time, with a dt

1. I get the FFT in time
2. I obtain the power of the FFT
3. I perform an average in my homogeneous direction

Then I get the frequencies, and I get my spectra.


In any case, since I expect my flow to have an homogeneous direction as well, so I can try to do as you do too.

[FMDenaro]

As you can see in the code, I pass one velocity component to the 1D FFT and then compute the modulus of the Fourier coefficient. Finally the ensemble average is performed.

Try to do the same, but if you use your buoyancy problem we cannot establish a correct behaviour without checking the spectrum versus a known one...

PS: you do not have to expect...you must know that ;-) if you prescribe periodicity in one direction then you know that the flow is homogeneous in that direction.

[juliom]

Agustin; I know that this issue is quire complex. It took me weeks and help from Professor Denaro to understand this.
My advise is to test your code with a well know dataset. For example you can use the JHTDB ( Johns Hopkins Turbulence databases). This is what I did, once I checked that my solution was coming out as I expected, then I use my subroutine in my LES/DNS computations.
I've always said about time spectrum. In fact the Navier Stokes equations are quasi - periodic in time. It means that you "must" do a windowing to perfrom the FFT, because the FFt is based on a series that are homogeneous. That is why Professor Denaro has insisted in the fact of the "homogeneous direction". Without an homogeneous direction you must consider another approach explained by Pope in his book. To be honest, I never understood it.
Nonetheless, people beleave ( I have no argument to debate against it) that performing time spectra is "almost the same" as space spectra, because time and space are closely related in turbulence. Like I said, my lack of experience and knowledge, does not allow me to elaborate more about that, besides the fact of the quasi-periodic nature of the NS.
Finally, I have not had time to test the time Vs space spectra, but this is in my bucket list. Other people argue that time correlation is the best way because this is how experiment are run. You probe at one point time, thus you have the data set in time at a specific point.
All the best.

[agustinvo]

Hi, sorry for disappearing these days,

I will try to do as you tell me, follow an already tested case and see if my code is ok or not. It is true that is more difficult the first time, and also when there are no so much natural convection spectra.

If I continue and have someting interesti, I will upload this thread.

[juliom]

Well, my opinion is that the specific process does not play an important role, except in very specific cases, i.e LES in compressible flows with shock wave or combustion. In natural convection the characteristic length I am sure that is way higher than the Kolmogorov scale, thus it does not affect the energy cascade, because at the ed of the day this is what we see in the spectrum, the energy cascade. As long as you perform the computation along the homogeneous direction, the final solution is the same (mathematically, from a physical point of view the process is unique).