Energy Spectrum
 

In this forum I want to ask about the energy spectrum (I searched in the forums and found that the available discussion are for some years ago and mostly about how it is calculated).
Dose any one know why energy spectrum has not been plotted in 3D so far? I mean with these axes: lambda_x, lambda_z, y? (I have read several papers and have seen it just plotted in 2D contours like for : lambda_x,y or lambda_z y or as 1D like : kx, or kz or lambda_x or lambda_z for premultiplied energy spectra). This function has been also plotted as a contour plot for these axes: lambda_x+, lambda_z+ (exp. in Del Alamo, JFM, 2004) but I couldn't find it plotted as I mentioned above. I am trying to plot it as I mentioned above but the code still has some bugs. However, any comment is appreciated here.
Thank you

I am not sure about your question, I suppose you are working on a 3d isotropic turbulence, right? You want to plot the energy spectrum over a spherical shell?

yes I am worrking on 3d isotropic turbulence in pipe. I mean that so far I have seen energy spectrum plotted on 2D or 1D like the figure in these pages:
http://www-vortex.mcs.st-and.ac.uk/constrain.html
(figure 3 in this paper):
http://iopscience.iop.org/article/10...3/20/11/115401

But I have never seen sth plotted like the second figure in this page:
http://torroja.dmt.upm.es/turbdata/blayers/

as you see in this figure the axes are x,y,z. It seems that if we calculate the 3d energy spectra, we can plot it in a similar way with these axes: lambda_x, y, lambda_z(the pipe flow is homogeneous and so periodic in x an z direction but not homogeneous in y direction which is wall normal). The question is that I dont know why nobody (especially very famous professors in this field) have not done it yet!

but if you work with turbulence in a pipe then you don't have homogeneity and isotropy ....in your case the presence of the walls does not allow a 3D assumption.

However, the spectrum can be seen as E=E(r) so that you can represent it as a function of kx,ky,kz wavenumbers in a 3D space.

So you mean it seem logical and not meaningless to plot it. Thank you very much